pax_global_header00006660000000000000000000000064141712271170014515gustar00rootroot0000000000000052 comment=742c19f3ecf2135b4e008a4f4a10b59add8b1045 xgboost-1.5.2/000077500000000000000000000000001417122711700132075ustar00rootroot00000000000000xgboost-1.5.2/.clang-tidy000066400000000000000000000036221417122711700152460ustar00rootroot00000000000000Checks: 'modernize-*,-modernize-make-*,-modernize-use-auto,-modernize-raw-string-literal,-modernize-avoid-c-arrays,-modernize-use-trailing-return-type,google-*,-google-default-arguments,-clang-diagnostic-#pragma-messages,readability-identifier-naming' CheckOptions: - { key: readability-identifier-naming.ClassCase, value: CamelCase } - { key: readability-identifier-naming.StructCase, value: CamelCase } - { key: readability-identifier-naming.TypeAliasCase, value: CamelCase } - { key: readability-identifier-naming.TypedefCase, value: CamelCase } - { key: readability-identifier-naming.TypeTemplateParameterCase, value: CamelCase } - { key: readability-identifier-naming.MemberCase, value: lower_case } - { key: readability-identifier-naming.PrivateMemberSuffix, value: '_' } - { key: readability-identifier-naming.ProtectedMemberSuffix, value: '_' } - { key: readability-identifier-naming.EnumCase, value: CamelCase } - { key: readability-identifier-naming.EnumConstant, value: CamelCase } - { key: readability-identifier-naming.EnumConstantPrefix, value: k } - { key: readability-identifier-naming.GlobalConstantCase, value: CamelCase } - { key: readability-identifier-naming.GlobalConstantPrefix, value: k } - { key: readability-identifier-naming.StaticConstantCase, value: CamelCase } - { key: readability-identifier-naming.StaticConstantPrefix, value: k } - { key: readability-identifier-naming.ConstexprVariableCase, value: CamelCase } - { key: readability-identifier-naming.ConstexprVariablePrefix, value: k } - { key: readability-identifier-naming.FunctionCase, value: CamelCase } - { key: readability-identifier-naming.NamespaceCase, value: lower_case } xgboost-1.5.2/.editorconfig000066400000000000000000000002151417122711700156620ustar00rootroot00000000000000root = true [*] charset=utf-8 indent_style = space indent_size = 2 insert_final_newline = true [*.py] indent_style = space indent_size = 4 xgboost-1.5.2/.github/000077500000000000000000000000001417122711700145475ustar00rootroot00000000000000xgboost-1.5.2/.github/FUNDING.yml000066400000000000000000000000751417122711700163660ustar00rootroot00000000000000open_collective: xgboost custom: https://xgboost.ai/sponsors xgboost-1.5.2/.github/ISSUE_TEMPLATE.md000066400000000000000000000015411417122711700172550ustar00rootroot00000000000000Thanks for participating in the XGBoost community! We use https://discuss.xgboost.ai for any general usage questions and discussions. The issue tracker is used for actionable items such as feature proposals discussion, roadmaps, and bug tracking. You are always welcomed to post on the forum first :) Issues that are inactive for a period of time may get closed. We adopt this policy so that we won't lose track of actionable issues that may fall at the bottom of the pile. Feel free to reopen a new one if you feel there is an additional problem that needs attention when an old one gets closed. For bug reports, to help the developer act on the issues, please include a description of your environment, preferably a minimum script to reproduce the problem. For feature proposals, list clear, small actionable items so we can track the progress of the change. xgboost-1.5.2/.github/lock.yml000066400000000000000000000015231417122711700162230ustar00rootroot00000000000000# Configuration for lock-threads - https://github.com/dessant/lock-threads # Number of days of inactivity before a closed issue or pull request is locked daysUntilLock: 90 # Issues and pull requests with these labels will not be locked. Set to `[]` to disable exemptLabels: - feature-request # Label to add before locking, such as `outdated`. Set to `false` to disable lockLabel: false # Comment to post before locking. Set to `false` to disable lockComment: false # Assign `resolved` as the reason for locking. Set to `false` to disable setLockReason: true # Limit to only `issues` or `pulls` # only: issues # Optionally, specify configuration settings just for `issues` or `pulls` # issues: # exemptLabels: # - help-wanted # lockLabel: outdated # pulls: # daysUntilLock: 30 # Repository to extend settings from # _extends: repo xgboost-1.5.2/.github/workflows/000077500000000000000000000000001417122711700166045ustar00rootroot00000000000000xgboost-1.5.2/.github/workflows/jvm_tests.yml000066400000000000000000000041401417122711700213440ustar00rootroot00000000000000name: XGBoost-JVM-Tests on: [push, pull_request] jobs: test-with-jvm: name: Test JVM on OS ${{ matrix.os }} runs-on: ${{ matrix.os }} strategy: fail-fast: false matrix: os: [windows-latest, ubuntu-latest, macos-10.15] steps: - uses: actions/checkout@v2 with: submodules: 'true' - uses: actions/setup-python@v2 with: python-version: '3.8' architecture: 'x64' - uses: actions/setup-java@v1 with: java-version: 1.8 - name: Install Python packages run: | python -m pip install wheel setuptools python -m pip install awscli - name: Cache Maven packages uses: actions/cache@v2 with: path: ~/.m2 key: ${{ runner.os }}-m2-${{ hashFiles('./jvm-packages/pom.xml') }} restore-keys: ${{ runner.os }}-m2 - name: Test XGBoost4J run: | cd jvm-packages mvn test -B -pl :xgboost4j_2.12 - name: Extract branch name shell: bash run: echo "##[set-output name=branch;]$(echo ${GITHUB_REF#refs/heads/})" id: extract_branch if: | (github.ref == 'refs/heads/master' || contains(github.ref, 'refs/heads/release_')) && matrix.os == 'windows-latest' - name: Publish artifact xgboost4j.dll to S3 run: | cd lib/ Rename-Item -Path xgboost4j.dll -NewName xgboost4j_${{ github.sha }}.dll dir python -m awscli s3 cp xgboost4j_${{ github.sha }}.dll s3://xgboost-nightly-builds/${{ steps.extract_branch.outputs.branch }}/ --acl public-read if: | (github.ref == 'refs/heads/master' || contains(github.ref, 'refs/heads/release_')) && matrix.os == 'windows-latest' env: AWS_ACCESS_KEY_ID: ${{ secrets.AWS_ACCESS_KEY_ID_IAM_S3_UPLOADER }} AWS_SECRET_ACCESS_KEY: ${{ secrets.AWS_SECRET_ACCESS_KEY_IAM_S3_UPLOADER }} - name: Test XGBoost4J-Spark run: | rm -rfv build/ cd jvm-packages mvn -B test if: matrix.os == 'ubuntu-latest' # Distributed training doesn't work on Windows env: RABIT_MOCK: ON xgboost-1.5.2/.github/workflows/main.yml000066400000000000000000000156151417122711700202630ustar00rootroot00000000000000# This is a basic workflow to help you get started with Actions name: XGBoost-CI # Controls when the action will run. Triggers the workflow on push or pull request # events but only for the master branch on: [push, pull_request] # A workflow run is made up of one or more jobs that can run sequentially or in parallel jobs: gtest-cpu: name: Test Google C++ test (CPU) runs-on: ${{ matrix.os }} strategy: fail-fast: false matrix: os: [macos-10.15] steps: - uses: actions/checkout@v2 with: submodules: 'true' - name: Install system packages run: | # Use libomp 11.1.0: https://github.com/dmlc/xgboost/issues/7039 wget https://raw.githubusercontent.com/Homebrew/homebrew-core/679923b4eb48a8dc7ecc1f05d06063cd79b3fc00/Formula/libomp.rb -O $(find $(brew --repository) -name libomp.rb) brew install ninja libomp brew pin libomp - name: Build gtest binary run: | mkdir build cd build cmake .. -DGOOGLE_TEST=ON -DUSE_OPENMP=ON -DUSE_DMLC_GTEST=ON -DPLUGIN_DENSE_PARSER=ON -GNinja ninja -v - name: Run gtest binary run: | cd build ./testxgboost ctest -R TestXGBoostCLI --extra-verbose gtest-cpu-nonomp: name: Test Google C++ unittest (CPU Non-OMP) runs-on: ${{ matrix.os }} strategy: fail-fast: false matrix: os: [ubuntu-latest] steps: - uses: actions/checkout@v2 with: submodules: 'true' - name: Install system packages run: | sudo apt-get install -y --no-install-recommends ninja-build - name: Build and install XGBoost shell: bash -l {0} run: | mkdir build cd build cmake .. -GNinja -DGOOGLE_TEST=ON -DUSE_DMLC_GTEST=ON -DUSE_OPENMP=OFF ninja -v - name: Run gtest binary run: | cd build ctest --extra-verbose c-api-demo: name: Test installing XGBoost lib + building the C API demo runs-on: ${{ matrix.os }} strategy: fail-fast: false matrix: os: ["ubuntu-latest"] python-version: ["3.8"] steps: - uses: actions/checkout@v2 with: submodules: 'true' - name: Install system packages run: | sudo apt-get install -y --no-install-recommends ninja-build - uses: conda-incubator/setup-miniconda@v2 with: auto-update-conda: true python-version: ${{ matrix.python-version }} activate-environment: test - name: Display Conda env shell: bash -l {0} run: | conda info conda list - name: Build and install XGBoost static library shell: bash -l {0} run: | mkdir build cd build cmake .. -DBUILD_STATIC_LIB=ON -DCMAKE_INSTALL_PREFIX=$CONDA_PREFIX -GNinja ninja -v install cd - - name: Build and run C API demo with static shell: bash -l {0} run: | pushd . cd demo/c-api/ mkdir build cd build cmake .. -GNinja -DCMAKE_PREFIX_PATH=$CONDA_PREFIX ninja -v ctest cd .. rm -rf ./build popd - name: Build and install XGBoost shared library shell: bash -l {0} run: | cd build cmake .. -DBUILD_STATIC_LIB=OFF -DCMAKE_INSTALL_PREFIX=$CONDA_PREFIX -GNinja ninja -v install cd - - name: Build and run C API demo with shared shell: bash -l {0} run: | pushd . cd demo/c-api/ mkdir build cd build cmake .. -GNinja -DCMAKE_PREFIX_PATH=$CONDA_PREFIX ninja -v ctest popd ./tests/ci_build/verify_link.sh ./demo/c-api/build/basic/api-demo ./tests/ci_build/verify_link.sh ./demo/c-api/build/external-memory/external-memory-demo lint: runs-on: ubuntu-latest name: Code linting for Python and C++ steps: - uses: actions/checkout@v2 with: submodules: 'true' - uses: actions/setup-python@v2 with: python-version: '3.7' architecture: 'x64' - name: Install Python packages run: | python -m pip install wheel setuptools python -m pip install pylint cpplint numpy scipy scikit-learn - name: Run lint run: | make lint mypy: runs-on: ubuntu-latest name: Type checking for Python steps: - uses: actions/checkout@v2 with: submodules: 'true' - uses: actions/setup-python@v2 with: python-version: '3.7' architecture: 'x64' - name: Install Python packages run: | python -m pip install wheel setuptools mypy pandas dask[complete] distributed - name: Run mypy run: | make mypy doxygen: runs-on: ubuntu-latest name: Generate C/C++ API doc using Doxygen steps: - uses: actions/checkout@v2 with: submodules: 'true' - uses: actions/setup-python@v2 with: python-version: '3.7' architecture: 'x64' - name: Install system packages run: | sudo apt-get install -y --no-install-recommends doxygen graphviz ninja-build python -m pip install wheel setuptools python -m pip install awscli - name: Run Doxygen run: | mkdir build cd build cmake .. -DBUILD_C_DOC=ON -GNinja ninja -v doc_doxygen - name: Extract branch name shell: bash run: echo "##[set-output name=branch;]$(echo ${GITHUB_REF#refs/heads/})" id: extract_branch if: github.ref == 'refs/heads/master' || contains(github.ref, 'refs/heads/release_') - name: Publish run: | cd build/ tar cvjf ${{ steps.extract_branch.outputs.branch }}.tar.bz2 doc_doxygen/ python -m awscli s3 cp ./${{ steps.extract_branch.outputs.branch }}.tar.bz2 s3://xgboost-docs/doxygen/ --acl public-read if: github.ref == 'refs/heads/master' || contains(github.ref, 'refs/heads/release_') env: AWS_ACCESS_KEY_ID: ${{ secrets.AWS_ACCESS_KEY_ID_IAM_S3_UPLOADER }} AWS_SECRET_ACCESS_KEY: ${{ secrets.AWS_SECRET_ACCESS_KEY_IAM_S3_UPLOADER }} sphinx: runs-on: ubuntu-latest name: Build docs using Sphinx steps: - uses: actions/checkout@v2 with: submodules: 'true' - uses: actions/setup-python@v2 with: python-version: '3.8' architecture: 'x64' - name: Install system packages run: | sudo apt-get install -y --no-install-recommends graphviz python -m pip install wheel setuptools python -m pip install -r doc/requirements.txt - name: Extract branch name shell: bash run: echo "##[set-output name=branch;]$(echo ${GITHUB_REF#refs/heads/})" id: extract_branch if: github.ref == 'refs/heads/master' || contains(github.ref, 'refs/heads/release_') - name: Run Sphinx run: | make -C doc html env: SPHINX_GIT_BRANCH: ${{ steps.extract_branch.outputs.branch }} xgboost-1.5.2/.github/workflows/python_tests.yml000066400000000000000000000120271417122711700220740ustar00rootroot00000000000000name: XGBoost-Python-Tests on: [push, pull_request] jobs: python-sdist-test: runs-on: ${{ matrix.os }} name: Test installing XGBoost Python source package on ${{ matrix.os }} strategy: matrix: os: [ubuntu-latest, macos-10.15, windows-latest] python-version: ["3.8"] steps: - uses: actions/checkout@v2 with: submodules: 'true' - name: Install osx system dependencies if: matrix.os == 'macos-10.15' run: | # Use libomp 11.1.0: https://github.com/dmlc/xgboost/issues/7039 wget https://raw.githubusercontent.com/Homebrew/homebrew-core/679923b4eb48a8dc7ecc1f05d06063cd79b3fc00/Formula/libomp.rb -O $(find $(brew --repository) -name libomp.rb) brew install ninja libomp brew pin libomp - name: Install Ubuntu system dependencies if: matrix.os == 'ubuntu-latest' run: | sudo apt-get install -y --no-install-recommends ninja-build - uses: conda-incubator/setup-miniconda@v2 with: auto-update-conda: true python-version: ${{ matrix.python-version }} activate-environment: test - name: Display Conda env shell: bash -l {0} run: | conda info conda list - name: Build and install XGBoost shell: bash -l {0} run: | cd python-package python --version python setup.py sdist pip install -v ./dist/xgboost-*.tar.gz cd .. python -c 'import xgboost' python-tests-on-win: name: Test XGBoost Python package on ${{ matrix.config.os }} runs-on: ${{ matrix.config.os }} strategy: matrix: config: - {os: windows-2016, python-version: '3.8'} steps: - uses: actions/checkout@v2 with: submodules: 'true' - uses: conda-incubator/setup-miniconda@v2 with: auto-update-conda: true python-version: ${{ matrix.config.python-version }} activate-environment: win64_env environment-file: tests/ci_build/conda_env/win64_cpu_test.yml - name: Display Conda env shell: bash -l {0} run: | conda info conda list - name: Build XGBoost on Windows shell: bash -l {0} run: | mkdir build_msvc cd build_msvc cmake .. -G"Visual Studio 15 2017" -DCMAKE_CONFIGURATION_TYPES="Release" -A x64 -DGOOGLE_TEST=ON -DUSE_DMLC_GTEST=ON cmake --build . --config Release --parallel $(nproc) - name: Install Python package shell: bash -l {0} run: | cd python-package python --version python setup.py bdist_wheel --universal pip install ./dist/*.whl - name: Test Python package shell: bash -l {0} run: | pytest -s -v ./tests/python python-tests-on-macos: name: Test XGBoost Python package on ${{ matrix.config.os }} runs-on: ${{ matrix.config.os }} strategy: matrix: config: - {os: macos-10.15, python-version "3.8" } steps: - uses: actions/checkout@v2 with: submodules: 'true' - uses: conda-incubator/setup-miniconda@v2 with: auto-update-conda: true python-version: ${{ matrix.config.python-version }} activate-environment: macos_test environment-file: tests/ci_build/conda_env/macos_cpu_test.yml - name: Display Conda env shell: bash -l {0} run: | conda info conda list - name: Build XGBoost on macos run: | wget https://raw.githubusercontent.com/Homebrew/homebrew-core/679923b4eb48a8dc7ecc1f05d06063cd79b3fc00/Formula/libomp.rb -O $(find $(brew --repository) -name libomp.rb) brew install ninja libomp brew pin libomp mkdir build cd build cmake .. -GNinja -DGOOGLE_TEST=ON -DUSE_DMLC_GTEST=ON ninja - name: Install Python package shell: bash -l {0} run: | cd python-package python --version python setup.py bdist_wheel --universal pip install ./dist/*.whl - name: Test Python package shell: bash -l {0} run: | pytest -s -v ./tests/python - name: Rename Python wheel shell: bash -l {0} run: | TAG=macosx_10_15_x86_64.macosx_11_0_x86_64.macosx_12_0_x86_64 python tests/ci_build/rename_whl.py python-package/dist/*.whl ${{ github.sha }} ${TAG} - name: Extract branch name shell: bash run: echo "##[set-output name=branch;]$(echo ${GITHUB_REF#refs/heads/})" id: extract_branch if: github.ref == 'refs/heads/master' || contains(github.ref, 'refs/heads/release_') - name: Upload Python wheel shell: bash -l {0} if: github.ref == 'refs/heads/master' || contains(github.ref, 'refs/heads/release_') run: | python -m awscli s3 cp python-package/dist/*.whl s3://xgboost-nightly-builds/${{ steps.extract_branch.outputs.branch }}/ --acl public-read env: AWS_ACCESS_KEY_ID: ${{ secrets.AWS_ACCESS_KEY_ID_IAM_S3_UPLOADER }} AWS_SECRET_ACCESS_KEY: ${{ secrets.AWS_SECRET_ACCESS_KEY_IAM_S3_UPLOADER }} xgboost-1.5.2/.github/workflows/r_nold.yml000066400000000000000000000027471417122711700206160ustar00rootroot00000000000000# Run R tests with noLD R. Only triggered by a pull request review # See discussion at https://github.com/dmlc/xgboost/pull/6378 name: XGBoost-R-noLD on: pull_request_review_comment: types: [created] env: R_PACKAGES: c('XML', 'igraph', 'data.table', 'ggplot2', 'DiagrammeR', 'Ckmeans.1d.dp', 'vcd', 'testthat', 'lintr', 'knitr', 'rmarkdown', 'e1071', 'cplm', 'devtools', 'float', 'titanic') jobs: test-R-noLD: if: github.event.comment.body == '/gha run r-nold-test' && contains('OWNER,MEMBER,COLLABORATOR', github.event.comment.author_association) timeout-minutes: 120 runs-on: ubuntu-latest container: rhub/debian-gcc-devel-nold steps: - name: Install git and system packages shell: bash run: | apt-get update && apt-get install -y git libcurl4-openssl-dev libssl-dev libssh2-1-dev libgit2-dev libxml2-dev - uses: actions/checkout@v2 with: submodules: 'true' - name: Install dependencies shell: bash run: | cat > install_libs.R </include> $) #-- End shared library #-- CLI for xgboost add_executable(runxgboost ${xgboost_SOURCE_DIR}/src/cli_main.cc) target_link_libraries(runxgboost PRIVATE objxgboost) target_include_directories(runxgboost PRIVATE ${xgboost_SOURCE_DIR}/include ${xgboost_SOURCE_DIR}/dmlc-core/include ${xgboost_SOURCE_DIR}/rabit/include ) set_target_properties(runxgboost PROPERTIES OUTPUT_NAME xgboost) #-- End CLI for xgboost # Common setup for all targets foreach(target xgboost objxgboost dmlc runxgboost) xgboost_target_properties(${target}) xgboost_target_link_libraries(${target}) xgboost_target_defs(${target}) endforeach() if (JVM_BINDINGS) xgboost_target_properties(xgboost4j) xgboost_target_link_libraries(xgboost4j) xgboost_target_defs(xgboost4j) endif (JVM_BINDINGS) set_output_directory(runxgboost ${xgboost_SOURCE_DIR}) set_output_directory(xgboost ${xgboost_SOURCE_DIR}/lib) # Ensure these two targets do not build simultaneously, as they produce outputs with conflicting names add_dependencies(xgboost runxgboost) #-- Installing XGBoost if (R_LIB) include(cmake/RPackageInstallTargetSetup.cmake) set_target_properties(xgboost PROPERTIES PREFIX "") if (APPLE) set_target_properties(xgboost PROPERTIES SUFFIX ".so") endif (APPLE) setup_rpackage_install_target(xgboost "${CMAKE_CURRENT_BINARY_DIR}/R-package-install") set(CMAKE_INSTALL_PREFIX "${CMAKE_CURRENT_BINARY_DIR}/dummy_inst") endif (R_LIB) if (MINGW) set_target_properties(xgboost PROPERTIES PREFIX "") endif (MINGW) if (BUILD_C_DOC) include(cmake/Doc.cmake) run_doxygen() endif (BUILD_C_DOC) include(CPack) include(GNUInstallDirs) # Install all headers. Please note that currently the C++ headers does not form an "API". install(DIRECTORY ${xgboost_SOURCE_DIR}/include/xgboost DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}) # Install libraries. If `xgboost` is a static lib, specify `objxgboost` also, to avoid the # following error: # # > install(EXPORT ...) includes target "xgboost" which requires target "objxgboost" that is not # > in any export set. # # https://github.com/dmlc/xgboost/issues/6085 if (BUILD_STATIC_LIB) set(INSTALL_TARGETS xgboost runxgboost objxgboost dmlc) else (BUILD_STATIC_LIB) set(INSTALL_TARGETS xgboost runxgboost) endif (BUILD_STATIC_LIB) install(TARGETS ${INSTALL_TARGETS} EXPORT XGBoostTargets ARCHIVE DESTINATION ${CMAKE_INSTALL_LIBDIR} LIBRARY DESTINATION ${CMAKE_INSTALL_LIBDIR} RUNTIME DESTINATION ${CMAKE_INSTALL_BINDIR} INCLUDES DESTINATION ${LIBLEGACY_INCLUDE_DIRS}) install(EXPORT XGBoostTargets FILE XGBoostTargets.cmake NAMESPACE xgboost:: DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/xgboost) include(CMakePackageConfigHelpers) configure_package_config_file( ${CMAKE_CURRENT_LIST_DIR}/cmake/xgboost-config.cmake.in ${CMAKE_CURRENT_BINARY_DIR}/cmake/xgboost-config.cmake INSTALL_DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/xgboost) write_basic_package_version_file( ${CMAKE_BINARY_DIR}/cmake/xgboost-config-version.cmake VERSION ${XGBOOST_VERSION} COMPATIBILITY AnyNewerVersion) install( FILES ${CMAKE_BINARY_DIR}/cmake/xgboost-config.cmake ${CMAKE_BINARY_DIR}/cmake/xgboost-config-version.cmake DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/xgboost) #-- Test if (GOOGLE_TEST) enable_testing() # Unittests. add_executable(testxgboost) target_link_libraries(testxgboost PRIVATE objxgboost) xgboost_target_properties(testxgboost) xgboost_target_link_libraries(testxgboost) xgboost_target_defs(testxgboost) add_subdirectory(${xgboost_SOURCE_DIR}/tests/cpp) add_test( NAME TestXGBoostLib COMMAND testxgboost WORKING_DIRECTORY ${xgboost_BINARY_DIR}) # CLI tests configure_file( ${xgboost_SOURCE_DIR}/tests/cli/machine.conf.in ${xgboost_BINARY_DIR}/tests/cli/machine.conf @ONLY) add_test( NAME TestXGBoostCLI COMMAND runxgboost ${xgboost_BINARY_DIR}/tests/cli/machine.conf WORKING_DIRECTORY ${xgboost_BINARY_DIR}) set_tests_properties(TestXGBoostCLI PROPERTIES PASS_REGULAR_EXPRESSION ".*test-rmse:0.087.*") endif (GOOGLE_TEST) # For MSVC: Call msvc_use_static_runtime() once again to completely # replace /MD with /MT. See https://github.com/dmlc/xgboost/issues/4462 # for issues caused by mixing of /MD and /MT flags msvc_use_static_runtime() # Add xgboost.pc if (ADD_PKGCONFIG) configure_file(${xgboost_SOURCE_DIR}/cmake/xgboost.pc.in ${xgboost_BINARY_DIR}/xgboost.pc @ONLY) install( FILES ${xgboost_BINARY_DIR}/xgboost.pc DESTINATION ${CMAKE_INSTALL_LIBDIR}/pkgconfig) endif (ADD_PKGCONFIG) xgboost-1.5.2/CONTRIBUTORS.md000066400000000000000000000143361417122711700154750ustar00rootroot00000000000000Contributors of DMLC/XGBoost ============================ XGBoost has been developed and used by a group of active community. Everyone is more than welcomed to is a great way to make the project better and more accessible to more users. Project Management Committee(PMC) ---------- The Project Management Committee(PMC) consists group of active committers that moderate the discussion, manage the project release, and proposes new committer/PMC members. * [Tianqi Chen](https://github.com/tqchen), University of Washington - Tianqi is a Ph.D. student working on large-scale machine learning. He is the creator of the project. * [Michael Benesty](https://github.com/pommedeterresautee) - Michael is a lawyer and data scientist in France. He is the creator of XGBoost interactive analysis module in R. * [Yuan Tang](https://github.com/terrytangyuan), Ant Group - Yuan is a software engineer in Ant Group. He contributed mostly in R and Python packages. * [Nan Zhu](https://github.com/CodingCat), Uber - Nan is a software engineer in Uber. He contributed mostly in JVM packages. * [Jiaming Yuan](https://github.com/trivialfis) - Jiaming contributed to the GPU algorithms. He has also introduced new abstractions to improve the quality of the C++ codebase. * [Hyunsu Cho](http://hyunsu-cho.io/), NVIDIA - Hyunsu is the maintainer of the XGBoost Python package. He also manages the Jenkins continuous integration system (https://xgboost-ci.net/). He is the initial author of the CPU 'hist' updater. * [Rory Mitchell](https://github.com/RAMitchell), University of Waikato - Rory is a Ph.D. student at University of Waikato. He is the original creator of the GPU training algorithms. He improved the CMake build system and continuous integration. * [Hongliang Liu](https://github.com/phunterlau) Committers ---------- Committers are people who have made substantial contribution to the project and granted write access to the project. * [Tong He](https://github.com/hetong007), Amazon AI - Tong is an applied scientist in Amazon AI. He is the maintainer of XGBoost R package. * [Vadim Khotilovich](https://github.com/khotilov) - Vadim contributes many improvements in R and core packages. * [Bing Xu](https://github.com/antinucleon) - Bing is the original creator of XGBoost Python package and currently the maintainer of [XGBoost.jl](https://github.com/antinucleon/XGBoost.jl). * [Sergei Lebedev](https://github.com/superbobry), Criteo - Sergei is a software engineer in Criteo. He contributed mostly in JVM packages. * [Scott Lundberg](http://scottlundberg.com/), University of Washington - Scott is a Ph.D. student at University of Washington. He is the creator of SHAP, a unified approach to explain the output of machine learning models such as decision tree ensembles. He also helps maintain the XGBoost Julia package. * [Egor Smirnov](https://github.com/SmirnovEgorRu), Intel - Egor has led a major effort to improve the performance of XGBoost on multi-core CPUs. Become a Committer ------------------ XGBoost is a open source project and we are actively looking for new committers who are willing to help maintaining and lead the project. Committers comes from contributors who: * Made substantial contribution to the project. * Willing to spent time on maintaining and lead the project. New committers will be proposed by current committer members, with support from more than two of current committers. List of Contributors -------------------- * [Full List of Contributors](https://github.com/dmlc/xgboost/graphs/contributors) - To contributors: please add your name to the list when you submit a patch to the project:) * [Kailong Chen](https://github.com/kalenhaha) - Kailong is an early contributor of XGBoost, he is creator of ranking objectives in XGBoost. * [Skipper Seabold](https://github.com/jseabold) - Skipper is the major contributor to the scikit-learn module of XGBoost. * [Zygmunt Zając](https://github.com/zygmuntz) - Zygmunt is the master behind the early stopping feature frequently used by Kagglers. * [Ajinkya Kale](https://github.com/ajkl) * [Boliang Chen](https://github.com/cblsjtu) * [Yangqing Men](https://github.com/yanqingmen) - Yangqing is the creator of XGBoost java package. * [Engpeng Yao](https://github.com/yepyao) * [Giulio](https://github.com/giuliohome) - Giulio is the creator of Windows project of XGBoost * [Jamie Hall](https://github.com/nerdcha) - Jamie is the initial creator of XGBoost scikit-learn module. * [Yen-Ying Lee](https://github.com/white1033) * [Masaaki Horikoshi](https://github.com/sinhrks) - Masaaki is the initial creator of XGBoost Python plotting module. * [daiyl0320](https://github.com/daiyl0320) - daiyl0320 contributed patch to XGBoost distributed version more robust, and scales stably on TB scale datasets. * [Huayi Zhang](https://github.com/irachex) * [Johan Manders](https://github.com/johanmanders) * [yoori](https://github.com/yoori) * [Mathias Müller](https://github.com/far0n) * [Sam Thomson](https://github.com/sammthomson) * [ganesh-krishnan](https://github.com/ganesh-krishnan) * [Damien Carol](https://github.com/damiencarol) * [Alex Bain](https://github.com/convexquad) * [Baltazar Bieniek](https://github.com/bbieniek) * [Adam Pocock](https://github.com/Craigacp) * [Gideon Whitehead](https://github.com/gaw89) * [Yi-Lin Juang](https://github.com/frankyjuang) * [Andrew Hannigan](https://github.com/andrewhannigan) * [Andy Adinets](https://github.com/canonizer) * [Henry Gouk](https://github.com/henrygouk) * [Pierre de Sahb](https://github.com/pdesahb) * [liuliang01](https://github.com/liuliang01) - liuliang01 added support for the qid column for LIBSVM input format. This makes ranking task easier in distributed setting. * [Andrew Thia](https://github.com/BlueTea88) - Andrew Thia implemented feature interaction constraints * [Wei Tian](https://github.com/weitian) * [Chen Qin](https://github.com/chenqin) * [Sam Wilkinson](https://samwilkinson.io) * [Matthew Jones](https://github.com/mt-jones) * [Jiaxiang Li](https://github.com/JiaxiangBU) * [Bryan Woods](https://github.com/bryan-woods) - Bryan added support for cross-validation for the ranking objective * [Haoda Fu](https://github.com/fuhaoda) * [Evan Kepner](https://github.com/EvanKepner) - Evan Kepner added support for os.PathLike file paths in Python xgboost-1.5.2/Jenkinsfile000066400000000000000000000450661417122711700154060ustar00rootroot00000000000000#!/usr/bin/groovy // -*- mode: groovy -*- // Jenkins pipeline // See documents at https://jenkins.io/doc/book/pipeline/jenkinsfile/ // Command to run command inside a docker container dockerRun = 'tests/ci_build/ci_build.sh' // Which CUDA version to use when building reference distribution wheel ref_cuda_ver = '10.1' import groovy.transform.Field @Field def commit_id // necessary to pass a variable from one stage to another pipeline { // Each stage specify its own agent agent none environment { DOCKER_CACHE_ECR_ID = '492475357299' DOCKER_CACHE_ECR_REGION = 'us-west-2' } // Setup common job properties options { ansiColor('xterm') timestamps() timeout(time: 240, unit: 'MINUTES') buildDiscarder(logRotator(numToKeepStr: '10')) preserveStashes() } // Build stages stages { stage('Jenkins Linux: Initialize') { agent { label 'job_initializer' } steps { script { def buildNumber = env.BUILD_NUMBER as int if (buildNumber > 1) milestone(buildNumber - 1) milestone(buildNumber) checkoutSrcs() commit_id = "${GIT_COMMIT}" } sh 'python3 tests/jenkins_get_approval.py' stash name: 'srcs' } } stage('Jenkins Linux: Build') { agent none steps { script { parallel ([ 'clang-tidy': { ClangTidy() }, 'build-cpu': { BuildCPU() }, 'build-cpu-arm64': { BuildCPUARM64() }, 'build-cpu-rabit-mock': { BuildCPUMock() }, // Build reference, distribution-ready Python wheel with CUDA 10.1 // using CentOS 7 image 'build-gpu-cuda10.1': { BuildCUDA(cuda_version: '10.1') }, // The build-gpu-* builds below use Ubuntu image 'build-gpu-cuda11.0': { BuildCUDA(cuda_version: '11.0', build_rmm: true) }, 'build-gpu-rpkg': { BuildRPackageWithCUDA(cuda_version: '10.1') }, 'build-jvm-packages-gpu-cuda10.1': { BuildJVMPackagesWithCUDA(spark_version: '3.0.0', cuda_version: '11.0') }, 'build-jvm-packages': { BuildJVMPackages(spark_version: '3.0.0') }, 'build-jvm-doc': { BuildJVMDoc() } ]) } } } stage('Jenkins Linux: Test') { agent none steps { script { parallel ([ 'test-python-cpu': { TestPythonCPU() }, 'test-python-cpu-arm64': { TestPythonCPUARM64() }, // artifact_cuda_version doesn't apply to RMM tests; RMM tests will always match CUDA version between artifact and host env 'test-python-gpu-cuda11.0-cross': { TestPythonGPU(artifact_cuda_version: '10.1', host_cuda_version: '11.0', test_rmm: true) }, 'test-python-gpu-cuda11.0': { TestPythonGPU(artifact_cuda_version: '11.0', host_cuda_version: '11.0') }, 'test-python-mgpu-cuda11.0': { TestPythonGPU(artifact_cuda_version: '10.1', host_cuda_version: '11.0', multi_gpu: true, test_rmm: true) }, 'test-cpp-gpu-cuda11.0': { TestCppGPU(artifact_cuda_version: '11.0', host_cuda_version: '11.0', test_rmm: true) }, 'test-jvm-jdk8': { CrossTestJVMwithJDK(jdk_version: '8', spark_version: '3.0.0') }, 'test-jvm-jdk11': { CrossTestJVMwithJDK(jdk_version: '11') }, 'test-jvm-jdk12': { CrossTestJVMwithJDK(jdk_version: '12') } ]) } } } stage('Jenkins Linux: Deploy') { agent none steps { script { parallel ([ 'deploy-jvm-packages': { DeployJVMPackages(spark_version: '3.0.0') } ]) } } } } } // check out source code from git def checkoutSrcs() { retry(5) { try { timeout(time: 2, unit: 'MINUTES') { checkout scm sh 'git submodule update --init' } } catch (exc) { deleteDir() error "Failed to fetch source codes" } } } def GetCUDABuildContainerType(cuda_version) { return (cuda_version == ref_cuda_ver) ? 'gpu_build_centos7' : 'gpu_build' } def ClangTidy() { node('linux && cpu_build') { unstash name: 'srcs' echo "Running clang-tidy job..." def container_type = "clang_tidy" def docker_binary = "docker" def dockerArgs = "--build-arg CUDA_VERSION_ARG=10.1" sh """ ${dockerRun} ${container_type} ${docker_binary} ${dockerArgs} python3 tests/ci_build/tidy.py """ deleteDir() } } def BuildCPU() { node('linux && cpu') { unstash name: 'srcs' echo "Build CPU" def container_type = "cpu" def docker_binary = "docker" sh """ ${dockerRun} ${container_type} ${docker_binary} rm -fv dmlc-core/include/dmlc/build_config_default.h # This step is not necessary, but here we include it, to ensure that DMLC_CORE_USE_CMAKE flag is correctly propagated # We want to make sure that we use the configured header build/dmlc/build_config.h instead of include/dmlc/build_config_default.h. # See discussion at https://github.com/dmlc/xgboost/issues/5510 ${dockerRun} ${container_type} ${docker_binary} tests/ci_build/build_via_cmake.sh -DPLUGIN_DENSE_PARSER=ON ${dockerRun} ${container_type} ${docker_binary} bash -c "cd build && ctest --extra-verbose" """ // Sanitizer test def docker_extra_params = "CI_DOCKER_EXTRA_PARAMS_INIT='-e ASAN_SYMBOLIZER_PATH=/usr/bin/llvm-symbolizer -e ASAN_OPTIONS=symbolize=1 -e UBSAN_OPTIONS=print_stacktrace=1:log_path=ubsan_error.log --cap-add SYS_PTRACE'" sh """ ${dockerRun} ${container_type} ${docker_binary} tests/ci_build/build_via_cmake.sh -DUSE_SANITIZER=ON -DENABLED_SANITIZERS="address;leak;undefined" \ -DCMAKE_BUILD_TYPE=Debug -DSANITIZER_PATH=/usr/lib/x86_64-linux-gnu/ ${docker_extra_params} ${dockerRun} ${container_type} ${docker_binary} bash -c "cd build && ctest --exclude-regex AllTestsInDMLCUnitTests --extra-verbose" """ stash name: 'xgboost_cli', includes: 'xgboost' deleteDir() } } def BuildCPUARM64() { node('linux && arm64') { unstash name: 'srcs' echo "Build CPU ARM64" def container_type = "aarch64" def docker_binary = "docker" def wheel_tag = "manylinux2014_aarch64" sh """ ${dockerRun} ${container_type} ${docker_binary} tests/ci_build/build_via_cmake.sh --conda-env=aarch64_test -DOPEN_MP:BOOL=ON -DHIDE_CXX_SYMBOL=ON ${dockerRun} ${container_type} ${docker_binary} bash -c "cd build && ctest --extra-verbose" ${dockerRun} ${container_type} ${docker_binary} bash -c "cd python-package && rm -rf dist/* && python setup.py bdist_wheel --universal" ${dockerRun} ${container_type} ${docker_binary} python tests/ci_build/rename_whl.py python-package/dist/*.whl ${commit_id} ${wheel_tag} ${dockerRun} ${container_type} ${docker_binary} bash -c "auditwheel repair --plat ${wheel_tag} python-package/dist/*.whl && python tests/ci_build/rename_whl.py wheelhouse/*.whl ${commit_id} ${wheel_tag}" mv -v wheelhouse/*.whl python-package/dist/ # Make sure that libgomp.so is vendored in the wheel ${dockerRun} ${container_type} ${docker_binary} bash -c "unzip -l python-package/dist/*.whl | grep libgomp || exit -1" """ echo 'Stashing Python wheel...' stash name: "xgboost_whl_arm64_cpu", includes: 'python-package/dist/*.whl' if (env.BRANCH_NAME == 'master' || env.BRANCH_NAME.startsWith('release')) { echo 'Uploading Python wheel...' path = ("${BRANCH_NAME}" == 'master') ? '' : "${BRANCH_NAME}/" s3Upload bucket: 'xgboost-nightly-builds', path: path, acl: 'PublicRead', workingDir: 'python-package/dist', includePathPattern:'**/*.whl' } stash name: 'xgboost_cli_arm64', includes: 'xgboost' deleteDir() } } def BuildCPUMock() { node('linux && cpu') { unstash name: 'srcs' echo "Build CPU with rabit mock" def container_type = "cpu" def docker_binary = "docker" sh """ ${dockerRun} ${container_type} ${docker_binary} tests/ci_build/build_mock_cmake.sh """ echo 'Stashing rabit C++ test executable (xgboost)...' stash name: 'xgboost_rabit_tests', includes: 'xgboost' deleteDir() } } def BuildCUDA(args) { node('linux && cpu_build') { unstash name: 'srcs' echo "Build with CUDA ${args.cuda_version}" def container_type = GetCUDABuildContainerType(args.cuda_version) def docker_binary = "docker" def docker_args = "--build-arg CUDA_VERSION_ARG=${args.cuda_version}" def arch_flag = "" if (env.BRANCH_NAME != 'master' && !(env.BRANCH_NAME.startsWith('release'))) { arch_flag = "-DGPU_COMPUTE_VER=75" } def wheel_tag = "manylinux2014_x86_64" sh """ ${dockerRun} ${container_type} ${docker_binary} ${docker_args} tests/ci_build/build_via_cmake.sh -DUSE_CUDA=ON -DUSE_NCCL=ON -DOPEN_MP:BOOL=ON -DHIDE_CXX_SYMBOLS=ON ${arch_flag} ${dockerRun} ${container_type} ${docker_binary} ${docker_args} bash -c "cd python-package && rm -rf dist/* && python setup.py bdist_wheel --universal" ${dockerRun} ${container_type} ${docker_binary} ${docker_args} python tests/ci_build/rename_whl.py python-package/dist/*.whl ${commit_id} ${wheel_tag} """ if (args.cuda_version == ref_cuda_ver) { sh """ ${dockerRun} auditwheel_x86_64 ${docker_binary} auditwheel repair --plat ${wheel_tag} python-package/dist/*.whl ${dockerRun} ${container_type} ${docker_binary} ${docker_args} python tests/ci_build/rename_whl.py wheelhouse/*.whl ${commit_id} ${wheel_tag} mv -v wheelhouse/*.whl python-package/dist/ # Make sure that libgomp.so is vendored in the wheel ${dockerRun} auditwheel_x86_64 ${docker_binary} bash -c "unzip -l python-package/dist/*.whl | grep libgomp || exit -1" """ } echo 'Stashing Python wheel...' stash name: "xgboost_whl_cuda${args.cuda_version}", includes: 'python-package/dist/*.whl' if (args.cuda_version == ref_cuda_ver && (env.BRANCH_NAME == 'master' || env.BRANCH_NAME.startsWith('release'))) { echo 'Uploading Python wheel...' path = ("${BRANCH_NAME}" == 'master') ? '' : "${BRANCH_NAME}/" s3Upload bucket: 'xgboost-nightly-builds', path: path, acl: 'PublicRead', workingDir: 'python-package/dist', includePathPattern:'**/*.whl' } echo 'Stashing C++ test executable (testxgboost)...' stash name: "xgboost_cpp_tests_cuda${args.cuda_version}", includes: 'build/testxgboost' if (args.build_rmm) { echo "Build with CUDA ${args.cuda_version} and RMM" container_type = "rmm" docker_binary = "docker" docker_args = "--build-arg CUDA_VERSION_ARG=${args.cuda_version}" sh """ rm -rf build/ ${dockerRun} ${container_type} ${docker_binary} ${docker_args} tests/ci_build/build_via_cmake.sh --conda-env=gpu_test -DUSE_CUDA=ON -DUSE_NCCL=ON -DPLUGIN_RMM=ON -DBUILD_WITH_CUDA_CUB=ON ${arch_flag} ${dockerRun} ${container_type} ${docker_binary} ${docker_args} bash -c "cd python-package && rm -rf dist/* && python setup.py bdist_wheel --universal" ${dockerRun} ${container_type} ${docker_binary} ${docker_args} python tests/ci_build/rename_whl.py python-package/dist/*.whl ${commit_id} manylinux2014_x86_64 """ echo 'Stashing Python wheel...' stash name: "xgboost_whl_rmm_cuda${args.cuda_version}", includes: 'python-package/dist/*.whl' echo 'Stashing C++ test executable (testxgboost)...' stash name: "xgboost_cpp_tests_rmm_cuda${args.cuda_version}", includes: 'build/testxgboost' } deleteDir() } } def BuildRPackageWithCUDA(args) { node('linux && cpu_build') { unstash name: 'srcs' def container_type = 'gpu_build_r_centos7' def docker_binary = "docker" def docker_args = "--build-arg CUDA_VERSION_ARG=${args.cuda_version}" if (env.BRANCH_NAME == 'master' || env.BRANCH_NAME.startsWith('release')) { sh """ ${dockerRun} ${container_type} ${docker_binary} ${docker_args} tests/ci_build/build_r_pkg_with_cuda.sh ${commit_id} """ echo 'Uploading R tarball...' path = ("${BRANCH_NAME}" == 'master') ? '' : "${BRANCH_NAME}/" s3Upload bucket: 'xgboost-nightly-builds', path: path, acl: 'PublicRead', includePathPattern:'xgboost_r_gpu_linux_*.tar.gz' } deleteDir() } } def BuildJVMPackagesWithCUDA(args) { node('linux && mgpu') { unstash name: 'srcs' echo "Build XGBoost4J-Spark with Spark ${args.spark_version}, CUDA ${args.cuda_version}" def container_type = "jvm_gpu_build" def docker_binary = "nvidia-docker" def docker_args = "--build-arg CUDA_VERSION_ARG=${args.cuda_version}" def arch_flag = "" if (env.BRANCH_NAME != 'master' && !(env.BRANCH_NAME.startsWith('release'))) { arch_flag = "-DGPU_COMPUTE_VER=75" } // Use only 4 CPU cores def docker_extra_params = "CI_DOCKER_EXTRA_PARAMS_INIT='--cpuset-cpus 0-3'" sh """ ${docker_extra_params} ${dockerRun} ${container_type} ${docker_binary} ${docker_args} tests/ci_build/build_jvm_packages.sh ${args.spark_version} -Duse.cuda=ON $arch_flag """ echo "Stashing XGBoost4J JAR with CUDA ${args.cuda_version} ..." stash name: 'xgboost4j_jar_gpu', includes: "jvm-packages/xgboost4j-gpu/target/*.jar,jvm-packages/xgboost4j-spark-gpu/target/*.jar" deleteDir() } } def BuildJVMPackages(args) { node('linux && cpu') { unstash name: 'srcs' echo "Build XGBoost4J-Spark with Spark ${args.spark_version}" def container_type = "jvm" def docker_binary = "docker" // Use only 4 CPU cores def docker_extra_params = "CI_DOCKER_EXTRA_PARAMS_INIT='--cpuset-cpus 0-3'" sh """ ${docker_extra_params} ${dockerRun} ${container_type} ${docker_binary} tests/ci_build/build_jvm_packages.sh ${args.spark_version} """ echo 'Stashing XGBoost4J JAR...' stash name: 'xgboost4j_jar', includes: "jvm-packages/xgboost4j/target/*.jar,jvm-packages/xgboost4j-spark/target/*.jar,jvm-packages/xgboost4j-example/target/*.jar" deleteDir() } } def BuildJVMDoc() { node('linux && cpu') { unstash name: 'srcs' echo "Building JVM doc..." def container_type = "jvm" def docker_binary = "docker" sh """ ${dockerRun} ${container_type} ${docker_binary} tests/ci_build/build_jvm_doc.sh ${BRANCH_NAME} """ if (env.BRANCH_NAME == 'master' || env.BRANCH_NAME.startsWith('release')) { echo 'Uploading doc...' s3Upload file: "jvm-packages/${BRANCH_NAME}.tar.bz2", bucket: 'xgboost-docs', acl: 'PublicRead', path: "${BRANCH_NAME}.tar.bz2" } deleteDir() } } def TestPythonCPU() { node('linux && cpu') { unstash name: "xgboost_whl_cuda${ref_cuda_ver}" unstash name: 'srcs' unstash name: 'xgboost_cli' echo "Test Python CPU" def container_type = "cpu" def docker_binary = "docker" sh """ ${dockerRun} ${container_type} ${docker_binary} tests/ci_build/test_python.sh cpu """ deleteDir() } } def TestPythonCPUARM64() { node('linux && arm64') { unstash name: "xgboost_whl_arm64_cpu" unstash name: 'srcs' unstash name: 'xgboost_cli_arm64' echo "Test Python CPU ARM64" def container_type = "aarch64" def docker_binary = "docker" sh """ ${dockerRun} ${container_type} ${docker_binary} tests/ci_build/test_python.sh cpu-arm64 """ deleteDir() } } def TestPythonGPU(args) { def nodeReq = (args.multi_gpu) ? 'linux && mgpu' : 'linux && gpu' def artifact_cuda_version = (args.artifact_cuda_version) ?: ref_cuda_ver node(nodeReq) { unstash name: "xgboost_whl_cuda${artifact_cuda_version}" unstash name: "xgboost_cpp_tests_cuda${artifact_cuda_version}" unstash name: 'srcs' echo "Test Python GPU: CUDA ${args.host_cuda_version}" def container_type = "gpu" def docker_binary = "nvidia-docker" def docker_args = "--build-arg CUDA_VERSION_ARG=${args.host_cuda_version}" def mgpu_indicator = (args.multi_gpu) ? 'mgpu' : 'gpu' // Allocate extra space in /dev/shm to enable NCCL def docker_extra_params = (args.multi_gpu) ? "CI_DOCKER_EXTRA_PARAMS_INIT='--shm-size=4g'" : '' sh "${docker_extra_params} ${dockerRun} ${container_type} ${docker_binary} ${docker_args} tests/ci_build/test_python.sh ${mgpu_indicator}" if (args.test_rmm) { sh "rm -rfv build/ python-package/dist/" unstash name: "xgboost_whl_rmm_cuda${args.host_cuda_version}" unstash name: "xgboost_cpp_tests_rmm_cuda${args.host_cuda_version}" sh "${docker_extra_params} ${dockerRun} ${container_type} ${docker_binary} ${docker_args} tests/ci_build/test_python.sh ${mgpu_indicator} --use-rmm-pool" } deleteDir() } } def TestCppGPU(args) { def nodeReq = 'linux && mgpu' def artifact_cuda_version = (args.artifact_cuda_version) ?: ref_cuda_ver node(nodeReq) { unstash name: "xgboost_cpp_tests_cuda${artifact_cuda_version}" unstash name: 'srcs' echo "Test C++, CUDA ${args.host_cuda_version}" def container_type = "gpu" def docker_binary = "nvidia-docker" def docker_args = "--build-arg CUDA_VERSION_ARG=${args.host_cuda_version}" sh "${dockerRun} ${container_type} ${docker_binary} ${docker_args} build/testxgboost" if (args.test_rmm) { sh "rm -rfv build/" unstash name: "xgboost_cpp_tests_rmm_cuda${args.host_cuda_version}" echo "Test C++, CUDA ${args.host_cuda_version} with RMM" container_type = "rmm" docker_binary = "nvidia-docker" docker_args = "--build-arg CUDA_VERSION_ARG=${args.host_cuda_version}" sh """ ${dockerRun} ${container_type} ${docker_binary} ${docker_args} bash -c "source activate gpu_test && build/testxgboost --use-rmm-pool --gtest_filter=-*DeathTest.*" """ } deleteDir() } } def CrossTestJVMwithJDK(args) { node('linux && cpu') { unstash name: 'xgboost4j_jar' unstash name: 'srcs' if (args.spark_version != null) { echo "Test XGBoost4J on a machine with JDK ${args.jdk_version}, Spark ${args.spark_version}" } else { echo "Test XGBoost4J on a machine with JDK ${args.jdk_version}" } def container_type = "jvm_cross" def docker_binary = "docker" def spark_arg = (args.spark_version != null) ? "--build-arg SPARK_VERSION=${args.spark_version}" : "" def docker_args = "--build-arg JDK_VERSION=${args.jdk_version} ${spark_arg}" // Run integration tests only when spark_version is given def docker_extra_params = (args.spark_version != null) ? "CI_DOCKER_EXTRA_PARAMS_INIT='-e RUN_INTEGRATION_TEST=1'" : "" sh """ ${docker_extra_params} ${dockerRun} ${container_type} ${docker_binary} ${docker_args} tests/ci_build/test_jvm_cross.sh """ deleteDir() } } def DeployJVMPackages(args) { node('linux && cpu') { unstash name: 'srcs' if (env.BRANCH_NAME == 'master' || env.BRANCH_NAME.startsWith('release')) { echo 'Deploying to xgboost-maven-repo S3 repo...' sh """ ${dockerRun} jvm_gpu_build docker --build-arg CUDA_VERSION_ARG=10.1 tests/ci_build/deploy_jvm_packages.sh ${args.spark_version} """ } deleteDir() } } xgboost-1.5.2/Jenkinsfile-win64000066400000000000000000000116751417122711700163520ustar00rootroot00000000000000#!/usr/bin/groovy // -*- mode: groovy -*- /* Jenkins pipeline for Windows AMD64 target */ import groovy.transform.Field @Field def commit_id // necessary to pass a variable from one stage to another pipeline { agent none // Setup common job properties options { timestamps() timeout(time: 240, unit: 'MINUTES') buildDiscarder(logRotator(numToKeepStr: '10')) preserveStashes() } // Build stages stages { stage('Jenkins Win64: Initialize') { agent { label 'job_initializer' } steps { script { def buildNumber = env.BUILD_NUMBER as int if (buildNumber > 1) milestone(buildNumber - 1) milestone(buildNumber) checkoutSrcs() commit_id = "${GIT_COMMIT}" } sh 'python3 tests/jenkins_get_approval.py' stash name: 'srcs' } } stage('Jenkins Win64: Build') { agent none steps { script { parallel ([ 'build-win64-cuda10.1': { BuildWin64() }, 'build-rpkg-win64-cuda10.1': { BuildRPackageWithCUDAWin64() } ]) } } } stage('Jenkins Win64: Test') { agent none steps { script { parallel ([ 'test-win64-cuda10.1': { TestWin64() }, ]) } } } } } // check out source code from git def checkoutSrcs() { retry(5) { try { timeout(time: 2, unit: 'MINUTES') { checkout scm sh 'git submodule update --init' } } catch (exc) { deleteDir() error "Failed to fetch source codes" } } } def BuildWin64() { node('win64 && cuda10_unified') { deleteDir() unstash name: 'srcs' echo "Building XGBoost for Windows AMD64 target..." bat "nvcc --version" def arch_flag = "" if (env.BRANCH_NAME != 'master' && !(env.BRANCH_NAME.startsWith('release'))) { arch_flag = "-DGPU_COMPUTE_VER=75" } bat """ mkdir build cd build cmake .. -G"Visual Studio 15 2017 Win64" -DUSE_CUDA=ON -DCMAKE_VERBOSE_MAKEFILE=ON -DGOOGLE_TEST=ON -DUSE_DMLC_GTEST=ON ${arch_flag} -DCMAKE_UNITY_BUILD=ON """ bat """ cd build "C:\\Program Files (x86)\\Microsoft Visual Studio\\2017\\Community\\MSBuild\\15.0\\Bin\\MSBuild.exe" xgboost.sln /m /p:Configuration=Release /nodeReuse:false """ bat """ cd python-package conda activate && python setup.py bdist_wheel --universal && for /R %%i in (dist\\*.whl) DO python ../tests/ci_build/rename_whl.py "%%i" ${commit_id} win_amd64 """ echo "Insert vcomp140.dll (OpenMP runtime) into the wheel..." bat """ cd python-package\\dist COPY /B ..\\..\\tests\\ci_build\\insert_vcomp140.py conda activate && python insert_vcomp140.py *.whl """ echo 'Stashing Python wheel...' stash name: 'xgboost_whl', includes: 'python-package/dist/*.whl' if (env.BRANCH_NAME == 'master' || env.BRANCH_NAME.startsWith('release')) { echo 'Uploading Python wheel...' path = ("${BRANCH_NAME}" == 'master') ? '' : "${BRANCH_NAME}/" s3Upload bucket: 'xgboost-nightly-builds', path: path, acl: 'PublicRead', workingDir: 'python-package/dist', includePathPattern:'**/*.whl' } echo 'Stashing C++ test executable (testxgboost)...' stash name: 'xgboost_cpp_tests', includes: 'build/testxgboost.exe' stash name: 'xgboost_cli', includes: 'xgboost.exe' deleteDir() } } def BuildRPackageWithCUDAWin64() { node('win64 && cuda10_unified') { deleteDir() unstash name: 'srcs' bat "nvcc --version" if (env.BRANCH_NAME == 'master' || env.BRANCH_NAME.startsWith('release')) { bat """ bash tests/ci_build/build_r_pkg_with_cuda_win64.sh ${commit_id} """ echo 'Uploading R tarball...' path = ("${BRANCH_NAME}" == 'master') ? '' : "${BRANCH_NAME}/" s3Upload bucket: 'xgboost-nightly-builds', path: path, acl: 'PublicRead', includePathPattern:'xgboost_r_gpu_win64_*.tar.gz' } deleteDir() } } def TestWin64() { node('win64 && cuda10_unified') { deleteDir() unstash name: 'srcs' unstash name: 'xgboost_whl' unstash name: 'xgboost_cli' unstash name: 'xgboost_cpp_tests' echo "Test Win64" bat "nvcc --version" echo "Running C++ tests..." bat "build\\testxgboost.exe" echo "Installing Python dependencies..." def env_name = 'win64_' + UUID.randomUUID().toString().replaceAll('-', '') bat "conda activate && mamba env create -n ${env_name} --file=tests/ci_build/conda_env/win64_test.yml" echo "Installing Python wheel..." bat """ conda activate ${env_name} && for /R %%i in (python-package\\dist\\*.whl) DO python -m pip install "%%i" """ echo "Running Python tests..." bat "conda activate ${env_name} && python -m pytest -v -s -rxXs --fulltrace tests\\python" bat """ conda activate ${env_name} && python -m pytest -v -s -rxXs --fulltrace -m "(not slow) and (not mgpu)" tests\\python-gpu """ bat "conda env remove --name ${env_name}" deleteDir() } } xgboost-1.5.2/LICENSE000066400000000000000000000261251417122711700142220ustar00rootroot00000000000000 Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 1. 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See the License for the specific language governing permissions and limitations under the License. xgboost-1.5.2/Makefile000066400000000000000000000122621417122711700146520ustar00rootroot00000000000000ifndef DMLC_CORE DMLC_CORE = dmlc-core endif ifndef RABIT RABIT = rabit endif ROOTDIR = $(CURDIR) # workarounds for some buggy old make & msys2 versions seen in windows ifeq (NA, $(shell test ! -d "$(ROOTDIR)" && echo NA )) $(warning Attempting to fix non-existing ROOTDIR [$(ROOTDIR)]) ROOTDIR := $(shell pwd) $(warning New ROOTDIR [$(ROOTDIR)] $(shell test -d "$(ROOTDIR)" && echo " is OK" )) endif MAKE_OK := $(shell "$(MAKE)" -v 2> /dev/null) ifndef MAKE_OK $(warning Attempting to recover non-functional MAKE [$(MAKE)]) MAKE := $(shell which make 2> /dev/null) MAKE_OK := $(shell "$(MAKE)" -v 2> /dev/null) endif $(warning MAKE [$(MAKE)] - $(if $(MAKE_OK),checked OK,PROBLEM)) include $(DMLC_CORE)/make/dmlc.mk # set compiler defaults for OSX versus *nix # let people override either OS := $(shell uname) ifeq ($(OS), Darwin) ifndef CC export CC = $(if $(shell which clang), clang, gcc) endif ifndef CXX export CXX = $(if $(shell which clang++), clang++, g++) endif else # linux defaults ifndef CC export CC = gcc endif ifndef CXX export CXX = g++ endif endif export CFLAGS= -DDMLC_LOG_CUSTOMIZE=1 -std=c++14 -Wall -Wno-unknown-pragmas -Iinclude $(ADD_CFLAGS) CFLAGS += -I$(DMLC_CORE)/include -I$(RABIT)/include -I$(GTEST_PATH)/include ifeq ($(TEST_COVER), 1) CFLAGS += -g -O0 -fprofile-arcs -ftest-coverage else CFLAGS += -O3 -funroll-loops endif ifndef LINT_LANG LINT_LANG= "all" endif # specify tensor path .PHONY: clean all lint clean_all doxygen rcpplint pypack Rpack Rbuild Rcheck build/%.o: src/%.cc @mkdir -p $(@D) $(CXX) $(CFLAGS) -MM -MT build/$*.o $< >build/$*.d $(CXX) -c $(CFLAGS) $< -o $@ # The should be equivalent to $(ALL_OBJ) except for build/cli_main.o amalgamation/xgboost-all0.o: amalgamation/xgboost-all0.cc $(CXX) -c $(CFLAGS) $< -o $@ rcpplint: python3 dmlc-core/scripts/lint.py xgboost ${LINT_LANG} R-package/src lint: rcpplint python3 dmlc-core/scripts/lint.py --exclude_path python-package/xgboost/dmlc-core \ python-package/xgboost/include python-package/xgboost/lib \ python-package/xgboost/make python-package/xgboost/rabit \ python-package/xgboost/src --pylint-rc ${PWD}/python-package/.pylintrc xgboost \ ${LINT_LANG} include src python-package ifeq ($(TEST_COVER), 1) cover: check @- $(foreach COV_OBJ, $(COVER_OBJ), \ gcov -pbcul -o $(shell dirname $(COV_OBJ)) $(COV_OBJ) > gcov.log || cat gcov.log; \ ) endif # dask is required to pass, others are not # If any of the dask tests failed, contributor won't see the other error. mypy: cd python-package; \ mypy ./xgboost/dask.py && \ mypy ./xgboost/rabit.py && \ mypy ../demo/guide-python/external_memory.py && \ mypy ../tests/python-gpu/test_gpu_with_dask.py && \ mypy ../tests/python/test_data_iterator.py && \ mypy ../tests/python-gpu/test_gpu_data_iterator.py && \ mypy ./xgboost/sklearn.py || exit 1; \ mypy . || true ; clean: $(RM) -rf build lib bin *~ */*~ */*/*~ */*/*/*~ */*.o */*/*.o */*/*/*.o #xgboost $(RM) -rf build_tests *.gcov tests/cpp/xgboost_test if [ -d "R-package/src" ]; then \ cd R-package/src; \ $(RM) -rf rabit src include dmlc-core amalgamation *.so *.dll; \ cd $(ROOTDIR); \ fi clean_all: clean cd $(DMLC_CORE); "$(MAKE)" clean; cd $(ROOTDIR) cd $(RABIT); "$(MAKE)" clean; cd $(ROOTDIR) # create pip source dist (sdist) pack for PyPI pippack: clean_all cd python-package; python setup.py sdist; mv dist/*.tar.gz ..; cd .. # Script to make a clean installable R package. Rpack: clean_all rm -rf xgboost xgboost*.tar.gz cp -r R-package xgboost rm -rf xgboost/src/*.o xgboost/src/*.so xgboost/src/*.dll rm -rf xgboost/src/*/*.o rm -rf xgboost/demo/*.model xgboost/demo/*.buffer xgboost/demo/*.txt rm -rf xgboost/demo/runall.R cp -r src xgboost/src/src cp -r include xgboost/src/include cp -r amalgamation xgboost/src/amalgamation mkdir -p xgboost/src/rabit cp -r rabit/include xgboost/src/rabit/include cp -r rabit/src xgboost/src/rabit/src rm -rf xgboost/src/rabit/src/*.o mkdir -p xgboost/src/dmlc-core cp -r dmlc-core/include xgboost/src/dmlc-core/include cp -r dmlc-core/src xgboost/src/dmlc-core/src cp ./LICENSE xgboost # Modify PKGROOT in Makevars.in cat R-package/src/Makevars.in|sed '2s/.*/PKGROOT=./' > xgboost/src/Makevars.in # Configure Makevars.win (Windows-specific Makevars, likely using MinGW) cp xgboost/src/Makevars.in xgboost/src/Makevars.win cat xgboost/src/Makevars.in| sed '3s/.*/ENABLE_STD_THREAD=0/' > xgboost/src/Makevars.win sed -i -e 's/@OPENMP_CXXFLAGS@/$$\(SHLIB_OPENMP_CXXFLAGS\)/g' xgboost/src/Makevars.win sed -i -e 's/-pthread/$$\(SHLIB_PTHREAD_FLAGS\)/g' xgboost/src/Makevars.win sed -i -e 's/@ENDIAN_FLAG@/-DDMLC_CMAKE_LITTLE_ENDIAN=1/g' xgboost/src/Makevars.win sed -i -e 's/@BACKTRACE_LIB@//g' xgboost/src/Makevars.win sed -i -e 's/@OPENMP_LIB@//g' xgboost/src/Makevars.win rm -f xgboost/src/Makevars.win-e # OSX sed create this extra file; remove it bash R-package/remove_warning_suppression_pragma.sh bash xgboost/remove_warning_suppression_pragma.sh rm xgboost/remove_warning_suppression_pragma.sh rm -rfv xgboost/tests/helper_scripts/ R ?= R Rbuild: Rpack $(R) CMD build xgboost rm -rf xgboost Rcheck: Rbuild $(R) CMD check --as-cran xgboost*.tar.gz -include build/*.d -include build/*/*.d xgboost-1.5.2/NEWS.md000066400000000000000000004364101417122711700143150ustar00rootroot00000000000000XGBoost Change Log ================== This file records the changes in xgboost library in reverse chronological order. ## v1.4.2 (2021.05.13) This is a patch release for Python package with following fixes: * Handle the latest version of cupy.ndarray in inplace_predict. (#6933) * Ensure output array from predict_leaf is (n_samples, ) when there's only 1 tree. 1.4.0 outputs (n_samples, 1). (#6889) * Fix empty dataset handling with multi-class AUC. (#6947) * Handle object type from pandas in inplace_predict. (#6927) ## v1.4.1 (2021.04.20) This is a bug fix release. * Fix GPU implementation of AUC on some large datasets. (#6866) ## v1.4.0 (2021.04.12) ### Introduction of pre-built binary package for R, with GPU support Starting with release 1.4.0, users now have the option of installing `{xgboost}` without having to build it from the source. This is particularly advantageous for users who want to take advantage of the GPU algorithm (`gpu_hist`), as previously they'd have to build `{xgboost}` from the source using CMake and NVCC. Now installing `{xgboost}` with GPU support is as easy as: `R CMD INSTALL ./xgboost_r_gpu_linux.tar.gz`. (#6827) See the instructions at https://xgboost.readthedocs.io/en/latest/build.html ### Improvements on prediction functions XGBoost has many prediction types including shap value computation and inplace prediction. In 1.4 we overhauled the underlying prediction functions for C API and Python API with an unified interface. (#6777, #6693, #6653, #6662, #6648, #6668, #6804) * Starting with 1.4, sklearn interface prediction will use inplace predict by default when input data is supported. * Users can use inplace predict with `dart` booster and enable GPU acceleration just like `gbtree`. * Also all prediction functions with tree models are now thread-safe. Inplace predict is improved with `base_margin` support. * A new set of C predict functions are exposed in the public interface. * A user-visible change is a newly added parameter called `strict_shape`. See https://xgboost.readthedocs.io/en/latest/prediction.html for more details. ### Improvement on Dask interface * Starting with 1.4, the Dask interface is considered to be feature-complete, which means all of the models found in the single node Python interface are now supported in Dask, including but not limited to ranking and random forest. Also, the prediction function is significantly faster and supports shap value computation. - Most of the parameters found in single node sklearn interface are supported by Dask interface. (#6471, #6591) - Implements learning to rank. On the Dask interface, we use the newly added support of query ID to enable group structure. (#6576) - The Dask interface has Python type hints support. (#6519) - All models can be safely pickled. (#6651) - Random forest estimators are now supported. (#6602) - Shap value computation is now supported. (#6575, #6645, #6614) - Evaluation result is printed on the scheduler process. (#6609) - `DaskDMatrix` (and device quantile dmatrix) now accepts all meta-information. (#6601) * Prediction optimization. We enhanced and speeded up the prediction function for the Dask interface. See the latest Dask tutorial page in our document for an overview of how you can optimize it even further. (#6650, #6645, #6648, #6668) * Bug fixes - If you are using the latest Dask and distributed where `distributed.MultiLock` is present, XGBoost supports training multiple models on the same cluster in parallel. (#6743) - A bug fix for when using `dask.client` to launch async task, XGBoost might use a different client object internally. (#6722) * Other improvements on documents, blogs, tutorials, and demos. (#6389, #6366, #6687, #6699, #6532, #6501) ### Python package With changes from Dask and general improvement on prediction, we have made some enhancements on the general Python interface and IO for booster information. Starting from 1.4, booster feature names and types can be saved into the JSON model. Also some model attributes like `best_iteration`, `best_score` are restored upon model load. On sklearn interface, some attributes are now implemented as Python object property with better documents. * Breaking change: All `data` parameters in prediction functions are renamed to `X` for better compliance to sklearn estimator interface guidelines. * Breaking change: XGBoost used to generate some pseudo feature names with `DMatrix` when inputs like `np.ndarray` don't have column names. The procedure is removed to avoid conflict with other inputs. (#6605) * Early stopping with training continuation is now supported. (#6506) * Optional import for Dask and cuDF are now lazy. (#6522) * As mentioned in the prediction improvement summary, the sklearn interface uses inplace prediction whenever possible. (#6718) * Booster information like feature names and feature types are now saved into the JSON model file. (#6605) * All `DMatrix` interfaces including `DeviceQuantileDMatrix` and counterparts in Dask interface (as mentioned in the Dask changes summary) now accept all the meta-information like `group` and `qid` in their constructor for better consistency. (#6601) * Booster attributes are restored upon model load so users don't have to call `attr` manually. (#6593) * On sklearn interface, all models accept `base_margin` for evaluation datasets. (#6591) * Improvements over the setup script including smaller sdist size and faster installation if the C++ library is already built (#6611, #6694, #6565). * Bug fixes for Python package: - Don't validate feature when number of rows is 0. (#6472) - Move metric configuration into booster. (#6504) - Calling XGBModel.fit() should clear the Booster by default (#6562) - Support `_estimator_type`. (#6582) - [dask, sklearn] Fix predict proba. (#6566, #6817) - Restore unknown data support. (#6595) - Fix learning rate scheduler with cv. (#6720) - Fixes small typo in sklearn documentation (#6717) - [python-package] Fix class Booster: feature_types = None (#6705) - Fix divide by 0 in feature importance when no split is found. (#6676) ### JVM package * [jvm-packages] fix early stopping doesn't work even without custom_eval setting (#6738) * fix potential TaskFailedListener's callback won't be called (#6612) * [jvm] Add ability to load booster direct from byte array (#6655) * [jvm-packages] JVM library loader extensions (#6630) ### R package * R documentation: Make construction of DMatrix consistent. * Fix R documentation for xgb.train. (#6764) ### ROC-AUC We re-implemented the ROC-AUC metric in XGBoost. The new implementation supports multi-class classification and has better support for learning to rank tasks that are not binary. Also, it has a better-defined average on distributed environments with additional handling for invalid datasets. (#6749, #6747, #6797) ### Global configuration. Starting from 1.4, XGBoost's Python, R and C interfaces support a new global configuration model where users can specify some global parameters. Currently, supported parameters are `verbosity` and `use_rmm`. The latter is experimental, see rmm plugin demo and related README file for details. (#6414, #6656) ### Other New features. * Better handling for input data types that support `__array_interface__`. For some data types including GPU inputs and `scipy.sparse.csr_matrix`, XGBoost employs `__array_interface__` for processing the underlying data. Starting from 1.4, XGBoost can accept arbitrary array strides (which means column-major is supported) without making data copies, potentially reducing a significant amount of memory consumption. Also version 3 of `__cuda_array_interface__` is now supported. (#6776, #6765, #6459, #6675) * Improved parameter validation, now feeding XGBoost with parameters that contain whitespace will trigger an error. (#6769) * For Python and R packages, file paths containing the home indicator `~` are supported. * As mentioned in the Python changes summary, the JSON model can now save feature information of the trained booster. The JSON schema is updated accordingly. (#6605) * Development of categorical data support is continued. Newly added weighted data support and `dart` booster support. (#6508, #6693) * As mentioned in Dask change summary, ranking now supports the `qid` parameter for query groups. (#6576) * `DMatrix.slice` can now consume a numpy array. (#6368) ### Other breaking changes * Aside from the feature name generation, there are 2 breaking changes: - Drop saving binary format for memory snapshot. (#6513, #6640) - Change default evaluation metric for binary:logitraw objective to logloss (#6647) ### CPU Optimization * Aside from the general changes on predict function, some optimizations are applied on CPU implementation. (#6683, #6550, #6696, #6700) * Also performance for sampling initialization in `hist` is improved. (#6410) ### Notable fixes in the core library These fixes do not reside in particular language bindings: * Fixes for gamma regression. This includes checking for invalid input values, fixes for gamma deviance metric, and better floating point guard for gamma negative log-likelihood metric. (#6778, #6537, #6761) * Random forest with `gpu_hist` might generate low accuracy in previous versions. (#6755) * Fix a bug in GPU sketching when data size exceeds limit of 32-bit integer. (#6826) * Memory consumption fix for row-major adapters (#6779) * Don't estimate sketch batch size when rmm is used. (#6807) (#6830) * Fix in-place predict with missing value. (#6787) * Re-introduce double buffer in UpdatePosition, to fix perf regression in gpu_hist (#6757) * Pass correct split_type to GPU predictor (#6491) * Fix DMatrix feature names/types IO. (#6507) * Use view for `SparsePage` exclusively to avoid some data access races. (#6590) * Check for invalid data. (#6742) * Fix relocatable include in CMakeList (#6734) (#6737) * Fix DMatrix slice with feature types. (#6689) ### Other deprecation notices: * This release will be the last release to support CUDA 10.0. (#6642) * Starting in the next release, the Python package will require Pip 19.3+ due to the use of manylinux2014 tag. Also, CentOS 6, RHEL 6 and other old distributions will not be supported. ### Known issue: MacOS build of the JVM packages doesn't support multi-threading out of the box. To enable multi-threading with JVM packages, MacOS users will need to build the JVM packages from the source. See https://xgboost.readthedocs.io/en/latest/jvm/index.html#installation-from-source ### Doc * Dedicated page for `tree_method` parameter is added. (#6564, #6633) * [doc] Add FLAML as a fast tuning tool for XGBoost (#6770) * Add document for tests directory. [skip ci] (#6760) * Fix doc string of config.py to use correct `versionadded` (#6458) * Update demo for prediction. (#6789) * [Doc] Document that AUCPR is for binary classification/ranking (#5899) * Update the C API comments (#6457) * Fix document. [skip ci] (#6669) ### Maintenance: Testing, continuous integration * Use CPU input for test_boost_from_prediction. (#6818) * [CI] Upload xgboost4j.dll to S3 (#6781) * Update dmlc-core submodule (#6745) * [CI] Use manylinux2010_x86_64 container to vendor libgomp (#6485) * Add conda-forge badge (#6502) * Fix merge conflict. (#6512) * [CI] Split up main.yml, add mypy. (#6515) * [Breaking] Upgrade cuDF and RMM to 0.18 nightlies; require RMM 0.18+ for RMM plugin (#6510) * "featue_map" typo changed to "feature_map" (#6540) * Add script for generating release tarball. (#6544) * Add credentials to .gitignore (#6559) * Remove warnings in tests. (#6554) * Update dmlc-core submodule and conform to new API (#6431) * Suppress hypothesis health check for dask client. (#6589) * Fix pylint. (#6714) * [CI] Clear R package cache (#6746) * Exclude dmlc test on github action. (#6625) * Tests for regression metrics with weights. (#6729) * Add helper script and doc for releasing pip package. (#6613) * Support pylint 2.7.0 (#6726) * Remove R cache in github action. (#6695) * [CI] Do not mix up stashed executable built for ARM and x86_64 platforms (#6646) * [CI] Add ARM64 test to Jenkins pipeline (#6643) * Disable s390x and arm64 tests on travis for now. (#6641) * Move sdist test to action. (#6635) * [dask] Rework base margin test. (#6627) ### Maintenance: Refactor code for legibility and maintainability * Improve OpenMP exception handling (#6680) * Improve string view to reduce string allocation. (#6644) * Simplify Span checks. (#6685) * Use generic dispatching routine for array interface. (#6672) ## v1.3.0 (2020.12.08) ### XGBoost4J-Spark: Exceptions should cancel jobs gracefully instead of killing SparkContext (#6019). * By default, exceptions in XGBoost4J-Spark causes the whole SparkContext to shut down, necessitating the restart of the Spark cluster. This behavior is often a major inconvenience. * Starting from 1.3.0 release, XGBoost adds a new parameter `killSparkContextOnWorkerFailure` to optionally prevent killing SparkContext. If this parameter is set, exceptions will gracefully cancel training jobs instead of killing SparkContext. ### GPUTreeSHAP: GPU acceleration of the TreeSHAP algorithm (#6038, #6064, #6087, #6099, #6163, #6281, #6332) * [SHAP (SHapley Additive exPlanations)](https://github.com/slundberg/shap) is a game theoretic approach to explain predictions of machine learning models. It computes feature importance scores for individual examples, establishing how each feature influences a particular prediction. TreeSHAP is an optimized SHAP algorithm specifically designed for decision tree ensembles. * Starting with 1.3.0 release, it is now possible to leverage CUDA-capable GPUs to accelerate the TreeSHAP algorithm. Check out [the demo notebook](https://github.com/dmlc/xgboost/blob/master/demo/gpu_acceleration/shap.ipynb). * The CUDA implementation of the TreeSHAP algorithm is hosted at [rapidsai/GPUTreeSHAP](https://github.com/rapidsai/gputreeshap). XGBoost imports it as a Git submodule. ### New style Python callback API (#6199, #6270, #6320, #6348, #6376, #6399, #6441) * The XGBoost Python package now offers a re-designed callback API. The new callback API lets you design various extensions of training in idomatic Python. In addition, the new callback API allows you to use early stopping with the native Dask API (`xgboost.dask`). Check out [the tutorial](https://xgboost.readthedocs.io/en/release_1.3.0/python/callbacks.html) and [the demo](https://github.com/dmlc/xgboost/blob/master/demo/guide-python/callbacks.py). ### Enable the use of `DeviceQuantileDMatrix` / `DaskDeviceQuantileDMatrix` with large data (#6201, #6229, #6234). * `DeviceQuantileDMatrix` can achieve memory saving by avoiding extra copies of the training data, and the saving is bigger for large data. Unfortunately, large data with more than 2^31 elements was triggering integer overflow bugs in CUB and Thrust. Tracking issue: #6228. * This release contains a series of work-arounds to allow the use of `DeviceQuantileDMatrix` with large data: - Loop over `copy_if` (#6201) - Loop over `thrust::reduce` (#6229) - Implement the inclusive scan algorithm in-house, to handle large offsets (#6234) ### Support slicing of tree models (#6302) * Accessing the best iteration of a model after the application of early stopping used to be error-prone, need to manually pass the `ntree_limit` argument to the `predict()` function. * Now we provide a simple interface to slice tree models by specifying a range of boosting rounds. The tree ensemble can be split into multiple sub-ensembles via the slicing interface. Check out [an example](https://xgboost.readthedocs.io/en/release_1.3.0/python/model.html). * In addition, the early stopping callback now supports `save_best` option. When enabled, XGBoost will save (persist) the model at the best boosting round and discard the trees that were fit subsequent to the best round. ### Weighted subsampling of features (columns) (#5962) * It is now possible to sample features (columns) via weighted subsampling, in which features with higher weights are more likely to be selected in the sample. Weighted subsampling allows you to encode domain knowledge by emphasizing a particular set of features in the choice of tree splits. In addition, you can prevent particular features from being used in any splits, by assigning them zero weights. * Check out [the demo](https://github.com/dmlc/xgboost/blob/master/demo/guide-python/feature_weights.py). ### Improved integration with Dask * Support reverse-proxy environment such as Google Kubernetes Engine (#6343, #6475) * An XGBoost training job will no longer use all available workers. Instead, it will only use the workers that contain input data (#6343). * The new callback API works well with the Dask training API. * The `predict()` and `fit()` function of `DaskXGBClassifier` and `DaskXGBRegressor` now accept a base margin (#6155). * Support more meta data in the Dask API (#6130, #6132, #6333). * Allow passing extra keyword arguments as `kwargs` in `predict()` (#6117) * Fix typo in dask interface: `sample_weights` -> `sample_weight` (#6240) * Allow empty data matrix in AFT survival, as Dask may produce empty partitions (#6379) * Speed up prediction by overlapping prediction jobs in all workers (#6412) ### Experimental support for direct splits with categorical features (#6028, #6128, #6137, #6140, #6164, #6165, #6166, #6179, #6194, #6219) * Currently, XGBoost requires users to one-hot-encode categorical variables. This has adverse performance implications, as the creation of many dummy variables results into higher memory consumption and may require fitting deeper trees to achieve equivalent model accuracy. * The 1.3.0 release of XGBoost contains an experimental support for direct handling of categorical variables in test nodes. Each test node will have the condition of form `feature_value \in match_set`, where the `match_set` on the right hand side contains one or more matching categories. The matching categories in `match_set` represent the condition for traversing to the right child node. Currently, XGBoost will only generate categorical splits with only a single matching category ("one-vs-rest split"). In a future release, we plan to remove this restriction and produce splits with multiple matching categories in `match_set`. * The categorical split requires the use of JSON model serialization. The legacy binary serialization method cannot be used to save (persist) models with categorical splits. * Note. This feature is currently highly experimental. Use it at your own risk. See the detailed list of limitations at [#5949](https://github.com/dmlc/xgboost/pull/5949). ### Experimental plugin for RAPIDS Memory Manager (#5873, #6131, #6146, #6150, #6182) * RAPIDS Memory Manager library ([rapidsai/rmm](https://github.com/rapidsai/rmm)) provides a collection of efficient memory allocators for NVIDIA GPUs. It is now possible to use XGBoost with memory allocators provided by RMM, by enabling the RMM integration plugin. With this plugin, XGBoost is now able to share a common GPU memory pool with other applications using RMM, such as the RAPIDS data science packages. * See [the demo](https://github.com/dmlc/xgboost/blob/master/demo/rmm_plugin/README.md) for a working example, as well as directions for building XGBoost with the RMM plugin. * The plugin will be soon considered non-experimental, once #6297 is resolved. ### Experimental plugin for oneAPI programming model (#5825) * oneAPI is a programming interface developed by Intel aimed at providing one programming model for many types of hardware such as CPU, GPU, FGPA and other hardware accelerators. * XGBoost now includes an experimental plugin for using oneAPI for the predictor and objective functions. The plugin is hosted in the directory `plugin/updater_oneapi`. * Roadmap: #5442 ### Pickling the XGBoost model will now trigger JSON serialization (#6027) * The pickle will now contain the JSON string representation of the XGBoost model, as well as related configuration. ### Performance improvements * Various performance improvement on multi-core CPUs - Optimize DMatrix build time by up to 3.7x. (#5877) - CPU predict performance improvement, by up to 3.6x. (#6127) - Optimize CPU sketch allreduce for sparse data (#6009) - Thread local memory allocation for BuildHist, leading to speedup up to 1.7x. (#6358) - Disable hyperthreading for DMatrix creation (#6386). This speeds up DMatrix creation by up to 2x. - Simple fix for static shedule in predict (#6357) * Unify thread configuration, to make it easy to utilize all CPU cores (#6186) * [jvm-packages] Clean the way deterministic paritioning is computed (#6033) * Speed up JSON serialization by implementing an intrusive pointer class (#6129). It leads to 1.5x-2x performance boost. ### API additions * [R] Add SHAP summary plot using ggplot2 (#5882) * Modin DataFrame can now be used as input (#6055) * [jvm-packages] Add `getNumFeature` method (#6075) * Add MAPE metric (#6119) * Implement GPU predict leaf. (#6187) * Enable cuDF/cuPy inputs in `XGBClassifier` (#6269) * Document tree method for feature weights. (#6312) * Add `fail_on_invalid_gpu_id` parameter, which will cause XGBoost to terminate upon seeing an invalid value of `gpu_id` (#6342) ### Breaking: the default evaluation metric for classification is changed to `logloss` / `mlogloss` (#6183) * The default metric used to be accuracy, and it is not statistically consistent to perform early stopping with the accuracy metric when we are really optimizing the log loss for the `binary:logistic` objective. * For statistical consistency, the default metric for classification has been changed to `logloss`. Users may choose to preserve the old behavior by explicitly specifying `eval_metric`. ### Breaking: `skmaker` is now removed (#5971) * The `skmaker` updater has not been documented nor tested. ### Breaking: the JSON model format no longer stores the leaf child count (#6094). * The leaf child count field has been deprecated and is not used anywhere in the XGBoost codebase. ### Breaking: XGBoost now requires MacOS 10.14 (Mojave) and later. * Homebrew has dropped support for MacOS 10.13 (High Sierra), so we are not able to install the OpenMP runtime (`libomp`) from Homebrew on MacOS 10.13. Please use MacOS 10.14 (Mojave) or later. ### Deprecation notices * The use of `LabelEncoder` in `XGBClassifier` is now deprecated and will be removed in the next minor release (#6269). The deprecation is necessary to support multiple types of inputs, such as cuDF data frames or cuPy arrays. * The use of certain positional arguments in the Python interface is deprecated (#6365). Users will use deprecation warnings for the use of position arguments for certain function parameters. New code should use keyword arguments as much as possible. We have not yet decided when we will fully require the use of keyword arguments. ### Bug-fixes * On big-endian arch, swap the byte order in the binary serializer to enable loading models that were produced by a little-endian machine (#5813). * [jvm-packages] Fix deterministic partitioning with dataset containing Double.NaN (#5996) * Limit tree depth for GPU hist to 31 to prevent integer overflow (#6045) * [jvm-packages] Set `maxBins` to 256 to align with the default value in the C++ code (#6066) * [R] Fix CRAN check (#6077) * Add back support for `scipy.sparse.coo_matrix` (#6162) * Handle duplicated values in sketching. (#6178) * Catch all standard exceptions in C API. (#6220) * Fix linear GPU input (#6255) * Fix inplace prediction interval. (#6259) * [R] allow `xgb.plot.importance()` calls to fill a grid (#6294) * Lazy import dask libraries. (#6309) * Deterministic data partitioning for external memory (#6317) * Avoid resetting seed for every configuration. (#6349) * Fix label errors in graph visualization (#6369) * [jvm-packages] fix potential unit test suites aborted issue due to race condition (#6373) * [R] Fix warnings from `R check --as-cran` (#6374) * [R] Fix a crash that occurs with noLD R (#6378) * [R] Do not convert continuous labels to factors (#6380) * [R] remove uses of `exists()` (#6387) * Propagate parameters to the underlying `Booster` handle from `XGBClassifier.set_param` / `XGBRegressor.set_param`. (#6416) * [R] Fix R package installation via CMake (#6423) * Enforce row-major order in cuPy array (#6459) * Fix filtering callable objects in the parameters passed to the scikit-learn API. (#6466) ### Maintenance: Testing, continuous integration, build system * [CI] Improve JVM test in GitHub Actions (#5930) * Refactor plotting test so that it can run independently (#6040) * [CI] Cancel builds on subsequent pushes (#6011) * Fix Dask Pytest fixture (#6024) * [CI] Migrate linters to GitHub Actions (#6035) * [CI] Remove win2016 JVM test from GitHub Actions (#6042) * Fix CMake build with `BUILD_STATIC_LIB` option (#6090) * Don't link imported target in CMake (#6093) * Work around a compiler bug in MacOS AppleClang 11 (#6103) * [CI] Fix CTest by running it in a correct directory (#6104) * [R] Check warnings explicitly for model compatibility tests (#6114) * [jvm-packages] add xgboost4j-gpu/xgboost4j-spark-gpu module to facilitate release (#6136) * [CI] Time GPU tests. (#6141) * [R] remove warning in configure.ac (#6152) * [CI] Upgrade cuDF and RMM to 0.16 nightlies; upgrade to Ubuntu 18.04 (#6157) * [CI] Test C API demo (#6159) * Option for generating device debug info. (#6168) * Update `.gitignore` (#6175, #6193, #6346) * Hide C++ symbols from dmlc-core (#6188) * [CI] Added arm64 job in Travis-CI (#6200) * [CI] Fix Docker build for CUDA 11 (#6202) * [CI] Move non-OpenMP gtest to GitHub Actions (#6210) * [jvm-packages] Fix up build for xgboost4j-gpu, xgboost4j-spark-gpu (#6216) * Add more tests for categorical data support (#6219) * [dask] Test for data initializaton. (#6226) * Bump junit from 4.11 to 4.13.1 in /jvm-packages/xgboost4j (#6230) * Bump junit from 4.11 to 4.13.1 in /jvm-packages/xgboost4j-gpu (#6233) * [CI] Reduce testing load with RMM (#6249) * [CI] Build a Python wheel for aarch64 platform (#6253) * [CI] Time the CPU tests on Jenkins. (#6257) * [CI] Skip Dask tests on ARM. (#6267) * Fix a typo in `is_arm()` in testing.py (#6271) * [CI] replace `egrep` with `grep -E` (#6287) * Support unity build. (#6295) * [CI] Mark flaky tests as XFAIL (#6299) * [CI] Use separate Docker cache for each CUDA version (#6305) * Added `USE_NCCL_LIB_PATH` option to enable user to set `NCCL_LIBRARY` during build (#6310) * Fix flaky data initialization test. (#6318) * Add a badge for GitHub Actions (#6321) * Optional `find_package` for sanitizers. (#6329) * Use pytest conventions consistently in Python tests (#6337) * Fix missing space in warning message (#6340) * Update `custom_metric_obj.rst` (#6367) * [CI] Run R check with `--as-cran` flag on GitHub Actions (#6371) * [CI] Remove R check from Jenkins (#6372) * Mark GPU external memory test as XFAIL. (#6381) * [CI] Add noLD R test (#6382) * Fix MPI build. (#6403) * [CI] Upgrade to MacOS Mojave image (#6406) * Fix flaky sparse page dmatrix test. (#6417) * [CI] Upgrade cuDF and RMM to 0.17 nightlies (#6434) * [CI] Fix CentOS 6 Docker images (#6467) * [CI] Vendor libgomp in the manylinux Python wheel (#6461) * [CI] Hot fix for libgomp vendoring (#6482) ### Maintenance: Clean up and merge the Rabit submodule (#6023, #6095, #6096, #6105, #6110, #6262, #6275, #6290) * The Rabit submodule is now maintained as part of the XGBoost codebase. * Tests for Rabit are now part of the test suites of XGBoost. * Rabit can now be built on the Windows platform. * We made various code re-formatting for the C++ code with clang-tidy. * Public headers of XGBoost no longer depend on Rabit headers. * Unused CMake targets for Rabit were removed. * Single-point model recovery has been dropped and removed from Rabit, simplifying the Rabit code greatly. The single-point model recovery feature has not been adequately maintained over the years. * We removed the parts of Rabit that were not useful for XGBoost. ### Maintenance: Refactor code for legibility and maintainability * Unify CPU hist sketching (#5880) * [R] fix uses of 1:length(x) and other small things (#5992) * Unify evaluation functions. (#6037) * Make binary bin search reusable. (#6058) * Unify set index data. (#6062) * [R] Remove `stringi` dependency (#6109) * Merge extract cuts into QuantileContainer. (#6125) * Reduce C++ compiler warnings (#6197, #6198, #6213, #6286, #6325) * Cleanup Python code. (#6223) * Small cleanup to evaluator. (#6400) ### Usability Improvements, Documentation * [jvm-packages] add example to handle missing value other than 0 (#5677) * Add DMatrix usage examples to the C API demo (#5854) * List `DaskDeviceQuantileDMatrix` in the doc. (#5975) * Update Python custom objective demo. (#5981) * Update the JSON model schema to document more objective functions. (#5982) * [Python] Fix warning when `missing` field is not used. (#5969) * Fix typo in tracker logging (#5994) * Move a warning about empty dataset, so that it's shown for all objectives and metrics (#5998) * Fix the instructions for installing the nightly build. (#6004) * [Doc] Add dtreeviz as a showcase example of integration with 3rd-party software (#6013) * [jvm-packages] [doc] Update install doc for JVM packages (#6051) * Fix typo in `xgboost.callback.early_stop` docstring (#6071) * Add cache suffix to the files used in the external memory demo. (#6088) * [Doc] Document the parameter `kill_spark_context_on_worker_failure` (#6097) * Fix link to the demo for custom objectives (#6100) * Update Dask doc. (#6108) * Validate weights are positive values. (#6115) * Document the updated CMake version requirement. (#6123) * Add demo for `DaskDeviceQuantileDMatrix`. (#6156) * Cosmetic fixes in `faq.rst` (#6161) * Fix error message. (#6176) * [Doc] Add list of winning solutions in data science competitions using XGBoost (#6177) * Fix a comment in demo to use correct reference (#6190) * Update the list of winning solutions using XGBoost (#6192) * Consistent style for build status badge (#6203) * [Doc] Add info on GPU compiler (#6204) * Update the list of winning solutions (#6222, #6254) * Add link to XGBoost's Twitter handle (#6244) * Fix minor typos in XGBClassifier methods' docstrings (#6247) * Add sponsors link to FUNDING.yml (#6252) * Group CLI demo into subdirectory. (#6258) * Reduce warning messages from `gbtree`. (#6273) * Create a tutorial for using the C API in a C/C++ application (#6285) * Update plugin instructions for CMake build (#6289) * [doc] make Dask distributed example copy-pastable (#6345) * [Python] Add option to use `libxgboost.so` from the system path (#6362) * Fixed few grammatical mistakes in doc (#6393) * Fix broken link in CLI doc (#6396) * Improve documentation for the Dask API (#6413) * Revise misleading exception information: no such param of `allow_non_zero_missing` (#6418) * Fix CLI ranking demo. (#6439) * Fix broken links. (#6455) ### Acknowledgement **Contributors**: Nan Zhu (@CodingCat), @FelixYBW, Jack Dunn (@JackDunnNZ), Jean Lescut-Muller (@JeanLescut), Boris Feld (@Lothiraldan), Nikhil Choudhary (@Nikhil1O1), Rory Mitchell (@RAMitchell), @ShvetsKS, Anthony D'Amato (@Totoketchup), @Wittty-Panda, neko (@akiyamaneko), Alexander Gugel (@alexanderGugel), @dependabot[bot], DIVYA CHAUHAN (@divya661), Daniel Steinberg (@dstein64), Akira Funahashi (@funasoul), Philip Hyunsu Cho (@hcho3), Tong He (@hetong007), Hristo Iliev (@hiliev), Honza Sterba (@honzasterba), @hzy001, Igor Moura (@igormp), @jameskrach, James Lamb (@jameslamb), Naveed Ahmed Saleem Janvekar (@janvekarnaveed), Kyle Nicholson (@kylejn27), lacrosse91 (@lacrosse91), Christian Lorentzen (@lorentzenchr), Manikya Bardhan (@manikyabard), @nabokovas, John Quitto-Graham (@nvidia-johnq), @odidev, Qi Zhang (@qzhang90), Sergio Gavilán (@sgavil), Tanuja Kirthi Doddapaneni (@tanuja3), Cuong Duong (@tcuongd), Yuan Tang (@terrytangyuan), Jiaming Yuan (@trivialfis), vcarpani (@vcarpani), Vladislav Epifanov (@vepifanov), Vitalie Spinu (@vspinu), Bobby Wang (@wbo4958), Zeno Gantner (@zenogantner), zhang_jf (@zuston) **Reviewers**: Nan Zhu (@CodingCat), John Zedlewski (@JohnZed), Rory Mitchell (@RAMitchell), @ShvetsKS, Egor Smirnov (@SmirnovEgorRu), Anthony D'Amato (@Totoketchup), @Wittty-Panda, Alexander Gugel (@alexanderGugel), Codecov Comments Bot (@codecov-commenter), Codecov (@codecov-io), DIVYA CHAUHAN (@divya661), Devin Robison (@drobison00), Geoffrey Blake (@geoffreyblake), Mark Harris (@harrism), Philip Hyunsu Cho (@hcho3), Honza Sterba (@honzasterba), Igor Moura (@igormp), @jakirkham, @jameskrach, James Lamb (@jameslamb), Janakarajan Natarajan (@janaknat), Jake Hemstad (@jrhemstad), Keith Kraus (@kkraus14), Kyle Nicholson (@kylejn27), Christian Lorentzen (@lorentzenchr), Michael Mayer (@mayer79), Nikolay Petrov (@napetrov), @odidev, PSEUDOTENSOR / Jonathan McKinney (@pseudotensor), Qi Zhang (@qzhang90), Sergio Gavilán (@sgavil), Scott Lundberg (@slundberg), Cuong Duong (@tcuongd), Yuan Tang (@terrytangyuan), Jiaming Yuan (@trivialfis), vcarpani (@vcarpani), Vladislav Epifanov (@vepifanov), Vincent Nijs (@vnijs), Vitalie Spinu (@vspinu), Bobby Wang (@wbo4958), William Hicks (@wphicks) ## v1.2.0 (2020.08.22) ### XGBoost4J-Spark now supports the GPU algorithm (#5171) * Now XGBoost4J-Spark is able to leverage NVIDIA GPU hardware to speed up training. * There is on-going work for accelerating the rest of the data pipeline with NVIDIA GPUs (#5950, #5972). ### XGBoost now supports CUDA 11 (#5808) * It is now possible to build XGBoost with CUDA 11. Note that we do not yet distribute pre-built binaries built with CUDA 11; all current distributions use CUDA 10.0. ### Better guidance for persisting XGBoost models in an R environment (#5940, #5964) * Users are strongly encouraged to use `xgb.save()` and `xgb.save.raw()` instead of `saveRDS()`. This is so that the persisted models can be accessed with future releases of XGBoost. * The previous release (1.1.0) had problems loading models that were saved with `saveRDS()`. This release adds a compatibility layer to restore access to the old RDS files. Note that this is meant to be a temporary measure; users are advised to stop using `saveRDS()` and migrate to `xgb.save()` and `xgb.save.raw()`. ### New objectives and metrics * The pseudo-Huber loss `reg:pseudohubererror` is added (#5647). The corresponding metric is `mphe`. Right now, the slope is hard-coded to 1. * The Accelerated Failure Time objective for survival analysis (`survival:aft`) is now accelerated on GPUs (#5714, #5716). The survival metrics `aft-nloglik` and `interval-regression-accuracy` are also accelerated on GPUs. ### Improved integration with scikit-learn * Added `n_features_in_` attribute to the scikit-learn interface to store the number of features used (#5780). This is useful for integrating with some scikit-learn features such as `StackingClassifier`. See [this link](https://scikit-learn-enhancement-proposals.readthedocs.io/en/latest/slep010/proposal.html) for more details. * `XGBoostError` now inherits `ValueError`, which conforms scikit-learn's exception requirement (#5696). ### Improved integration with Dask * The XGBoost Dask API now exposes an asynchronous interface (#5862). See [the document](https://xgboost.readthedocs.io/en/latest/tutorials/dask.html#working-with-asyncio) for details. * Zero-copy ingestion of GPU arrays via `DaskDeviceQuantileDMatrix` (#5623, #5799, #5800, #5803, #5837, #5874, #5901): Previously, the Dask interface had to make 2 data copies: one for concatenating the Dask partition/block into a single block and another for internal representation. To save memory, we introduce `DaskDeviceQuantileDMatrix`. As long as Dask partitions are resident in the GPU memory, `DaskDeviceQuantileDMatrix` is able to ingest them directly without making copies. This matrix type wraps `DeviceQuantileDMatrix`. * The prediction function now returns GPU Series type if the input is from Dask-cuDF (#5710). This is to preserve the input data type. ### Robust handling of external data types (#5689, #5893) - As we support more and more external data types, the handling logic has proliferated all over the code base and became hard to keep track. It also became unclear how missing values and threads are handled. We refactored the Python package code to collect all data handling logic to a central location, and now we have an explicit list of of all supported data types. ### Improvements in GPU-side data matrix (`DeviceQuantileDMatrix`) * The GPU-side data matrix now implements its own quantile sketching logic, so that data don't have to be transported back to the main memory (#5700, #5747, #5760, #5846, #5870, #5898). The GK sketching algorithm is also now better documented. - Now we can load extremely sparse dataset like URL, although performance is still sub-optimal. * The GPU-side data matrix now exposes an iterative interface (#5783), so that users are able to construct a matrix from a data iterator. See the [Python demo](https://github.com/dmlc/xgboost/blob/release_1.2.0/demo/guide-python/data_iterator.py). ### New language binding: Swift (#5728) * Visit https://github.com/kongzii/SwiftXGBoost for more details. ### Robust model serialization with JSON (#5772, #5804, #5831, #5857, #5934) * We continue efforts from the 1.0.0 release to adopt JSON as the format to save and load models robustly. * JSON model IO is significantly faster and produces smaller model files. * Round-trip reproducibility is guaranteed, via the introduction of an efficient float-to-string conversion algorithm known as [the Ryū algorithm](https://dl.acm.org/doi/10.1145/3192366.3192369). The conversion is locale-independent, producing consistent numeric representation regardless of the locale setting of the user's machine. * We fixed an issue in loading large JSON files to memory. * It is now possible to load a JSON file from a remote source such as S3. ### Performance improvements * CPU hist tree method optimization - Skip missing lookup in hist row partitioning if data is dense. (#5644) - Specialize training procedures for CPU hist tree method on distributed environment. (#5557) - Add single point histogram for CPU hist. Previously gradient histogram for CPU hist is hard coded to be 64 bit, now users can specify the parameter `single_precision_histogram` to use 32 bit histogram instead for faster training performance. (#5624, #5811) * GPU hist tree method optimization - Removed some unnecessary synchronizations and better memory allocation pattern. (#5707) - Optimize GPU Hist for wide dataset. Previously for wide dataset the atomic operation is performed on global memory, now it can run on shared memory for faster histogram building. But there's a known small regression on GeForce cards with dense data. (#5795, #5926, #5948, #5631) ### API additions * Support passing fmap to importance plot (#5719). Now importance plot can show actual names of features instead of default ones. * Support 64bit seed. (#5643) * A new C API `XGBoosterGetNumFeature` is added for getting number of features in booster (#5856). * Feature names and feature types are now stored in C++ core and saved in binary DMatrix (#5858). ### Breaking: The `predict()` method of `DaskXGBClassifier` now produces class predictions (#5986). Use `predict_proba()` to obtain probability predictions. * Previously, `DaskXGBClassifier.predict()` produced probability predictions. This is inconsistent with the behavior of other scikit-learn classifiers, where `predict()` returns class predictions. We make a breaking change in 1.2.0 release so that `DaskXGBClassifier.predict()` now correctly produces class predictions and thus behave like other scikit-learn classifiers. Furthermore, we introduce the `predict_proba()` method for obtaining probability predictions, again to be in line with other scikit-learn classifiers. ### Breaking: Custom evaluation metric now receives raw prediction (#5954) * Previously, the custom evaluation metric received a transformed prediction result when used with a classifier. Now the custom metric will receive a raw (untransformed) prediction and will need to transform the prediction itself. See [demo/guide-python/custom\_softmax.py](https://github.com/dmlc/xgboost/blob/release_1.2.0/demo/guide-python/custom_softmax.py) for an example. * This change is to make the custom metric behave consistently with the custom objective, which already receives raw prediction (#5564). ### Breaking: XGBoost4J-Spark now requires Spark 3.0 and Scala 2.12 (#5836, #5890) * Starting with version 3.0, Spark can manage GPU resources and allocate them among executors. * Spark 3.0 dropped support for Scala 2.11 and now only supports Scala 2.12. Thus, XGBoost4J-Spark also only supports Scala 2.12. ### Breaking: XGBoost Python package now requires Python 3.6 and later (#5715) * Python 3.6 has many useful features such as f-strings. ### Breaking: XGBoost now adopts the C++14 standard (#5664) * Make sure to use a sufficiently modern C++ compiler that supports C++14, such as Visual Studio 2017, GCC 5.0+, and Clang 3.4+. ### Bug-fixes * Fix a data race in the prediction function (#5853). As a byproduct, the prediction function now uses a thread-local data store and became thread-safe. * Restore capability to run prediction when the test input has fewer features than the training data (#5955). This capability is necessary to support predicting with LIBSVM inputs. The previous release (1.1) had broken this capability, so we restore it in this version with better tests. * Fix OpenMP build with CMake for R package, to support CMake 3.13 (#5895). * Fix Windows 2016 build (#5902, #5918). * Fix edge cases in scikit-learn interface with Pandas input by disabling feature validation. (#5953) * [R] Enable weighted learning to rank (#5945) * [R] Fix early stopping with custom objective (#5923) * Fix NDK Build (#5886) * Add missing explicit template specializations for greater portability (#5921) * Handle empty rows in data iterators correctly (#5929). This bug affects file loader and JVM data frames. * Fix `IsDense` (#5702) * [jvm-packages] Fix wrong method name `setAllowZeroForMissingValue` (#5740) * Fix shape inference for Dask predict (#5989) ### Usability Improvements, Documentation * [Doc] Document that CUDA 10.0 is required (#5872) * Refactored command line interface (CLI). Now CLI is able to handle user errors and output basic document. (#5574) * Better error handling in Python: use `raise from` syntax to preserve full stacktrace (#5787). * The JSON model dump now has a formal schema (#5660, #5818). The benefit is to prevent `dump_model()` function from breaking. See [this document](https://xgboost.readthedocs.io/en/latest/tutorials/saving_model.html#difference-between-saving-model-and-dumping-model) to understand the difference between saving and dumping models. * Add a reference to the GPU external memory paper (#5684) * Document more objective parameters in the R package (#5682) * Document the existence of pre-built binary wheels for MacOS (#5711) * Remove `max.depth` in the R gblinear example. (#5753) * Added conda environment file for building docs (#5773) * Mention dask blog post in the doc, which introduces using Dask with GPU and some internal workings. (#5789) * Fix rendering of Markdown docs (#5821) * Document new objectives and metrics available on GPUs (#5909) * Better message when no GPU is found. (#5594) * Remove the use of `silent` parameter from R demos. (#5675) * Don't use masked array in array interface. (#5730) * Update affiliation of @terrytangyuan: Ant Financial -> Ant Group (#5827) * Move dask tutorial closer other distributed tutorials (#5613) * Update XGBoost + Dask overview documentation (#5961) * Show `n_estimators` in the docstring of the scikit-learn interface (#6041) * Fix a type in a doctring of the scikit-learn interface (#5980) ### Maintenance: testing, continuous integration, build system * [CI] Remove CUDA 9.0 from CI (#5674, #5745) * Require CUDA 10.0+ in CMake build (#5718) * [R] Remove dependency on gendef for Visual Studio builds (fixes #5608) (#5764). This enables building XGBoost with GPU support with R 4.x. * [R-package] Reduce duplication in configure.ac (#5693) * Bump com.esotericsoftware to 4.0.2 (#5690) * Migrate some tests from AppVeyor to GitHub Actions to speed up the tests. (#5911, #5917, #5919, #5922, #5928) * Reduce cost of the Jenkins CI server (#5884, #5904, #5892). We now enforce a daily budget via an automated monitor. We also dramatically reduced the workload for the Windows platform, since the cloud VM cost is vastly greater for Windows. * [R] Set up automated R linter (#5944) * [R] replace uses of T and F with TRUE and FALSE (#5778) * Update Docker container 'CPU' (#5956) * Simplify CMake build with modern CMake techniques (#5871) * Use `hypothesis` package for testing (#5759, #5835, #5849). * Define `_CRT_SECURE_NO_WARNINGS` to remove unneeded warnings in MSVC (#5434) * Run all Python demos in CI, to ensure that they don't break (#5651) * Enhance nvtx support (#5636). Now we can use unified timer between CPU and GPU. Also CMake is able to find nvtx automatically. * Speed up python test. (#5752) * Add helper for generating batches of data. (#5756) * Add c-api-demo to .gitignore (#5855) * Add option to enable all compiler warnings in GCC/Clang (#5897) * Make Python model compatibility test runnable locally (#5941) * Add cupy to Windows CI (#5797) * [CI] Fix cuDF install; merge 'gpu' and 'cudf' test suite (#5814) * Update rabit submodule (#5680, #5876) * Force colored output for Ninja build. (#5959) * [CI] Assign larger /dev/shm to NCCL (#5966) * Add missing Pytest marks to AsyncIO unit test (#5968) * [CI] Use latest cuDF and dask-cudf (#6048) * Add CMake flag to log C API invocations, to aid debugging (#5925) * Fix a unit test on CLI, to handle RC versions (#6050) * [CI] Use mgpu machine to run gpu hist unit tests (#6050) * [CI] Build GPU-enabled JAR artifact and deploy to xgboost-maven-repo (#6050) ### Maintenance: Refactor code for legibility and maintainability * Remove dead code in DMatrix initialization. (#5635) * Catch dmlc error by ref. (#5678) * Refactor the `gpu_hist` split evaluation in preparation for batched nodes enumeration. (#5610) * Remove column major specialization. (#5755) * Remove unused imports in Python (#5776) * Avoid including `c_api.h` in header files. (#5782) * Remove unweighted GK quantile, which is unused. (#5816) * Add Python binding for rabit ops. (#5743) * Implement `Empty` method for host device vector. (#5781) * Remove print (#5867) * Enforce tree order in JSON (#5974) ### Acknowledgement **Contributors**: Nan Zhu (@CodingCat), @LionOrCatThatIsTheQuestion, Dmitry Mottl (@Mottl), Rory Mitchell (@RAMitchell), @ShvetsKS, Alex Wozniakowski (@a-wozniakowski), Alexander Gugel (@alexanderGugel), @anttisaukko, @boxdot, Andy Adinets (@canonizer), Ram Rachum (@cool-RR), Elliot Hershberg (@elliothershberg), Jason E. Aten, Ph.D. (@glycerine), Philip Hyunsu Cho (@hcho3), @jameskrach, James Lamb (@jameslamb), James Bourbeau (@jrbourbeau), Peter Jung (@kongzii), Lorenz Walthert (@lorenzwalthert), Oleksandr Kuvshynov (@okuvshynov), Rong Ou (@rongou), Shaochen Shi (@shishaochen), Yuan Tang (@terrytangyuan), Jiaming Yuan (@trivialfis), Bobby Wang (@wbo4958), Zhang Zhang (@zhangzhang10) **Reviewers**: Nan Zhu (@CodingCat), @LionOrCatThatIsTheQuestion, Hao Yang (@QuantHao), Rory Mitchell (@RAMitchell), @ShvetsKS, Egor Smirnov (@SmirnovEgorRu), Alex Wozniakowski (@a-wozniakowski), Amit Kumar (@aktech), Avinash Barnwal (@avinashbarnwal), @boxdot, Andy Adinets (@canonizer), Chandra Shekhar Reddy (@chandrureddy), Ram Rachum (@cool-RR), Cristiano Goncalves (@cristianogoncalves), Elliot Hershberg (@elliothershberg), Jason E. Aten, Ph.D. (@glycerine), Philip Hyunsu Cho (@hcho3), Tong He (@hetong007), James Lamb (@jameslamb), James Bourbeau (@jrbourbeau), Lee Drake (@leedrake5), DougM (@mengdong), Oleksandr Kuvshynov (@okuvshynov), RongOu (@rongou), Shaochen Shi (@shishaochen), Xu Xiao (@sperlingxx), Yuan Tang (@terrytangyuan), Theodore Vasiloudis (@thvasilo), Jiaming Yuan (@trivialfis), Bobby Wang (@wbo4958), Zhang Zhang (@zhangzhang10) ## v1.1.1 (2020.06.06) This patch release applies the following patches to 1.1.0 release: * CPU performance improvement in the PyPI wheels (#5720) * Fix loading old model (#5724) * Install pkg-config file (#5744) ## v1.1.0 (2020.05.17) ### Better performance on multi-core CPUs (#5244, #5334, #5522) * Poor performance scaling of the `hist` algorithm for multi-core CPUs has been under investigation (#3810). #5244 concludes the ongoing effort to improve performance scaling on multi-CPUs, in particular Intel CPUs. Roadmap: #5104 * #5334 makes steps toward reducing memory consumption for the `hist` tree method on CPU. * #5522 optimizes random number generation for data sampling. ### Deterministic GPU algorithm for regression and classification (#5361) * GPU algorithm for regression and classification tasks is now deterministic. * Roadmap: #5023. Currently only single-GPU training is deterministic. Distributed training with multiple GPUs is not yet deterministic. ### Improve external memory support on GPUs (#5093, #5365) * Starting from 1.0.0 release, we added support for external memory on GPUs to enable training with larger datasets. Gradient-based sampling (#5093) speeds up the external memory algorithm by intelligently sampling a subset of the training data to copy into the GPU memory. [Learn more about out-of-core GPU gradient boosting.](https://arxiv.org/abs/2005.09148) * GPU-side data sketching now works with data from external memory (#5365). ### Parameter validation: detection of unused or incorrect parameters (#5477, #5569, #5508) * Mis-spelled training parameter is a common user mistake. In previous versions of XGBoost, mis-spelled parameters were silently ignored. Starting with 1.0.0 release, XGBoost will produce a warning message if there is any unused training parameters. The 1.1.0 release makes parameter validation available to the scikit-learn interface (#5477) and the R binding (#5569). ### Thread-safe, in-place prediction method (#5389, #5512) * Previously, the prediction method was not thread-safe (#5339). This release adds a new API function `inplace_predict()` that is thread-safe. It is now possible to serve concurrent requests for prediction using a shared model object. * It is now possible to compute prediction in-place for selected data formats (`numpy.ndarray` / `scipy.sparse.csr_matrix` / `cupy.ndarray` / `cudf.DataFrame` / `pd.DataFrame`) without creating a `DMatrix` object. ### Addition of Accelerated Failure Time objective for survival analysis (#4763, #5473, #5486, #5552, #5553) * Survival analysis (regression) models the time it takes for an event of interest to occur. The target label is potentially censored, i.e. the label is a range rather than a single number. We added a new objective `survival:aft` to support survival analysis. Also added is the new API to specify the ranged labels. Check out [the tutorial](https://xgboost.readthedocs.io/en/release_1.1.0/tutorials/aft_survival_analysis.html) and the [demos](https://github.com/dmlc/xgboost/tree/release_1.1.0/demo/aft_survival). * GPU support is work in progress (#5714). ### Improved installation experience on Mac OSX (#5597, #5602, #5606, #5701) * It only takes two commands to install the XGBoost Python package: `brew install libomp` followed by `pip install xgboost`. The installed XGBoost will use all CPU cores. Even better, starting with this release, we distribute pre-compiled binary wheels targeting Mac OSX. Now the install command `pip install xgboost` finishes instantly, as it no longer compiles the C++ source of XGBoost. The last three Mac versions (High Sierra, Mojave, Catalina) are supported. * R package: the 1.1.0 release fixes the error `Initializing libomp.dylib, but found libomp.dylib already initialized` (#5701) ### Ranking metrics are now accelerated on GPUs (#5380, #5387, #5398) ### GPU-side data matrix to ingest data directly from other GPU libraries (#5420, #5465) * Previously, data on GPU memory had to be copied back to the main memory before it could be used by XGBoost. Starting with 1.1.0 release, XGBoost provides a dedicated interface (`DeviceQuantileDMatrix`) so that it can ingest data from GPU memory directly. The result is that XGBoost interoperates better with GPU-accelerated data science libraries, such as cuDF, cuPy, and PyTorch. * Set device in device dmatrix. (#5596) ### Robust model serialization with JSON (#5123, #5217) * We continue efforts from the 1.0.0 release to adopt JSON as the format to save and load models robustly. Refer to the release note for 1.0.0 to learn more. * It is now possible to store internal configuration of the trained model (`Booster`) object in R as a JSON string (#5123, #5217). ### Improved integration with Dask * Pass through `verbose` parameter for dask fit (#5413) * Use `DMLC_TASK_ID`. (#5415) * Order the prediction result. (#5416) * Honor `nthreads` from dask worker. (#5414) * Enable grid searching with scikit-learn. (#5417) * Check non-equal when setting threads. (#5421) * Accept other inputs for prediction. (#5428) * Fix missing value for scikit-learn interface. (#5435) ### XGBoost4J-Spark: Check number of columns in the data iterator (#5202, #5303) * Before, the native layer in XGBoost did not know the number of columns (features) ahead of time and had to guess the number of columns by counting the feature index when ingesting data. This method has a failure more in distributed setting: if the training data is highly sparse, some features may be completely missing in one or more worker partitions. Thus, one or more workers may deduce an incorrect data shape, leading to crashes or silently wrong models. * Enforce correct data shape by passing the number of columns explicitly from the JVM layer into the native layer. ### Major refactoring of the `DMatrix` class * Continued from 1.0.0 release. * Remove update prediction cache from predictors. (#5312) * Predict on Ellpack. (#5327) * Partial rewrite EllpackPage (#5352) * Use ellpack for prediction only when sparsepage doesn't exist. (#5504) * RFC: #4354, Roadmap: #5143 ### Breaking: XGBoost Python package now requires Pip 19.0 and higher (#5589) * Your Linux machine may have an old version of Pip and may attempt to install a source package, leading to long installation time. This is because we are now using `manylinux2010` tag in the binary wheel release. Ensure you have Pip 19.0 or newer by running `python3 -m pip -V` to check the version. Upgrade Pip with command ``` python3 -m pip install --upgrade pip ``` Upgrading to latest pip allows us to depend on newer versions of system libraries. [TensorFlow](https://www.tensorflow.org/install/pip) also requires Pip 19.0+. ### Breaking: GPU algorithm now requires CUDA 10.0 and higher (#5649) * CUDA 10.0 is necessary to make the GPU algorithm deterministic (#5361). ### Breaking: `silent` parameter is now removed (#5476) * Please use `verbosity` instead. ### Breaking: Set `output_margin` to True for custom objectives (#5564) * Now both R and Python interface custom objectives get un-transformed (raw) prediction outputs. ### Breaking: `Makefile` is now removed. We use CMake exclusively to build XGBoost (#5513) * Exception: the R package uses Autotools, as the CRAN ecosystem did not yet adopt CMake widely. ### Breaking: `distcol` updater is now removed (#5507) * The `distcol` updater has been long broken, and currently we lack resources to implement a working implementation from scratch. ### Deprecation notices * **Python 3.5**. This release is the last release to support Python 3.5. The following release (1.2.0) will require Python 3.6. * **Scala 2.11**. Currently XGBoost4J supports Scala 2.11. However, if a future release of XGBoost adopts Spark 3, it will not support Scala 2.11, as Spark 3 requires Scala 2.12+. We do not yet know which XGBoost release will adopt Spark 3. ### Known limitations * (Python package) When early stopping is activated with `early_stopping_rounds` at training time, the prediction method (`xgb.predict()`) behaves in a surprising way. If XGBoost runs for M rounds and chooses iteration N (N < M) as the best iteration, then the prediction method will use M trees by default. To use the best iteration (N trees), users will need to manually take the best iteration field `bst.best_iteration` and pass it as the `ntree_limit` argument to `xgb.predict()`. See #5209 and #4052 for additional context. * GPU ranking objective is currently not deterministic (#5561). * When training parameter `reg_lambda` is set to zero, some leaf nodes may be assigned a NaN value. (See [discussion](https://discuss.xgboost.ai/t/still-getting-unexplained-nans-new-replication-code/1383/9).) For now, please set `reg_lambda` to a nonzero value. ### Community and Governance * The XGBoost Project Management Committee (PMC) is pleased to announce a new committer: Egor Smirnov (@SmirnovEgorRu). He has led a major initiative to improve the performance of XGBoost on multi-core CPUs. ### Bug-fixes * Improved compatibility with scikit-learn (#5255, #5505, #5538) * Remove f-string, since it's not supported by Python 3.5 (#5330). Note that Python 3.5 support is deprecated and schedule to be dropped in the upcoming release (1.2.0). * Fix the pruner so that it doesn't prune the same branch twice (#5335) * Enforce only major version in JSON model schema (#5336). Any major revision of the model schema would bump up the major version. * Fix a small typo in sklearn.py that broke multiple eval metrics (#5341) * Restore loading model from a memory buffer (#5360) * Define lazy isinstance for Python compat (#5364) * [R] fixed uses of `class()` (#5426) * Force compressed buffer to be 4 bytes aligned, to keep cuda-memcheck happy (#5441) * Remove warning for calling host function (`std::max`) on a GPU device (#5453) * Fix uninitialized value bug in xgboost callback (#5463) * Fix model dump in CLI (#5485) * Fix out-of-bound array access in `WQSummary::SetPrune()` (#5493) * Ensure that configured `dmlc/build_config.h` is picked up by Rabit and XGBoost, to fix build on Alpine (#5514) * Fix a misspelled method, made in a git merge (#5509) * Fix a bug in binary model serialization (#5532) * Fix CLI model IO (#5535) * Don't use `uint` for threads (#5542) * Fix R interaction constraints to handle more than 100000 features (#5543) * [jvm-packages] XGBoost Spark should deal with NaN when parsing evaluation output (#5546) * GPU-side data sketching is now aware of query groups in learning-to-rank data (#5551) * Fix DMatrix slicing for newly added fields (#5552) * Fix configuration status with loading binary model (#5562) * Fix build when OpenMP is disabled (#5566) * R compatibility patches (#5577, #5600) * gpu\_hist performance fixes (#5558) * Don't set seed on CLI interface (#5563) * [R] When serializing model, preserve model attributes related to early stopping (#5573) * Avoid rabit calls in learner configuration (#5581) * Hide C++ symbols in libxgboost.so when building Python wheel (#5590). This fixes apache/incubator-tvm#4953. * Fix compilation on Mac OSX High Sierra (10.13) (#5597) * Fix build on big endian CPUs (#5617) * Resolve crash due to use of `vector::iterator` (#5642) * Validation JSON model dump using JSON schema (#5660) ### Performance improvements * Wide dataset quantile performance improvement (#5306) * Reduce memory usage of GPU-side data sketching (#5407) * Reduce span check overhead (#5464) * Serialise booster after training to free up GPU memory (#5484) * Use the maximum amount of GPU shared memory available to speed up the histogram kernel (#5491) * Use non-synchronising scan in Thrust (#5560) * Use `cudaDeviceGetAttribute()` instead of `cudaGetDeviceProperties()` for speed (#5570) ### API changes * Support importing data from a Pandas SparseArray (#5431) * `HostDeviceVector` (vector shared between CPU and GPU memory) now exposes `HostSpan` interface, to enable access on the CPU side with bound check (#5459) * Accept other gradient types for `SplitEntry` (#5467) ### Usability Improvements, Documentation * Add `JVM_CHECK_CALL` to prevent C++ exceptions from leaking into the JVM layer (#5199) * Updated Windows build docs (#5283) * Update affiliation of @hcho3 (#5292) * Display Sponsor button, link to OpenCollective (#5325) * Update docs for GPU external memory (#5332) * Add link to GPU documentation (#5437) * Small updates to GPU documentation (#5483) * Edits on tutorial for XGBoost job on Kubernetes (#5487) * Add reference to GPU external memory (#5490) * Fix typos (#5346, #5371, #5384, #5399, #5482, #5515) * Update Python doc (#5517) * Add Neptune and Optuna to list of examples (#5528) * Raise error if the number of data weights doesn't match the number of data sets (#5540) * Add a note about GPU ranking (#5572) * Clarify meaning of `training` parameter in the C API function `XGBoosterPredict()` (#5604) * Better error handling for situations where existing trees cannot be modified (#5406, #5418). This feature is enabled when `process_type` is set to `update`. ### Maintenance: testing, continuous integration, build system * Add C++ test coverage for data sketching (#5251) * Ignore gdb\_history (#5257) * Rewrite setup.py. (#5271, #5280) * Use `scikit-learn` in extra dependencies (#5310) * Add CMake option to build static library (#5397) * [R] changed FindLibR to take advantage of CMake cache (#5427) * [R] fixed inconsistency in R -e calls in FindLibR.cmake (#5438) * Refactor tests with data generator (#5439) * Resolve failing Travis CI (#5445) * Update dmlc-core. (#5466) * [CI] Use clang-tidy 10 (#5469) * De-duplicate code for checking maximum number of nodes (#5497) * [CI] Use Ubuntu 18.04 LTS in JVM CI, because 19.04 is EOL (#5537) * [jvm-packages] [CI] Create a Maven repository to host SNAPSHOT JARs (#5533) * [jvm-packages] [CI] Publish XGBoost4J JARs with Scala 2.11 and 2.12 (#5539) * [CI] Use Vault repository to re-gain access to devtoolset-4 (#5589) ### Maintenance: Refactor code for legibility and maintainability * Move prediction cache to Learner (#5220, #5302) * Remove SimpleCSRSource (#5315) * Refactor SparsePageSource, delete cache files after use (#5321) * Remove unnecessary DMatrix methods (#5324) * Split up `LearnerImpl` (#5350) * Move segment sorter to common (#5378) * Move thread local entry into Learner (#5396) * Split up test helpers header (#5455) * Requires setting leaf stat when expanding tree (#5501) * Purge device\_helpers.cuh (#5534) * Use thrust functions instead of custom functions (#5544) ### Acknowledgement **Contributors**: Nan Zhu (@CodingCat), Rory Mitchell (@RAMitchell), @ShvetsKS, Egor Smirnov (@SmirnovEgorRu), Andrew Kane (@ankane), Avinash Barnwal (@avinashbarnwal), Bart Broere (@bartbroere), Andy Adinets (@canonizer), Chen Qin (@chenqin), Daiki Katsuragawa (@daikikatsuragawa), David Díaz Vico (@daviddiazvico), Darius Kharazi (@dkharazi), Darby Payne (@dpayne), Jason E. Aten, Ph.D. (@glycerine), Philip Hyunsu Cho (@hcho3), James Lamb (@jameslamb), Jan Borchmann (@jborchma), Kamil A. Kaczmarek (@kamil-kaczmarek), Melissa Kohl (@mjkohl32), Nicolas Scozzaro (@nscozzaro), Paul Kaefer (@paulkaefer), Rong Ou (@rongou), Samrat Pandiri (@samratp), Sriram Chandramouli (@sriramch), Yuan Tang (@terrytangyuan), Jiaming Yuan (@trivialfis), Liang-Chi Hsieh (@viirya), Bobby Wang (@wbo4958), Zhang Zhang (@zhangzhang10), **Reviewers**: Nan Zhu (@CodingCat), @LeZhengThu, Rory Mitchell (@RAMitchell), @ShvetsKS, Egor Smirnov (@SmirnovEgorRu), Steve Bronder (@SteveBronder), Nikita Titov (@StrikerRUS), Andrew Kane (@ankane), Avinash Barnwal (@avinashbarnwal), @brydag, Andy Adinets (@canonizer), Chandra Shekhar Reddy (@chandrureddy), Chen Qin (@chenqin), Codecov (@codecov-io), David Díaz Vico (@daviddiazvico), Darby Payne (@dpayne), Jason E. Aten, Ph.D. (@glycerine), Philip Hyunsu Cho (@hcho3), James Lamb (@jameslamb), @johnny-cat, Mu Li (@mli), Mate Soos (@msoos), @rnyak, Rong Ou (@rongou), Sriram Chandramouli (@sriramch), Toby Dylan Hocking (@tdhock), Yuan Tang (@terrytangyuan), Oleksandr Pryimak (@trams), Jiaming Yuan (@trivialfis), Liang-Chi Hsieh (@viirya), Bobby Wang (@wbo4958), ## v1.0.2 (2020.03.03) This patch release applies the following patches to 1.0.0 release: * Fix a small typo in sklearn.py that broke multiple eval metrics (#5341) * Restore loading model from buffer (#5360) * Use type name for data type check (#5364) ## v1.0.1 (2020.02.21) This release is identical to the 1.0.0 release, except that it fixes a small bug that rendered 1.0.0 incompatible with Python 3.5. See #5328. ## v1.0.0 (2020.02.19) This release marks a major milestone for the XGBoost project. ### Apache-style governance, contribution policy, and semantic versioning (#4646, #4659) * Starting with 1.0.0 release, the XGBoost Project is adopting Apache-style governance. The full community guideline is [available in the doc website](https://xgboost.readthedocs.io/en/release_1.0.0/contrib/community.html). Note that we now have Project Management Committee (PMC) who would steward the project on the long-term basis. The PMC is also entrusted to run and fund the project's continuous integration (CI) infrastructure (https://xgboost-ci.net). * We also adopt the [semantic versioning](https://semver.org/). See [our release versioning policy](https://xgboost.readthedocs.io/en/release_1.0.0/contrib/release.html). ### Better performance scaling for multi-core CPUs (#4502, #4529, #4716, #4851, #5008, #5107, #5138, #5156) * Poor performance scaling of the `hist` algorithm for multi-core CPUs has been under investigation (#3810). Previous effort #4529 was replaced with a series of pull requests (#5107, #5138, #5156) aimed at achieving the same performance benefits while keeping the C++ codebase legible. The latest performance benchmark results show [up to 5x speedup on Intel CPUs with many cores](https://github.com/dmlc/xgboost/pull/5156#issuecomment-580024413). Note: #5244, which concludes the effort, will become part of the upcoming release 1.1.0. ### Improved installation experience on Mac OSX (#4672, #5074, #5080, #5146, #5240) * It used to be quite complicated to install XGBoost on Mac OSX. XGBoost uses OpenMP to distribute work among multiple CPU cores, and Mac's default C++ compiler (Apple Clang) does not come with OpenMP. Existing work-around (using another C++ compiler) was complex and prone to fail with cryptic diagnosis (#4933, #4949, #4969). * Now it only takes two commands to install XGBoost: `brew install libomp` followed by `pip install xgboost`. The installed XGBoost will use all CPU cores. * Even better, XGBoost is now available from Homebrew: `brew install xgboost`. See Homebrew/homebrew-core#50467. * Previously, if you installed the XGBoost R package using the command `install.packages('xgboost')`, it could only use a single CPU core and you would experience slow training performance. With 1.0.0 release, the R package will use all CPU cores out of box. ### Distributed XGBoost now available on Kubernetes (#4621, #4939) * Check out the [tutorial for setting up distributed XGBoost on a Kubernetes cluster](https://xgboost.readthedocs.io/en/release_1.0.0/tutorials/kubernetes.html). ### Ruby binding for XGBoost (#4856) ### New Native Dask interface for multi-GPU and multi-node scaling (#4473, #4507, #4617, #4819, #4907, #4914, #4941, #4942, #4951, #4973, #5048, #5077, #5144, #5270) * XGBoost now integrates seamlessly with [Dask](https://dask.org/), a lightweight distributed framework for data processing. Together with the first-class support for cuDF data frames (see below), it is now easier than ever to create end-to-end data pipeline running on one or more NVIDIA GPUs. * Multi-GPU training with Dask is now up to 20% faster than the previous release (#4914, #4951). ### First-class support for cuDF data frames and cuPy arrays (#4737, #4745, #4794, #4850, #4891, #4902, #4918, #4927, #4928, #5053, #5189, #5194, #5206, #5219, #5225) * [cuDF](https://github.com/rapidsai/cudf) is a data frame library for loading and processing tabular data on NVIDIA GPUs. It provides a Pandas-like API. * [cuPy](https://github.com/cupy/cupy) implements a NumPy-compatible multi-dimensional array on NVIDIA GPUs. * Now users can keep the data on the GPU memory throughout the end-to-end data pipeline, obviating the need for copying data between the main memory and GPU memory. * XGBoost can accept any data structure that exposes `__array_interface__` signature, opening way to support other columar formats that are compatible with Apache Arrow. ### [Feature interaction constraint](https://xgboost.readthedocs.io/en/release_1.0.0/tutorials/feature_interaction_constraint.html) is now available with `approx` and `gpu_hist` algorithms (#4534, #4587, #4596, #5034). ### Learning to rank is now GPU accelerated (#4873, #5004, #5129) * Supported ranking objectives: NDGC, Map, Pairwise. * [Up to 2x improved training performance on GPUs](https://devblogs.nvidia.com/learning-to-rank-with-xgboost-and-gpu/). ### Enable `gamma` parameter for GPU training (#4874, #4953) * The `gamma` parameter specifies the minimum loss reduction required to add a new split in a tree. A larger value for `gamma` has the effect of pre-pruning the tree, by making harder to add splits. ### External memory for GPU training (#4486, #4526, #4747, #4833, #4879, #5014) * It is now possible to use NVIDIA GPUs even when the size of training data exceeds the available GPU memory. Note that the external memory support for GPU is still experimental. #5093 will further improve performance and will become part of the upcoming release 1.1.0. * RFC for enabling external memory with GPU algorithms: #4357 ### Improve Scikit-Learn interface (#4558, #4842, #4929, #5049, #5151, #5130, #5227) * Many users of XGBoost enjoy the convenience and breadth of Scikit-Learn ecosystem. In this release, we revise the Scikit-Learn API of XGBoost (`XGBRegressor`, `XGBClassifier`, and `XGBRanker`) to achieve feature parity with the traditional XGBoost interface (`xgboost.train()`). * Insert check to validate data shapes. * Produce an error message if `eval_set` is not a tuple. An error message is better than silently crashing. * Allow using `numpy.RandomState` object. * Add `n_jobs` as an alias of `nthread`. * Roadmap: #5152 ### XGBoost4J-Spark: Redesigning checkpointing mechanism * RFC is available at #4786 * Clean up checkpoint file after a successful training job (#4754): The current implementation in XGBoost4J-Spark does not clean up the checkpoint file after a successful training job. If the user runs another job with the same checkpointing directory, she will get a wrong model because the second job will re-use the checkpoint file left over from the first job. To prevent this scenario, we propose to always clean up the checkpoint file after every successful training job. * Avoid Multiple Jobs for Checkpointing (#5082): The current method for checkpoint is to collect the booster produced at the last iteration of each checkpoint internal to Driver and persist it in HDFS. The major issue with this approach is that it needs to re-perform the data preparation for training if the user did not choose to cache the training dataset. To avoid re-performing data prep, we build external-memory checkpointing in the XGBoost4J layer as well. * Enable deterministic repartitioning when checkpoint is enabled (#4807): Distributed algorithm for gradient boosting assumes a fixed partition of the training data between multiple iterations. In previous versions, there was no guarantee that data partition would stay the same, especially when a worker goes down and some data had to recovered from previous checkpoint. In this release, we make data partition deterministic by using the data hash value of each data row in computing the partition. ### XGBoost4J-Spark: handle errors thrown by the native code (#4560) * All core logic of XGBoost is written in C++, so XGBoost4J-Spark internally uses the C++ code via Java Native Interface (JNI). #4560 adds a proper error handling for any errors or exceptions arising from the C++ code, so that the XGBoost Spark application can be torn down in an orderly fashion. ### XGBoost4J-Spark: Refine method to count the number of alive cores (#4858) * The `SparkParallelismTracker` class ensures that sufficient number of executor cores are alive. To that end, it is important to query the number of alive cores reliably. ### XGBoost4J: Add `BigDenseMatrix` to store more than `Integer.MAX_VALUE` elements (#4383) ### Robust model serialization with JSON (#4632, #4708, #4739, #4868, #4936, #4945, #4974, #5086, #5087, #5089, #5091, #5094, #5110, #5111, #5112, #5120, #5137, #5218, #5222, #5236, #5245, #5248, #5281) * In this release, we introduce an experimental support of using [JSON](https://www.json.org/json-en.html) for serializing (saving/loading) XGBoost models and related hyperparameters for training. We would like to eventually replace the old binary format with JSON, since it is an open format and parsers are available in many programming languages and platforms. See [the documentation for model I/O using JSON](https://xgboost.readthedocs.io/en/release_1.0.0/tutorials/saving_model.html). #3980 explains why JSON was chosen over other alternatives. * To maximize interoperability and compatibility of the serialized models, we now split serialization into two parts (#4855): 1. Model, e.g. decision trees and strictly related metadata like `num_features`. 2. Internal configuration, consisting of training parameters and other configurable parameters. For example, `max_delta_step`, `tree_method`, `objective`, `predictor`, `gpu_id`. Previously, users often ran into issues where the model file produced by one machine could not load or run on another machine. For example, models trained using a machine with an NVIDIA GPU could not run on another machine without a GPU (#5291, #5234). The reason is that the old binary format saved some internal configuration that were not universally applicable to all machines, e.g. `predictor='gpu_predictor'`. Now, model saving function (`Booster.save_model()` in Python) will save only the model, without internal configuration. This will guarantee that your model file would be used anywhere. Internal configuration will be serialized in limited circumstances such as: * Multiple nodes in a distributed system exchange model details over the network. * Model checkpointing, to recover from possible crashes. This work proved to be useful for parameter validation as well (see below). * Starting with 1.0.0 release, we will use semantic versioning to indicate whether the model produced by one version of XGBoost would be compatible with another version of XGBoost. Any change in the major version indicates a breaking change in the serialization format. * We now provide a robust method to save and load scikit-learn related attributes (#5245). Previously, we used Python pickle to save Python attributes related to `XGBClassifier`, `XGBRegressor`, and `XGBRanker` objects. The attributes are necessary to properly interact with scikit-learn. See #4639 for more details. The use of pickling hampered interoperability, as a pickle from one machine may not necessarily work on another machine. Starting with this release, we use an alternative method to serialize the scikit-learn related attributes. The use of Python pickle is now discouraged (#5236, #5281). ### Parameter validation: detection of unused or incorrect parameters (#4553, #4577, #4738, #4801, #4961, #5101, #5157, #5167, #5256) * Mis-spelled training parameter is a common user mistake. In previous versions of XGBoost, mis-spelled parameters were silently ignored. Starting with 1.0.0 release, XGBoost will produce a warning message if there is any unused training parameters. Currently, parameter validation is available to R users and Python XGBoost API users. We are working to extend its support to scikit-learn users. * Configuration steps now have well-defined semantics (#4542, #4738), so we know exactly where and how the internal configurable parameters are changed. * The user can now use `save_config()` function to inspect all (used) training parameters. This is helpful for debugging model performance. ### Allow individual workers to recover from faults (#4808, #4966) * Status quo: if a worker fails, all workers are shut down and restarted, and learning resumes from the last checkpoint. This involves requesting resources from the scheduler (e.g. Spark) and shuffling all the data again from scratch. Both of these operations can be quite costly and block training for extended periods of time, especially if the training data is big and the number of worker nodes is in the hundreds. * The proposed solution is to recover the single node that failed, instead of shutting down all workers. The rest of the clusters wait until the single failed worker is bootstrapped and catches up with the rest. * See roadmap at #4753. Note that this is work in progress. In particular, the feature is not yet available from XGBoost4J-Spark. ### Accurate prediction for DART models * Use DART tree weights when computing SHAPs (#5050) * Don't drop trees during DART prediction by default (#5115) * Fix DART prediction in R (#5204) ### Make external memory more robust * Fix issues with training with external memory on cpu (#4487) * Fix crash with approx tree method on cpu (#4510) * Fix external memory race in `exact` (#4980). Note: `dmlc::ThreadedIter` is not actually thread-safe. We would like to re-design it in the long term. ### Major refactoring of the `DMatrix` class (#4686, #4744, #4748, #5044, #5092, #5108, #5188, #5198) * Goal 1: improve performance and reduce memory consumption. Right now, if the user trains a model with a NumPy array as training data, the array gets copies 2-3 times before training begins. We'd like to reduce duplication of the data matrix. * Goal 2: Expose a common interface to external data, unify the way DMatrix objects are constructed and simplify the process of adding new external data sources. This work is essential for ingesting cuPy arrays. * Goal 3: Handle missing values consistently. * RFC: #4354, Roadmap: #5143 * This work is also relevant to external memory support on GPUs. ### Breaking: XGBoost Python package now requires Python 3.5 or newer (#5021, #5274) * Python 3.4 has reached its end-of-life on March 16, 2019, so we now require Python 3.5 or newer. ### Breaking: GPU algorithm now requires CUDA 9.0 and higher (#4527, #4580) ### Breaking: `n_gpus` parameter removed; multi-GPU training now requires a distributed framework (#4579, #4749, #4773, #4810, #4867, #4908) * #4531 proposed removing support for single-process multi-GPU training. Contributors would focus on multi-GPU support through distributed frameworks such as Dask and Spark, where the framework would be expected to assign a worker process for each GPU independently. By delegating GPU management and data movement to the distributed framework, we can greatly simplify the core XGBoost codebase, make multi-GPU training more robust, and reduce burden for future development. ### Breaking: Some deprecated features have been removed * ``gpu_exact`` training method (#4527, #4742, #4777). Use ``gpu_hist`` instead. * ``learning_rates`` parameter in Python (#5155). Use the callback API instead. * ``num_roots`` (#5059, #5165), since the current training code always uses a single root node. * GPU-specific objectives (#4690), such as `gpu:reg:linear`. Use objectives without `gpu:` prefix; GPU will be used automatically if your machine has one. ### Breaking: the C API function `XGBoosterPredict()` now asks for an extra parameter `training`. ### Breaking: We now use CMake exclusively to build XGBoost. `Makefile` is being sunset. * Exception: the R package uses Autotools, as the CRAN ecosystem did not yet adopt CMake widely. ### Performance improvements * Smarter choice of histogram construction for distributed `gpu_hist` (#4519) * Optimizations for quantization on device (#4572) * Introduce caching memory allocator to avoid latency associated with GPU memory allocation (#4554, #4615) * Optimize the initialization stage of the CPU `hist` algorithm for sparse datasets (#4625) * Prevent unnecessary data copies from GPU memory to the host (#4795) * Improve operation efficiency for single prediction (#5016) * Group builder modified for incremental building, to speed up building large `DMatrix` (#5098) ### Bug-fixes * Eliminate `FutureWarning: Series.base is deprecated` (#4337) * Ensure pandas DataFrame column names are treated as strings in type error message (#4481) * [jvm-packages] Add back `reg:linear` for scala, as it is only deprecated and not meant to be removed yet (#4490) * Fix library loading for Cygwin users (#4499) * Fix prediction from loaded pickle (#4516) * Enforce exclusion between `pred_interactions=True` and `pred_interactions=True` (#4522) * Do not return dangling reference to local `std::string` (#4543) * Set the appropriate device before freeing device memory (#4566) * Mark `SparsePageDmatrix` destructor default. (#4568) * Choose the appropriate tree method only when the tree method is 'auto' (#4571) * Fix `benchmark_tree.py` (#4593) * [jvm-packages] Fix silly bug in feature scoring (#4604) * Fix GPU predictor when the test data matrix has different number of features than the training data matrix used to train the model (#4613) * Fix external memory for get column batches. (#4622) * [R] Use built-in label when xgb.DMatrix is given to xgb.cv() (#4631) * Fix early stopping in the Python package (#4638) * Fix AUC error in distributed mode caused by imbalanced dataset (#4645, #4798) * [jvm-packages] Expose `setMissing` method in `XGBoostClassificationModel` / `XGBoostRegressionModel` (#4643) * Remove initializing stringstream reference. (#4788) * [R] `xgb.get.handle` now checks all class listed of `object` (#4800) * Do not use `gpu_predictor` unless data comes from GPU (#4836) * Fix data loading (#4862) * Workaround `isnan` across different environments. (#4883) * [jvm-packages] Handle Long-type parameter (#4885) * Don't `set_params` at the end of `set_state` (#4947). Ensure that the model does not change after pickling and unpickling multiple times. * C++ exceptions should not crash OpenMP loops (#4960) * Fix `usegpu` flag in DART. (#4984) * Run training with empty `DMatrix` (#4990, #5159) * Ensure that no two processes can use the same GPU (#4990) * Fix repeated split and 0 cover nodes (#5010) * Reset histogram hit counter between multiple data batches (#5035) * Fix `feature_name` crated from int64index dataframe. (#5081) * Don't use 0 for "fresh leaf" (#5084) * Throw error when user attempts to use multi-GPU training and XGBoost has not been compiled with NCCL (#5170) * Fix metric name loading (#5122) * Quick fix for memory leak in CPU `hist` algorithm (#5153) * Fix wrapping GPU ID and prevent data copying (#5160) * Fix signature of Span constructor (#5166) * Lazy initialization of device vector, so that XGBoost compiled with CUDA can run on a machine without any GPU (#5173) * Model loading should not change system locale (#5314) * Distributed training jobs would sometimes hang; revert Rabit to fix this regression (dmlc/rabit#132, #5237) ### API changes * Add support for cross-validation using query ID (#4474) * Enable feature importance property for DART model (#4525) * Add `rmsle` metric and `reg:squaredlogerror` objective (#4541) * All objective and evaluation metrics are now exposed to JVM packages (#4560) * `dump_model()` and `get_dump()` now support exporting in GraphViz language (#4602) * Support metrics `ndcg-` and `map-` (#4635) * [jvm-packages] Allow chaining prediction (transform) in XGBoost4J-Spark (#4667) * [jvm-packages] Add option to bypass missing value check in the Spark layer (#4805). Only use this option if you know what you are doing. * [jvm-packages] Add public group getter (#4838) * `XGDMatrixSetGroup` C API is now deprecated (#4864). Use `XGDMatrixSetUIntInfo` instead. * [R] Added new `train_folds` parameter to `xgb.cv()` (#5114) * Ingest meta information from Pandas DataFrame, such as data weights (#5216) ### Maintenance: Refactor code for legibility and maintainability * De-duplicate GPU parameters (#4454) * Simplify INI-style config reader using C++11 STL (#4478, #4521) * Refactor histogram building code for `gpu_hist` (#4528) * Overload device memory allocator, to enable instrumentation for compiling memory usage statistics (#4532) * Refactor out row partitioning logic from `gpu_hist` (#4554) * Remove an unused variable (#4588) * Implement tree model dump with code generator, to de-duplicate code for generating dumps in 3 different formats (#4602) * Remove `RowSet` class which is no longer being used (#4697) * Remove some unused functions as reported by cppcheck (#4743) * Mimic CUDA assert output in Span check (#4762) * [jvm-packages] Refactor `XGBoost.scala` to put all params processing in one place (#4815) * Add some comments for GPU row partitioner (#4832) * Span: use `size_t' for index_type, add `front' and `back'. (#4935) * Remove dead code in `exact` algorithm (#5034, #5105) * Unify integer types used for row and column indices (#5034) * Extract feature interaction constraint from `SplitEvaluator` class. (#5034) * [Breaking] De-duplicate paramters and docstrings in the constructors of Scikit-Learn models (#5130) * Remove benchmark code from GPU tests (#5141) * Clean up Python 2 compatibility code. (#5161) * Extensible binary serialization format for `DMatrix::MetaInfo` (#5187). This will be useful for implementing censored labels for survival analysis applications. * Cleanup clang-tidy warnings. (#5247) ### Maintenance: testing, continuous integration, build system * Use `yaml.safe_load` instead of `yaml.load`. (#4537) * Ensure GCC is at least 5.x (#4538) * Remove all mention of `reg:linear` from tests (#4544) * [jvm-packages] Upgrade to Scala 2.12 (#4574) * [jvm-packages] Update kryo dependency to 2.22 (#4575) * [CI] Specify account ID when logging into ECR Docker registry (#4584) * Use Sphinx 2.1+ to compile documentation (#4609) * Make Pandas optional for running Python unit tests (#4620) * Fix spark tests on machines with many cores (#4634) * [jvm-packages] Update local dev build process (#4640) * Add optional dependencies to setup.py (#4655) * [jvm-packages] Fix maven warnings (#4664) * Remove extraneous files from the R package, to comply with CRAN policy (#4699) * Remove VC-2013 support, since it is not C++11 compliant (#4701) * [CI] Fix broken installation of Pandas (#4704, #4722) * [jvm-packages] Clean up temporary files afer running tests (#4706) * Specify version macro in CMake. (#4730) * Include dmlc-tracker into XGBoost Python package (#4731) * [CI] Use long key ID for Ubuntu repository fingerprints. (#4783) * Remove plugin, CUDA related code in automake & autoconf files (#4789) * Skip related tests when scikit-learn is not installed. (#4791) * Ignore vscode and clion files (#4866) * Use bundled Google Test by default (#4900) * [CI] Raise timeout threshold in Jenkins (#4938) * Copy CMake parameter from dmlc-core. (#4948) * Set correct file permission. (#4964) * [CI] Update lint configuration to support latest pylint convention (#4971) * [CI] Upload nightly builds to S3 (#4976, #4979) * Add asan.so.5 to cmake script. (#4999) * [CI] Fix Travis tests. (#5062) * [CI] Locate vcomp140.dll from System32 directory (#5078) * Implement training observer to dump internal states of objects (#5088). This will be useful for debugging. * Fix visual studio output library directories (#5119) * [jvm-packages] Comply with scala style convention + fix broken unit test (#5134) * [CI] Repair download URL for Maven 3.6.1 (#5139) * Don't use modernize-use-trailing-return-type in clang-tidy. (#5169) * Explicitly use UTF-8 codepage when using MSVC (#5197) * Add CMake option to run Undefined Behavior Sanitizer (UBSan) (#5211) * Make some GPU tests deterministic (#5229) * [R] Robust endian detection in CRAN xgboost build (#5232) * Support FreeBSD (#5233) * Make `pip install xgboost*.tar.gz` work by fixing build-python.sh (#5241) * Fix compilation error due to 64-bit integer narrowing to `size_t` (#5250) * Remove use of `std::cout` from R package, to comply with CRAN policy (#5261) * Update DMLC-Core submodule (#4674, #4688, #4726, #4924) * Update Rabit submodule (#4560, #4667, #4718, #4808, #4966, #5237) ### Usability Improvements, Documentation * Add Random Forest API to Python API doc (#4500) * Fix Python demo and doc. (#4545) * Remove doc about not supporting CUDA 10.1 (#4578) * Address some sphinx warnings and errors, add doc for building doc. (#4589) * Add instruction to run formatting checks locally (#4591) * Fix docstring for `XGBModel.predict()` (#4592) * Doc and demo for customized metric and objective (#4598, #4608) * Add to documentation how to run tests locally (#4610) * Empty evaluation list in early stopping should produce meaningful error message (#4633) * Fixed year to 2019 in conf.py, helpers.h and LICENSE (#4661) * Minor updates to links and grammar (#4673) * Remove `silent` in doc (#4689) * Remove old Python trouble shooting doc (#4729) * Add `os.PathLike` support for file paths to DMatrix and Booster Python classes (#4757) * Update XGBoost4J-Spark doc (#4804) * Regular formatting for evaluation metrics (#4803) * [jvm-packages] Refine documentation for handling missing values in XGBoost4J-Spark (#4805) * Monitor for distributed environment (#4829). This is useful for identifying performance bottleneck. * Add check for length of weights and produce a good error message (#4872) * Fix DMatrix doc (#4884) * Export C++ headers in CMake installation (#4897) * Update license year in README.md to 2019 (#4940) * Fix incorrectly displayed Note in the doc (#4943) * Follow PEP 257 Docstring Conventions (#4959) * Document minimum version required for Google Test (#5001) * Add better error message for invalid feature names (#5024) * Some guidelines on device memory usage (#5038) * [doc] Some notes for external memory. (#5065) * Update document for `tree_method` (#5106) * Update demo for ranking. (#5154) * Add new lines for Spark XGBoost missing values section (#5180) * Fix simple typo: utilty -> utility (#5182) * Update R doc by roxygen2 (#5201) * [R] Direct user to use `set.seed()` instead of setting `seed` parameter (#5125) * Add Optuna badge to `README.md` (#5208) * Fix compilation error in `c-api-demo.c` (#5215) ### Acknowledgement **Contributors**: Nan Zhu (@CodingCat), Crissman Loomis (@Crissman), Cyprien Ricque (@Cyprien-Ricque), Evan Kepner (@EvanKepner), K.O. (@Hi-king), KaiJin Ji (@KerryJi), Peter Badida (@KeyWeeUsr), Kodi Arfer (@Kodiologist), Rory Mitchell (@RAMitchell), Egor Smirnov (@SmirnovEgorRu), Jacob Kim (@TheJacobKim), Vibhu Jawa (@VibhuJawa), Marcos (@astrowonk), Andy Adinets (@canonizer), Chen Qin (@chenqin), Christopher Cowden (@cowden), @cpfarrell, @david-cortes, Liangcai Li (@firestarman), @fuhaoda, Philip Hyunsu Cho (@hcho3), @here-nagini, Tong He (@hetong007), Michal Kurka (@michalkurka), Honza Sterba (@honzasterba), @iblumin, @koertkuipers, mattn (@mattn), Mingjie Tang (@merlintang), OrdoAbChao (@mglowacki100), Matthew Jones (@mt-jones), mitama (@nigimitama), Nathan Moore (@nmoorenz), Daniel Stahl (@phillyfan1138), Michaël Benesty (@pommedeterresautee), Rong Ou (@rongou), Sebastian (@sfahnens), Xu Xiao (@sperlingxx), @sriramch, Sean Owen (@srowen), Stephanie Yang (@stpyang), Yuan Tang (@terrytangyuan), Mathew Wicks (@thesuperzapper), Tim Gates (@timgates42), TinkleG (@tinkle1129), Oleksandr Pryimak (@trams), Jiaming Yuan (@trivialfis), Matvey Turkov (@turk0v), Bobby Wang (@wbo4958), yage (@yage99), @yellowdolphin **Reviewers**: Nan Zhu (@CodingCat), Crissman Loomis (@Crissman), Cyprien Ricque (@Cyprien-Ricque), Evan Kepner (@EvanKepner), John Zedlewski (@JohnZed), KOLANICH (@KOLANICH), KaiJin Ji (@KerryJi), Kodi Arfer (@Kodiologist), Rory Mitchell (@RAMitchell), Egor Smirnov (@SmirnovEgorRu), Nikita Titov (@StrikerRUS), Jacob Kim (@TheJacobKim), Vibhu Jawa (@VibhuJawa), Andrew Kane (@ankane), Arno Candel (@arnocandel), Marcos (@astrowonk), Bryan Woods (@bryan-woods), Andy Adinets (@canonizer), Chen Qin (@chenqin), Thomas Franke (@coding-komek), Peter (@codingforfun), @cpfarrell, Joshua Patterson (@datametrician), @fuhaoda, Philip Hyunsu Cho (@hcho3), Tong He (@hetong007), Honza Sterba (@honzasterba), @iblumin, @jakirkham, Vadim Khotilovich (@khotilov), Keith Kraus (@kkraus14), @koertkuipers, @melonki, Mingjie Tang (@merlintang), OrdoAbChao (@mglowacki100), Daniel Mahler (@mhlr), Matthew Rocklin (@mrocklin), Matthew Jones (@mt-jones), Michaël Benesty (@pommedeterresautee), PSEUDOTENSOR / Jonathan McKinney (@pseudotensor), Rong Ou (@rongou), Vladimir (@sh1ng), Scott Lundberg (@slundberg), Xu Xiao (@sperlingxx), @sriramch, Pasha Stetsenko (@st-pasha), Stephanie Yang (@stpyang), Yuan Tang (@terrytangyuan), Mathew Wicks (@thesuperzapper), Theodore Vasiloudis (@thvasilo), TinkleG (@tinkle1129), Oleksandr Pryimak (@trams), Jiaming Yuan (@trivialfis), Bobby Wang (@wbo4958), yage (@yage99), @yellowdolphin, Yin Lou (@yinlou) ## v0.90 (2019.05.18) ### XGBoost Python package drops Python 2.x (#4379, #4381) Python 2.x is reaching its end-of-life at the end of this year. [Many scientific Python packages are now moving to drop Python 2.x](https://python3statement.org/). ### XGBoost4J-Spark now requires Spark 2.4.x (#4377) * Spark 2.3 is reaching its end-of-life soon. See discussion at #4389. * **Consistent handling of missing values** (#4309, #4349, #4411): Many users had reported issue with inconsistent predictions between XGBoost4J-Spark and the Python XGBoost package. The issue was caused by Spark mis-handling non-zero missing values (NaN, -1, 999 etc). We now alert the user whenever Spark doesn't handle missing values correctly (#4309, #4349). See [the tutorial for dealing with missing values in XGBoost4J-Spark](https://xgboost.readthedocs.io/en/release_0.90/jvm/xgboost4j_spark_tutorial.html#dealing-with-missing-values). This fix also depends on the availability of Spark 2.4.x. ### Roadmap: better performance scaling for multi-core CPUs (#4310) * Poor performance scaling of the `hist` algorithm for multi-core CPUs has been under investigation (#3810). #4310 optimizes quantile sketches and other pre-processing tasks. Special thanks to @SmirnovEgorRu. ### Roadmap: Harden distributed training (#4250) * Make distributed training in XGBoost more robust by hardening [Rabit](https://github.com/dmlc/rabit), which implements [the AllReduce primitive](https://en.wikipedia.org/wiki/Reduce_%28parallel_pattern%29). In particular, improve test coverage on mechanisms for fault tolerance and recovery. Special thanks to @chenqin. ### New feature: Multi-class metric functions for GPUs (#4368) * Metrics for multi-class classification have been ported to GPU: `merror`, `mlogloss`. Special thanks to @trivialfis. * With supported metrics, XGBoost will select the correct devices based on your system and `n_gpus` parameter. ### New feature: Scikit-learn-like random forest API (#4148, #4255, #4258) * XGBoost Python package now offers `XGBRFClassifier` and `XGBRFRegressor` API to train random forests. See [the tutorial](https://xgboost.readthedocs.io/en/release_0.90/tutorials/rf.html). Special thanks to @canonizer ### New feature: use external memory in GPU predictor (#4284, #4396, #4438, #4457) * It is now possible to make predictions on GPU when the input is read from external memory. This is useful when you want to make predictions with big dataset that does not fit into the GPU memory. Special thanks to @rongou, @canonizer, @sriramch. ```python dtest = xgboost.DMatrix('test_data.libsvm#dtest.cache') bst.set_param('predictor', 'gpu_predictor') bst.predict(dtest) ``` * Coming soon: GPU training (`gpu_hist`) with external memory ### New feature: XGBoost can now handle comments in LIBSVM files (#4430) * Special thanks to @trivialfis and @hcho3 ### New feature: Embed XGBoost in your C/C++ applications using CMake (#4323, #4333, #4453) * It is now easier than ever to embed XGBoost in your C/C++ applications. In your CMakeLists.txt, add `xgboost::xgboost` as a linked library: ```cmake find_package(xgboost REQUIRED) add_executable(api-demo c-api-demo.c) target_link_libraries(api-demo xgboost::xgboost) ``` [XGBoost C API documentation is available.](https://xgboost.readthedocs.io/en/release_0.90/dev) Special thanks to @trivialfis ### Performance improvements * Use feature interaction constraints to narrow split search space (#4341, #4428) * Additional optimizations for `gpu_hist` (#4248, #4283) * Reduce OpenMP thread launches in `gpu_hist` (#4343) * Additional optimizations for multi-node multi-GPU random forests. (#4238) * Allocate unique prediction buffer for each input matrix, to avoid re-sizing GPU array (#4275) * Remove various synchronisations from CUDA API calls (#4205) * XGBoost4J-Spark - Allow the user to control whether to cache partitioned training data, to potentially reduce execution time (#4268) ### Bug-fixes * Fix node reuse in `hist` (#4404) * Fix GPU histogram allocation (#4347) * Fix matrix attributes not sliced (#4311) * Revise AUC and AUCPR metrics now work with weighted ranking task (#4216, #4436) * Fix timer invocation for InitDataOnce() in `gpu_hist` (#4206) * Fix R-devel errors (#4251) * Make gradient update in GPU linear updater thread-safe (#4259) * Prevent out-of-range access in column matrix (#4231) * Don't store DMatrix handle in Python object until it's initialized, to improve exception safety (#4317) * XGBoost4J-Spark - Fix non-deterministic order within a zipped partition on prediction (#4388) - Remove race condition on tracker shutdown (#4224) - Allow set the parameter `maxLeaves`. (#4226) - Allow partial evaluation of dataframe before prediction (#4407) - Automatically set `maximize_evaluation_metrics` if not explicitly given (#4446) ### API changes * Deprecate `reg:linear` in favor of `reg:squarederror`. (#4267, #4427) * Add attribute getter and setter to the Booster object in XGBoost4J (#4336) ### Maintenance: Refactor C++ code for legibility and maintainability * Fix clang-tidy warnings. (#4149) * Remove deprecated C APIs. (#4266) * Use Monitor class to time functions in `hist`. (#4273) * Retire DVec class in favour of c++20 style span for device memory. (#4293) * Improve HostDeviceVector exception safety (#4301) ### Maintenance: testing, continuous integration, build system * **Major refactor of CMakeLists.txt** (#4323, #4333, #4453): adopt modern CMake and export XGBoost as a target * **Major improvement in Jenkins CI pipeline** (#4234) - Migrate all Linux tests to Jenkins (#4401) - Builds and tests are now de-coupled, to test an artifact against multiple versions of CUDA, JDK, and other dependencies (#4401) - Add Windows GPU to Jenkins CI pipeline (#4463, #4469) * Support CUDA 10.1 (#4223, #4232, #4265, #4468) * Python wheels are now built with CUDA 9.0, so that JIT is not required on Volta architecture (#4459) * Integrate with NVTX CUDA profiler (#4205) * Add a test for cpu predictor using external memory (#4308) * Refactor tests to get rid of duplication (#4358) * Remove test dependency on `craigcitro/r-travis`, since it's deprecated (#4353) * Add files from local R build to `.gitignore` (#4346) * Make XGBoost4J compatible with Java 9+ by revising NativeLibLoader (#4351) * Jenkins build for CUDA 10.0 (#4281) * Remove remaining `silent` and `debug_verbose` in Python tests (#4299) * Use all cores to build XGBoost4J lib on linux (#4304) * Upgrade Jenkins Linux build environment to GCC 5.3.1, CMake 3.6.0 (#4306) * Make CMakeLists.txt compatible with CMake 3.3 (#4420) * Add OpenMP option in CMakeLists.txt (#4339) * Get rid of a few trivial compiler warnings (#4312) * Add external Docker build cache, to speed up builds on Jenkins CI (#4331, #4334, #4458) * Fix Windows tests (#4403) * Fix a broken python test (#4395) * Use a fixed seed to split data in XGBoost4J-Spark tests, for reproducibility (#4417) * Add additional Python tests to test training under constraints (#4426) * Enable building with shared NCCL. (#4447) ### Usability Improvements, Documentation * Document limitation of one-split-at-a-time Greedy tree learning heuristic (#4233) * Update build doc: PyPI wheel now support multi-GPU (#4219) * Fix docs for `num_parallel_tree` (#4221) * Fix document about `colsample_by*` parameter (#4340) * Make the train and test input with same colnames. (#4329) * Update R contribute link. (#4236) * Fix travis R tests (#4277) * Log version number in crash log in XGBoost4J-Spark (#4271, #4303) * Allow supression of Rabit output in Booster::train in XGBoost4J (#4262) * Add tutorial on handling missing values in XGBoost4J-Spark (#4425) * Fix typos (#4345, #4393, #4432, #4435) * Added language classifier in setup.py (#4327) * Added Travis CI badge (#4344) * Add BentoML to use case section (#4400) * Remove subtly sexist remark (#4418) * Add R vignette about parsing JSON dumps (#4439) ### Acknowledgement **Contributors**: Nan Zhu (@CodingCat), Adam Pocock (@Craigacp), Daniel Hen (@Daniel8hen), Jiaxiang Li (@JiaxiangBU), Rory Mitchell (@RAMitchell), Egor Smirnov (@SmirnovEgorRu), Andy Adinets (@canonizer), Jonas (@elcombato), Harry Braviner (@harrybraviner), Philip Hyunsu Cho (@hcho3), Tong He (@hetong007), James Lamb (@jameslamb), Jean-Francois Zinque (@jeffzi), Yang Yang (@jokerkeny), Mayank Suman (@mayanksuman), jess (@monkeywithacupcake), Hajime Morrita (@omo), Ravi Kalia (@project-delphi), @ras44, Rong Ou (@rongou), Shaochen Shi (@shishaochen), Xu Xiao (@sperlingxx), @sriramch, Jiaming Yuan (@trivialfis), Christopher Suchanek (@wsuchy), Bozhao (@yubozhao) **Reviewers**: Nan Zhu (@CodingCat), Adam Pocock (@Craigacp), Daniel Hen (@Daniel8hen), Jiaxiang Li (@JiaxiangBU), Laurae (@Laurae2), Rory Mitchell (@RAMitchell), Egor Smirnov (@SmirnovEgorRu), @alois-bissuel, Andy Adinets (@canonizer), Chen Qin (@chenqin), Harry Braviner (@harrybraviner), Philip Hyunsu Cho (@hcho3), Tong He (@hetong007), @jakirkham, James Lamb (@jameslamb), Julien Schueller (@jschueller), Mayank Suman (@mayanksuman), Hajime Morrita (@omo), Rong Ou (@rongou), Sara Robinson (@sararob), Shaochen Shi (@shishaochen), Xu Xiao (@sperlingxx), @sriramch, Sean Owen (@srowen), Sergei Lebedev (@superbobry), Yuan (Terry) Tang (@terrytangyuan), Theodore Vasiloudis (@thvasilo), Matthew Tovbin (@tovbinm), Jiaming Yuan (@trivialfis), Xin Yin (@xydrolase) ## v0.82 (2019.03.03) This release is packed with many new features and bug fixes. ### Roadmap: better performance scaling for multi-core CPUs (#3957) * Poor performance scaling of the `hist` algorithm for multi-core CPUs has been under investigation (#3810). #3957 marks an important step toward better performance scaling, by using software pre-fetching and replacing STL vectors with C-style arrays. Special thanks to @Laurae2 and @SmirnovEgorRu. * See #3810 for latest progress on this roadmap. ### New feature: Distributed Fast Histogram Algorithm (`hist`) (#4011, #4102, #4140, #4128) * It is now possible to run the `hist` algorithm in distributed setting. Special thanks to @CodingCat. The benefits include: 1. Faster local computation via feature binning 2. Support for monotonic constraints and feature interaction constraints 3. Simpler codebase than `approx`, allowing for future improvement * Depth-wise tree growing is now performed in a separate code path, so that cross-node syncronization is performed only once per level. ### New feature: Multi-Node, Multi-GPU training (#4095) * Distributed training is now able to utilize clusters equipped with NVIDIA GPUs. In particular, the rabit AllReduce layer will communicate GPU device information. Special thanks to @mt-jones, @RAMitchell, @rongou, @trivialfis, @canonizer, and @jeffdk. * Resource management systems will be able to assign a rank for each GPU in the cluster. * In Dask, users will be able to construct a collection of XGBoost processes over an inhomogeneous device cluster (i.e. workers with different number and/or kinds of GPUs). ### New feature: Multiple validation datasets in XGBoost4J-Spark (#3904, #3910) * You can now track the performance of the model during training with multiple evaluation datasets. By specifying `eval_sets` or call `setEvalSets` over a `XGBoostClassifier` or `XGBoostRegressor`, you can pass in multiple evaluation datasets typed as a `Map` from `String` to `DataFrame`. Special thanks to @CodingCat. * See the usage of multiple validation datasets [here](https://github.com/dmlc/xgboost/blob/0c1d5f1120c0a159f2567b267f0ec4ffadee00d0/jvm-packages/xgboost4j-example/src/main/scala/ml/dmlc/xgboost4j/scala/example/spark/SparkTraining.scala#L66-L78) ### New feature: Additional metric functions for GPUs (#3952) * Element-wise metrics have been ported to GPU: `rmse`, `mae`, `logloss`, `poisson-nloglik`, `gamma-deviance`, `gamma-nloglik`, `error`, `tweedie-nloglik`. Special thanks to @trivialfis and @RAMitchell. * With supported metrics, XGBoost will select the correct devices based on your system and `n_gpus` parameter. ### New feature: Column sampling at individual nodes (splits) (#3971) * Columns (features) can now be sampled at individual tree nodes, in addition to per-tree and per-level sampling. To enable per-node sampling, set `colsample_bynode` parameter, which represents the fraction of columns sampled at each node. This parameter is set to 1.0 by default (i.e. no sampling per node). Special thanks to @canonizer. * The `colsample_bynode` parameter works cumulatively with other `colsample_by*` parameters: for example, `{'colsample_bynode':0.5, 'colsample_bytree':0.5}` with 100 columns will give 25 features to choose from at each split. ### Major API change: consistent logging level via `verbosity` (#3982, #4002, #4138) * XGBoost now allows fine-grained control over logging. You can set `verbosity` to 0 (silent), 1 (warning), 2 (info), and 3 (debug). This is useful for controlling the amount of logging outputs. Special thanks to @trivialfis. * Parameters `silent` and `debug_verbose` are now deprecated. * Note: Sometimes XGBoost tries to change configurations based on heuristics, which is displayed as warning message. If there's unexpected behaviour, please try to increase value of verbosity. ### Major bug fix: external memory (#4040, #4193) * Clarify object ownership in multi-threaded prefetcher, to avoid memory error. * Correctly merge two column batches (which uses [CSC layout](https://en.wikipedia.org/wiki/Sparse_matrix#Compressed_sparse_column_(CSC_or_CCS))). * Add unit tests for external memory. * Special thanks to @trivialfis and @hcho3. ### Major bug fix: early stopping fixed in XGBoost4J and XGBoost4J-Spark (#3928, #4176) * Early stopping in XGBoost4J and XGBoost4J-Spark is now consistent with its counterpart in the Python package. Training stops if the current iteration is `earlyStoppingSteps` away from the best iteration. If there are multiple evaluation sets, only the last one is used to determinate early stop. * See the updated documentation [here](https://xgboost.readthedocs.io/en/release_0.82/jvm/xgboost4j_spark_tutorial.html#early-stopping) * Special thanks to @CodingCat, @yanboliang, and @mingyang. ### Major bug fix: infrequent features should not crash distributed training (#4045) * For infrequently occuring features, some partitions may not get any instance. This scenario used to crash distributed training due to mal-formed ranges. The problem has now been fixed. * In practice, one-hot-encoded categorical variables tend to produce rare features, particularly when the cardinality is high. * Special thanks to @CodingCat. ### Performance improvements * Faster, more space-efficient radix sorting in `gpu_hist` (#3895) * Subtraction trick in histogram calculation in `gpu_hist` (#3945) * More performant re-partition in XGBoost4J-Spark (#4049) ### Bug-fixes * Fix semantics of `gpu_id` when running multiple XGBoost processes on a multi-GPU machine (#3851) * Fix page storage path for external memory on Windows (#3869) * Fix configuration setup so that DART utilizes GPU (#4024) * Eliminate NAN values from SHAP prediction (#3943) * Prevent empty quantile sketches in `hist` (#4155) * Enable running objectives with 0 GPU (#3878) * Parameters are no longer dependent on system locale (#3891, #3907) * Use consistent data type in the GPU coordinate descent code (#3917) * Remove undefined behavior in the CLI config parser on the ARM platform (#3976) * Initialize counters in GPU AllReduce (#3987) * Prevent deadlocks in GPU AllReduce (#4113) * Load correct values from sliced NumPy arrays (#4147, #4165) * Fix incorrect GPU device selection (#4161) * Make feature binning logic in `hist` aware of query groups when running a ranking task (#4115). For ranking task, query groups are weighted, not individual instances. * Generate correct C++ exception type for `LOG(FATAL)` macro (#4159) * Python package - Python package should run on system without `PATH` environment variable (#3845) - Fix `coef_` and `intercept_` signature to be compatible with `sklearn.RFECV` (#3873) - Use UTF-8 encoding in Python package README, to support non-English locale (#3867) - Add AUC-PR to list of metrics to maximize for early stopping (#3936) - Allow loading pickles without `self.booster` attribute, for backward compatibility (#3938, #3944) - White-list DART for feature importances (#4073) - Update usage of [h2oai/datatable](https://github.com/h2oai/datatable) (#4123) * XGBoost4J-Spark - Address scalability issue in prediction (#4033) - Enforce the use of per-group weights for ranking task (#4118) - Fix vector size of `rawPredictionCol` in `XGBoostClassificationModel` (#3932) - More robust error handling in Spark tracker (#4046, #4108) - Fix return type of `setEvalSets` (#4105) - Return correct value of `getMaxLeaves` (#4114) ### API changes * Add experimental parameter `single_precision_histogram` to use single-precision histograms for the `gpu_hist` algorithm (#3965) * Python package - Add option to select type of feature importances in the scikit-learn inferface (#3876) - Add `trees_to_df()` method to dump decision trees as Pandas data frame (#4153) - Add options to control node shapes in the GraphViz plotting function (#3859) - Add `xgb_model` option to `XGBClassifier`, to load previously saved model (#4092) - Passing lists into `DMatrix` is now deprecated (#3970) * XGBoost4J - Support multiple feature importance features (#3801) ### Maintenance: Refactor C++ code for legibility and maintainability * Refactor `hist` algorithm code and add unit tests (#3836) * Minor refactoring of split evaluator in `gpu_hist` (#3889) * Removed unused leaf vector field in the tree model (#3989) * Simplify the tree representation by combining `TreeModel` and `RegTree` classes (#3995) * Simplify and harden tree expansion code (#4008, #4015) * De-duplicate parameter classes in the linear model algorithms (#4013) * Robust handling of ranges with C++20 span in `gpu_exact` and `gpu_coord_descent` (#4020, #4029) * Simplify tree training code (#3825). Also use Span class for robust handling of ranges. ### Maintenance: testing, continuous integration, build system * Disallow `std::regex` since it's not supported by GCC 4.8.x (#3870) * Add multi-GPU tests for coordinate descent algorithm for linear models (#3893, #3974) * Enforce naming style in Python lint (#3896) * Refactor Python tests (#3897, #3901): Use pytest exclusively, display full trace upon failure * Address `DeprecationWarning` when using Python collections (#3909) * Use correct group for maven site plugin (#3937) * Jenkins CI is now using on-demand EC2 instances exclusively, due to unreliability of Spot instances (#3948) * Better GPU performance logging (#3945) * Fix GPU tests on machines with only 1 GPU (#4053) * Eliminate CRAN check warnings and notes (#3988) * Add unit tests for tree serialization (#3989) * Add unit tests for tree fitting functions in `hist` (#4155) * Add a unit test for `gpu_exact` algorithm (#4020) * Correct JVM CMake GPU flag (#4071) * Fix failing Travis CI on Mac (#4086) * Speed up Jenkins by not compiling CMake (#4099) * Analyze C++ and CUDA code using clang-tidy, as part of Jenkins CI pipeline (#4034) * Fix broken R test: Install Homebrew GCC (#4142) * Check for empty datasets in GPU unit tests (#4151) * Fix Windows compilation (#4139) * Comply with latest convention of cpplint (#4157) * Fix a unit test in `gpu_hist` (#4158) * Speed up data generation in Python tests (#4164) ### Usability Improvements * Add link to [InfoWorld 2019 Technology of the Year Award](https://www.infoworld.com/article/3336072/application-development/infoworlds-2019-technology-of-the-year-award-winners.html) (#4116) * Remove outdated AWS YARN tutorial (#3885) * Document current limitation in number of features (#3886) * Remove unnecessary warning when `gblinear` is selected (#3888) * Document limitation of CSV parser: header not supported (#3934) * Log training parameters in XGBoost4J-Spark (#4091) * Clarify early stopping behavior in the scikit-learn interface (#3967) * Clarify behavior of `max_depth` parameter (#4078) * Revise Python docstrings for ranking task (#4121). In particular, weights must be per-group in learning-to-rank setting. * Document parameter `num_parallel_tree` (#4022) * Add Jenkins status badge (#4090) * Warn users against using internal functions of `Booster` object (#4066) * Reformat `benchmark_tree.py` to comply with Python style convention (#4126) * Clarify a comment in `objectiveTrait` (#4174) * Fix typos and broken links in documentation (#3890, #3872, #3902, #3919, #3975, #4027, #4156, #4167) ### Acknowledgement **Contributors** (in no particular order): Jiaming Yuan (@trivialfis), Hyunsu Cho (@hcho3), Nan Zhu (@CodingCat), Rory Mitchell (@RAMitchell), Yanbo Liang (@yanboliang), Andy Adinets (@canonizer), Tong He (@hetong007), Yuan Tang (@terrytangyuan) **First-time Contributors** (in no particular order): Jelle Zijlstra (@JelleZijlstra), Jiacheng Xu (@jiachengxu), @ajing, Kashif Rasul (@kashif), @theycallhimavi, Joey Gao (@pjgao), Prabakaran Kumaresshan (@nixphix), Huafeng Wang (@huafengw), @lyxthe, Sam Wilkinson (@scwilkinson), Tatsuhito Kato (@stabacov), Shayak Banerjee (@shayakbanerjee), Kodi Arfer (@Kodiologist), @KyleLi1985, Egor Smirnov (@SmirnovEgorRu), @tmitanitky, Pasha Stetsenko (@st-pasha), Kenichi Nagahara (@keni-chi), Abhai Kollara Dilip (@abhaikollara), Patrick Ford (@pford221), @hshujuan, Matthew Jones (@mt-jones), Thejaswi Rao (@teju85), Adam November (@anovember) **First-time Reviewers** (in no particular order): Mingyang Hu (@mingyang), Theodore Vasiloudis (@thvasilo), Jakub Troszok (@troszok), Rong Ou (@rongou), @Denisevi4, Matthew Jones (@mt-jones), Jeff Kaplan (@jeffdk) ## v0.81 (2018.11.04) ### New feature: feature interaction constraints * Users are now able to control which features (independent variables) are allowed to interact by specifying feature interaction constraints (#3466). * [Tutorial](https://xgboost.readthedocs.io/en/release_0.81/tutorials/feature_interaction_constraint.html) is available, as well as [R](https://github.com/dmlc/xgboost/blob/9254c58e4dfff6a59dc0829a2ceb02e45ed17cd0/R-package/demo/interaction_constraints.R) and [Python](https://github.com/dmlc/xgboost/blob/9254c58e4dfff6a59dc0829a2ceb02e45ed17cd0/tests/python/test_interaction_constraints.py) examples. ### New feature: learning to rank using scikit-learn interface * Learning to rank task is now available for the scikit-learn interface of the Python package (#3560, #3848). It is now possible to integrate the XGBoost ranking model into the scikit-learn learning pipeline. * Examples of using `XGBRanker` class is found at [demo/rank/rank_sklearn.py](https://github.com/dmlc/xgboost/blob/24a268a2e3cb17302db3d72da8f04016b7d352d9/demo/rank/rank_sklearn.py). ### New feature: R interface for SHAP interactions * SHAP (SHapley Additive exPlanations) is a unified approach to explain the output of any machine learning model. Previously, this feature was only available from the Python package; now it is available from the R package as well (#3636). ### New feature: GPU predictor now use multiple GPUs to predict * GPU predictor is now able to utilize multiple GPUs at once to accelerate prediction (#3738) ### New feature: Scale distributed XGBoost to large-scale clusters * Fix OS file descriptor limit assertion error on large cluster (#3835, dmlc/rabit#73) by replacing `select()` based AllReduce/Broadcast with `poll()` based implementation. * Mitigate tracker "thundering herd" issue on large cluster. Add exponential backoff retry when workers connect to tracker. * With this change, we were able to scale to 1.5k executors on a 12 billion row dataset after some tweaks here and there. ### New feature: Additional objective functions for GPUs * New objective functions ported to GPU: `hinge`, `multi:softmax`, `multi:softprob`, `count:poisson`, `reg:gamma`, `"reg:tweedie`. * With supported objectives, XGBoost will select the correct devices based on your system and `n_gpus` parameter. ### Major bug fix: learning to rank with XGBoost4J-Spark * Previously, `repartitionForData` would shuffle data and lose ordering necessary for ranking task. * To fix this issue, data points within each RDD partition is explicitly group by their group (query session) IDs (#3654). Also handle empty RDD partition carefully (#3750). ### Major bug fix: early stopping fixed in XGBoost4J-Spark * Earlier implementation of early stopping had incorrect semantics and didn't let users to specify direction for optimizing (maximize / minimize) * A parameter `maximize_evaluation_metrics` is defined so as to tell whether a metric should be maximized or minimized as part of early stopping criteria (#3808). Also early stopping now has correct semantics. ### API changes * Column sampling by level (`colsample_bylevel`) is now functional for `hist` algorithm (#3635, #3862) * GPU tag `gpu:` for regression objectives are now deprecated. XGBoost will select the correct devices automatically (#3643) * Add `disable_default_eval_metric` parameter to disable default metric (#3606) * Experimental AVX support for gradient computation is removed (#3752) * XGBoost4J-Spark - Add `rank:ndcg` and `rank:map` to supported objectives (#3697) * Python package - Add `callbacks` argument to `fit()` function of sciki-learn API (#3682) - Add `XGBRanker` to scikit-learn interface (#3560, #3848) - Add `validate_features` argument to `predict()` function of scikit-learn API (#3653) - Allow scikit-learn grid search over parameters specified as keyword arguments (#3791) - Add `coef_` and `intercept_` as properties of scikit-learn wrapper (#3855). Some scikit-learn functions expect these properties. ### Performance improvements * Address very high GPU memory usage for large data (#3635) * Fix performance regression within `EvaluateSplits()` of `gpu_hist` algorithm. (#3680) ### Bug-fixes * Fix a problem in GPU quantile sketch with tiny instance weights. (#3628) * Fix copy constructor for `HostDeviceVectorImpl` to prevent dangling pointers (#3657) * Fix a bug in partitioned file loading (#3673) * Fixed an uninitialized pointer in `gpu_hist` (#3703) * Reshared data among GPUs when number of GPUs is changed (#3721) * Add back `max_delta_step` to split evaluation (#3668) * Do not round up integer thresholds for integer features in JSON dump (#3717) * Use `dmlc::TemporaryDirectory` to handle temporaries in cross-platform way (#3783) * Fix accuracy problem with `gpu_hist` when `min_child_weight` and `lambda` are set to 0 (#3793) * Make sure that `tree_method` parameter is recognized and not silently ignored (#3849) * XGBoost4J-Spark - Make sure `thresholds` are considered when executing `predict()` method (#3577) - Avoid losing precision when computing probabilities by converting to `Double` early (#3576) - `getTreeLimit()` should return `Int` (#3602) - Fix checkpoint serialization on HDFS (#3614) - Throw `ControlThrowable` instead of `InterruptedException` so that it is properly re-thrown (#3632) - Remove extraneous output to stdout (#3665) - Allow specification of task type for custom objectives and evaluations (#3646) - Fix distributed updater check (#3739) - Fix issue when spark job execution thread cannot return before we execute `first()` (#3758) * Python package - Fix accessing `DMatrix.handle` before it is set (#3599) - `XGBClassifier.predict()` should return margin scores when `output_margin` is set to true (#3651) - Early stopping callback should maximize metric of form `NDCG@n-` (#3685) - Preserve feature names when slicing `DMatrix` (#3766) * R package - Replace `nround` with `nrounds` to match actual parameter (#3592) - Amend `xgb.createFolds` to handle classes of a single element (#3630) - Fix buggy random generator and make `colsample_bytree` functional (#3781) ### Maintenance: testing, continuous integration, build system * Add sanitizers tests to Travis CI (#3557) * Add NumPy, Matplotlib, Graphviz as requirements for doc build (#3669) * Comply with CRAN submission policy (#3660, #3728) * Remove copy-paste error in JVM test suite (#3692) * Disable flaky tests in `R-package/tests/testthat/test_update.R` (#3723) * Make Python tests compatible with scikit-learn 0.20 release (#3731) * Separate out restricted and unrestricted tasks, so that pull requests don't build downloadable artifacts (#3736) * Add multi-GPU unit test environment (#3741) * Allow plug-ins to be built by CMake (#3752) * Test wheel compatibility on CPU containers for pull requests (#3762) * Fix broken doc build due to Matplotlib 3.0 release (#3764) * Produce `xgboost.so` for XGBoost-R on Mac OSX, so that `make install` works (#3767) * Retry Jenkins CI tests up to 3 times to improve reliability (#3769, #3769, #3775, #3776, #3777) * Add basic unit tests for `gpu_hist` algorithm (#3785) * Fix Python environment for distributed unit tests (#3806) * Test wheels on CUDA 10.0 container for compatibility (#3838) * Fix JVM doc build (#3853) ### Maintenance: Refactor C++ code for legibility and maintainability * Merge generic device helper functions into `GPUSet` class (#3626) * Re-factor column sampling logic into `ColumnSampler` class (#3635, #3637) * Replace `std::vector` with `HostDeviceVector` in `MetaInfo` and `SparsePage` (#3446) * Simplify `DMatrix` class (#3395) * De-duplicate CPU/GPU code using `Transform` class (#3643, #3751) * Remove obsoleted `QuantileHistMaker` class (#3761) * Remove obsoleted `NoConstraint` class (#3792) ### Other Features * C++20-compliant Span class for safe pointer indexing (#3548, #3588) * Add helper functions to manipulate multiple GPU devices (#3693) * XGBoost4J-Spark - Allow specifying host ip from the `xgboost-tracker.properties file` (#3833). This comes in handy when `hosts` files doesn't correctly define localhost. ### Usability Improvements * Add reference to GitHub repository in `pom.xml` of JVM packages (#3589) * Add R demo of multi-class classification (#3695) * Document JSON dump functionality (#3600, #3603) * Document CUDA requirement and lack of external memory for GPU algorithms (#3624) * Document LambdaMART objectives, both pairwise and listwise (#3672) * Document `aucpr` evaluation metric (#3687) * Document gblinear parameters: `feature_selector` and `top_k` (#3780) * Add instructions for using MinGW-built XGBoost with Python. (#3774) * Removed nonexistent parameter `use_buffer` from documentation (#3610) * Update Python API doc to include all classes and members (#3619, #3682) * Fix typos and broken links in documentation (#3618, #3640, #3676, #3713, #3759, #3784, #3843, #3852) * Binary classification demo should produce LIBSVM with 0-based indexing (#3652) * Process data once for Python and CLI examples of learning to rank (#3666) * Include full text of Apache 2.0 license in the repository (#3698) * Save predictor parameters in model file (#3856) * JVM packages - Let users specify feature names when calling `getModelDump` and `getFeatureScore` (#3733) - Warn the user about the lack of over-the-wire encryption (#3667) - Fix errors in examples (#3719) - Document choice of trackers (#3831) - Document that vanilla Apache Spark is required (#3854) * Python package - Document that custom objective can't contain colon (:) (#3601) - Show a better error message for failed library loading (#3690) - Document that feature importance is unavailable for non-tree learners (#3765) - Document behavior of `get_fscore()` for zero-importance features (#3763) - Recommend pickling as the way to save `XGBClassifier` / `XGBRegressor` / `XGBRanker` (#3829) * R package - Enlarge variable importance plot to make it more visible (#3820) ### BREAKING CHANGES * External memory page files have changed, breaking backwards compatibility for temporary storage used during external memory training. This only affects external memory users upgrading their xgboost version - we recommend clearing all `*.page` files before resuming training. Model serialization is unaffected. ### Known issues * Quantile sketcher fails to produce any quantile for some edge cases (#2943) * The `hist` algorithm leaks memory when used with learning rate decay callback (#3579) * Using custom evaluation function together with early stopping causes assertion failure in XGBoost4J-Spark (#3595) * Early stopping doesn't work with `gblinear` learner (#3789) * Label and weight vectors are not reshared upon the change in number of GPUs (#3794). To get around this issue, delete the `DMatrix` object and re-load. * The `DMatrix` Python objects are initialized with incorrect values when given array slices (#3841) * The `gpu_id` parameter is broken and not yet properly supported (#3850) ### Acknowledgement **Contributors** (in no particular order): Hyunsu Cho (@hcho3), Jiaming Yuan (@trivialfis), Nan Zhu (@CodingCat), Rory Mitchell (@RAMitchell), Andy Adinets (@canonizer), Vadim Khotilovich (@khotilov), Sergei Lebedev (@superbobry) **First-time Contributors** (in no particular order): Matthew Tovbin (@tovbinm), Jakob Richter (@jakob-r), Grace Lam (@grace-lam), Grant W Schneider (@grantschneider), Andrew Thia (@BlueTea88), Sergei Chipiga (@schipiga), Joseph Bradley (@jkbradley), Chen Qin (@chenqin), Jerry Lin (@linjer), Dmitriy Rybalko (@rdtft), Michael Mui (@mmui), Takahiro Kojima (@515hikaru), Bruce Zhao (@BruceZhaoR), Wei Tian (@weitian), Saumya Bhatnagar (@Sam1301), Juzer Shakir (@JuzerShakir), Zhao Hang (@cleghom), Jonathan Friedman (@jontonsoup), Bruno Tremblay (@meztez), Boris Filippov (@frenzykryger), @Shiki-H, @mrgutkun, @gorogm, @htgeis, @jakehoare, @zengxy, @KOLANICH **First-time Reviewers** (in no particular order): Nikita Titov (@StrikerRUS), Xiangrui Meng (@mengxr), Nirmal Borah (@Nirmal-Neel) ## v0.80 (2018.08.13) * **JVM packages received a major upgrade**: To consolidate the APIs and improve the user experience, we refactored the design of XGBoost4J-Spark in a significant manner. (#3387) - Consolidated APIs: It is now much easier to integrate XGBoost models into a Spark ML pipeline. Users can control behaviors like output leaf prediction results by setting corresponding column names. Training is now more consistent with other Estimators in Spark MLLIB: there is now one single method `fit()` to train decision trees. - Better user experience: we refactored the parameters relevant modules in XGBoost4J-Spark to provide both camel-case (Spark ML style) and underscore (XGBoost style) parameters - A brand-new tutorial is [available](https://xgboost.readthedocs.io/en/release_0.80/jvm/xgboost4j_spark_tutorial.html) for XGBoost4J-Spark. - Latest API documentation is now hosted at https://xgboost.readthedocs.io/. * XGBoost documentation now keeps track of multiple versions: - Latest master: https://xgboost.readthedocs.io/en/latest - 0.80 stable: https://xgboost.readthedocs.io/en/release_0.80 - 0.72 stable: https://xgboost.readthedocs.io/en/release_0.72 * Support for per-group weights in ranking objective (#3379) * Fix inaccurate decimal parsing (#3546) * New functionality - Query ID column support in LIBSVM data files (#2749). This is convenient for performing ranking task in distributed setting. - Hinge loss for binary classification (`binary:hinge`) (#3477) - Ability to specify delimiter and instance weight column for CSV files (#3546) - Ability to use 1-based indexing instead of 0-based (#3546) * GPU support - Quantile sketch, binning, and index compression are now performed on GPU, eliminating PCIe transfer for 'gpu_hist' algorithm (#3319, #3393) - Upgrade to NCCL2 for multi-GPU training (#3404). - Use shared memory atomics for faster training (#3384). - Dynamically allocate GPU memory, to prevent large allocations for deep trees (#3519) - Fix memory copy bug for large files (#3472) * Python package - Importing data from Python datatable (#3272) - Pre-built binary wheels available for 64-bit Linux and Windows (#3424, #3443) - Add new importance measures 'total_gain', 'total_cover' (#3498) - Sklearn API now supports saving and loading models (#3192) - Arbitrary cross validation fold indices (#3353) - `predict()` function in Sklearn API uses `best_ntree_limit` if available, to make early stopping easier to use (#3445) - Informational messages are now directed to Python's `print()` rather than standard output (#3438). This way, messages appear inside Jupyter notebooks. * R package - Oracle Solaris support, per CRAN policy (#3372) * JVM packages - Single-instance prediction (#3464) - Pre-built JARs are now available from Maven Central (#3401) - Add NULL pointer check (#3021) - Consider `spark.task.cpus` when controlling parallelism (#3530) - Handle missing values in prediction (#3529) - Eliminate outputs of `System.out` (#3572) * Refactored C++ DMatrix class for simplicity and de-duplication (#3301) * Refactored C++ histogram facilities (#3564) * Refactored constraints / regularization mechanism for split finding (#3335, #3429). Users may specify an elastic net (L2 + L1 regularization) on leaf weights as well as monotonic constraints on test nodes. The refactor will be useful for a future addition of feature interaction constraints. * Statically link `libstdc++` for MinGW32 (#3430) * Enable loading from `group`, `base_margin` and `weight` (see [here](http://xgboost.readthedocs.io/en/latest/tutorials/input_format.html#auxiliary-files-for-additional-information)) for Python, R, and JVM packages (#3431) * Fix model saving for `count:possion` so that `max_delta_step` doesn't get truncated (#3515) * Fix loading of sparse CSC matrix (#3553) * Fix incorrect handling of `base_score` parameter for Tweedie regression (#3295) ## v0.72.1 (2018.07.08) This version is only applicable for the Python package. The content is identical to that of v0.72. ## v0.72 (2018.06.01) * Starting with this release, we plan to make a new release every two months. See #3252 for more details. * Fix a pathological behavior (near-zero second-order gradients) in multiclass objective (#3304) * Tree dumps now use high precision in storing floating-point values (#3298) * Submodules `rabit` and `dmlc-core` have been brought up to date, bringing bug fixes (#3330, #3221). * GPU support - Continuous integration tests for GPU code (#3294, #3309) - GPU accelerated coordinate descent algorithm (#3178) - Abstract 1D vector class now works with multiple GPUs (#3287) - Generate PTX code for most recent architecture (#3316) - Fix a memory bug on NVIDIA K80 cards (#3293) - Address performance instability for single-GPU, multi-core machines (#3324) * Python package - FreeBSD support (#3247) - Validation of feature names in `Booster.predict()` is now optional (#3323) * Updated Sklearn API - Validation sets now support instance weights (#2354) - `XGBClassifier.predict_proba()` should not support `output_margin` option. (#3343) See BREAKING CHANGES below. * R package: - Better handling of NULL in `print.xgb.Booster()` (#3338) - Comply with CRAN policy by removing compiler warning suppression (#3329) - Updated CRAN submission * JVM packages - JVM packages will now use the same versioning scheme as other packages (#3253) - Update Spark to 2.3 (#3254) - Add scripts to cross-build and deploy artifacts (#3276, #3307) - Fix a compilation error for Scala 2.10 (#3332) * BREAKING CHANGES - `XGBClassifier.predict_proba()` no longer accepts parameter `output_margin`. The parameter makes no sense for `predict_proba()` because the method is to predict class probabilities, not raw margin scores. ## v0.71 (2018.04.11) * This is a minor release, mainly motivated by issues concerning `pip install`, e.g. #2426, #3189, #3118, and #3194. With this release, users of Linux and MacOS will be able to run `pip install` for the most part. * Refactored linear booster class (`gblinear`), so as to support multiple coordinate descent updaters (#3103, #3134). See BREAKING CHANGES below. * Fix slow training for multiclass classification with high number of classes (#3109) * Fix a corner case in approximate quantile sketch (#3167). Applicable for 'hist' and 'gpu_hist' algorithms * Fix memory leak in DMatrix (#3182) * New functionality - Better linear booster class (#3103, #3134) - Pairwise SHAP interaction effects (#3043) - Cox loss (#3043) - AUC-PR metric for ranking task (#3172) - Monotonic constraints for 'hist' algorithm (#3085) * GPU support - Create an abstract 1D vector class that moves data seamlessly between the main and GPU memory (#2935, #3116, #3068). This eliminates unnecessary PCIe data transfer during training time. - Fix minor bugs (#3051, #3217) - Fix compatibility error for CUDA 9.1 (#3218) * Python package: - Correctly handle parameter `verbose_eval=0` (#3115) * R package: - Eliminate segmentation fault on 32-bit Windows platform (#2994) * JVM packages - Fix a memory bug involving double-freeing Booster objects (#3005, #3011) - Handle empty partition in predict (#3014) - Update docs and unify terminology (#3024) - Delete cache files after job finishes (#3022) - Compatibility fixes for latest Spark versions (#3062, #3093) * BREAKING CHANGES: Updated linear modelling algorithms. In particular L1/L2 regularisation penalties are now normalised to number of training examples. This makes the implementation consistent with sklearn/glmnet. L2 regularisation has also been removed from the intercept. To produce linear models with the old regularisation behaviour, the alpha/lambda regularisation parameters can be manually scaled by dividing them by the number of training examples. ## v0.7 (2017.12.30) * **This version represents a major change from the last release (v0.6), which was released one year and half ago.** * Updated Sklearn API - Add compatibility layer for scikit-learn v0.18: `sklearn.cross_validation` now deprecated - Updated to allow use of all XGBoost parameters via `**kwargs`. - Updated `nthread` to `n_jobs` and `seed` to `random_state` (as per Sklearn convention); `nthread` and `seed` are now marked as deprecated - Updated to allow choice of Booster (`gbtree`, `gblinear`, or `dart`) - `XGBRegressor` now supports instance weights (specify `sample_weight` parameter) - Pass `n_jobs` parameter to the `DMatrix` constructor - Add `xgb_model` parameter to `fit` method, to allow continuation of training * Refactored gbm to allow more friendly cache strategy - Specialized some prediction routine * Robust `DMatrix` construction from a sparse matrix * Faster construction of `DMatrix` from 2D NumPy matrices: elide copies, use of multiple threads * Automatically remove nan from input data when it is sparse. - This can solve some of user reported problem of istart != hist.size * Fix the single-instance prediction function to obtain correct predictions * Minor fixes - Thread local variable is upgraded so it is automatically freed at thread exit. - Fix saving and loading `count::poisson` models - Fix CalcDCG to use base-2 logarithm - Messages are now written to stderr instead of stdout - Keep built-in evaluations while using customized evaluation functions - Use `bst_float` consistently to minimize type conversion - Copy the base margin when slicing `DMatrix` - Evaluation metrics are now saved to the model file - Use `int32_t` explicitly when serializing version - In distributed training, synchronize the number of features after loading a data matrix. * Migrate to C++11 - The current master version now requires C++11 enabled compiled(g++4.8 or higher) * Predictor interface was factored out (in a manner similar to the updater interface). * Makefile support for Solaris and ARM * Test code coverage using Codecov * Add CPP tests * Add `Dockerfile` and `Jenkinsfile` to support continuous integration for GPU code * New functionality - Ability to adjust tree model's statistics to a new dataset without changing tree structures. - Ability to extract feature contributions from individual predictions, as described in [here](http://blog.datadive.net/interpreting-random-forests/) and [here](https://arxiv.org/abs/1706.06060). - Faster, histogram-based tree algorithm (`tree_method='hist'`) . - GPU/CUDA accelerated tree algorithms (`tree_method='gpu_hist'` or `'gpu_exact'`), including the GPU-based predictor. - Monotonic constraints: when other features are fixed, force the prediction to be monotonic increasing with respect to a certain specified feature. - Faster gradient calculation using AVX SIMD - Ability to export models in JSON format - Support for Tweedie regression - Additional dropout options for DART: binomial+1, epsilon - Ability to update an existing model in-place: this is useful for many applications, such as determining feature importance * Python package: - New parameters: - `learning_rates` in `cv()` - `shuffle` in `mknfold()` - `max_features` and `show_values` in `plot_importance()` - `sample_weight` in `XGBRegressor.fit()` - Support binary wheel builds - Fix `MultiIndex` detection to support Pandas 0.21.0 and higher - Support metrics and evaluation sets whose names contain `-` - Support feature maps when plotting trees - Compatibility fix for Python 2.6 - Call `print_evaluation` callback at last iteration - Use appropriate integer types when calling native code, to prevent truncation and memory error - Fix shared library loading on Mac OS X * R package: - New parameters: - `silent` in `xgb.DMatrix()` - `use_int_id` in `xgb.model.dt.tree()` - `predcontrib` in `predict()` - `monotone_constraints` in `xgb.train()` - Default value of the `save_period` parameter in `xgboost()` changed to NULL (consistent with `xgb.train()`). - It's possible to custom-build the R package with GPU acceleration support. - Enable JVM build for Mac OS X and Windows - Integration with AppVeyor CI - Improved safety for garbage collection - Store numeric attributes with higher precision - Easier installation for devel version - Improved `xgb.plot.tree()` - Various minor fixes to improve user experience and robustness - Register native code to pass CRAN check - Updated CRAN submission * JVM packages - Add Spark pipeline persistence API - Fix data persistence: loss evaluation on test data had wrongly used caches for training data. - Clean external cache after training - Implement early stopping - Enable training of multiple models by distinguishing stage IDs - Better Spark integration: support RDD / dataframe / dataset, integrate with Spark ML package - XGBoost4j now supports ranking task - Support training with missing data - Refactor JVM package to separate regression and classification models to be consistent with other machine learning libraries - Support XGBoost4j compilation on Windows - Parameter tuning tool - Publish source code for XGBoost4j to maven local repo - Scala implementation of the Rabit tracker (drop-in replacement for the Java implementation) - Better exception handling for the Rabit tracker - Persist `num_class`, number of classes (for classification task) - `XGBoostModel` now holds `BoosterParams` - libxgboost4j is now part of CMake build - Release `DMatrix` when no longer needed, to conserve memory - Expose `baseMargin`, to allow initialization of boosting with predictions from an external model - Support instance weights - Use `SparkParallelismTracker` to prevent jobs from hanging forever - Expose train-time evaluation metrics via `XGBoostModel.summary` - Option to specify `host-ip` explicitly in the Rabit tracker * Documentation - Better math notation for gradient boosting - Updated build instructions for Mac OS X - Template for GitHub issues - Add `CITATION` file for citing XGBoost in scientific writing - Fix dropdown menu in xgboost.readthedocs.io - Document `updater_seq` parameter - Style fixes for Python documentation - Links to additional examples and tutorials - Clarify installation requirements * Changes that break backward compatibility - [#1519](https://github.com/dmlc/xgboost/pull/1519) XGBoost-spark no longer contains APIs for DMatrix; use the public booster interface instead. - [#2476](https://github.com/dmlc/xgboost/pull/2476) `XGBoostModel.predict()` now has a different signature ## v0.6 (2016.07.29) * Version 0.5 is skipped due to major improvements in the core * Major refactor of core library. - Goal: more flexible and modular code as a portable library. - Switch to use of c++11 standard code. - Random number generator defaults to ```std::mt19937```. - Share the data loading pipeline and logging module from dmlc-core. - Enable registry pattern to allow optionally plugin of objective, metric, tree constructor, data loader. - Future plugin modules can be put into xgboost/plugin and register back to the library. - Remove most of the raw pointers to smart ptrs, for RAII safety. * Add official option to approximate algorithm `tree_method` to parameter. - Change default behavior to switch to prefer faster algorithm. - User will get a message when approximate algorithm is chosen. * Change library name to libxgboost.so * Backward compatiblity - The binary buffer file is not backward compatible with previous version. - The model file is backward compatible on 64 bit platforms. * The model file is compatible between 64/32 bit platforms(not yet tested). * External memory version and other advanced features will be exposed to R library as well on linux. - Previously some of the features are blocked due to C++11 and threading limits. - The windows version is still blocked due to Rtools do not support ```std::thread```. * rabit and dmlc-core are maintained through git submodule - Anyone can open PR to update these dependencies now. * Improvements - Rabit and xgboost libs are not thread-safe and use thread local PRNGs - This could fix some of the previous problem which runs xgboost on multiple threads. * JVM Package - Enable xgboost4j for java and scala - XGBoost distributed now runs on Flink and Spark. * Support model attributes listing for meta data. - https://github.com/dmlc/xgboost/pull/1198 - https://github.com/dmlc/xgboost/pull/1166 * Support callback API - https://github.com/dmlc/xgboost/issues/892 - https://github.com/dmlc/xgboost/pull/1211 - https://github.com/dmlc/xgboost/pull/1264 * Support new booster DART(dropout in tree boosting) - https://github.com/dmlc/xgboost/pull/1220 * Add CMake build system - https://github.com/dmlc/xgboost/pull/1314 ## v0.47 (2016.01.14) * Changes in R library - fixed possible problem of poisson regression. - switched from 0 to NA for missing values. - exposed access to additional model parameters. * Changes in Python library - throws exception instead of crash terminal when a parameter error happens. - has importance plot and tree plot functions. - accepts different learning rates for each boosting round. - allows model training continuation from previously saved model. - allows early stopping in CV. - allows feval to return a list of tuples. - allows eval_metric to handle additional format. - improved compatibility in sklearn module. - additional parameters added for sklearn wrapper. - added pip installation functionality. - supports more Pandas DataFrame dtypes. - added best_ntree_limit attribute, in addition to best_score and best_iteration. * Java api is ready for use * Added more test cases and continuous integration to make each build more robust. ## v0.4 (2015.05.11) * Distributed version of xgboost that runs on YARN, scales to billions of examples * Direct save/load data and model from/to S3 and HDFS * Feature importance visualization in R module, by Michael Benesty * Predict leaf index * Poisson regression for counts data * Early stopping option in training * Native save load support in R and python - xgboost models now can be saved using save/load in R - xgboost python model is now pickable * sklearn wrapper is supported in python module * Experimental External memory version ## v0.3 (2014.09.07) * Faster tree construction module - Allows subsample columns during tree construction via ```bst:col_samplebytree=ratio``` * Support for boosting from initial predictions * Experimental version of LambdaRank * Linear booster is now parallelized, using parallel coordinated descent. * Add [Code Guide](src/README.md) for customizing objective function and evaluation * Add R module ## v0.2x (2014.05.20) * Python module * Weighted samples instances * Initial version of pairwise rank ## v0.1 (2014.03.26) * Initial release xgboost-1.5.2/R-package/000077500000000000000000000000001417122711700150015ustar00rootroot00000000000000xgboost-1.5.2/R-package/.Rbuildignore000066400000000000000000000000701417122711700174240ustar00rootroot00000000000000\.o$ \.so$ \.dll$ ^.*\.Rproj$ ^\.Rproj\.user$ README.md xgboost-1.5.2/R-package/CMakeLists.txt000066400000000000000000000026731417122711700175510ustar00rootroot00000000000000find_package(LibR REQUIRED) message(STATUS "LIBR_CORE_LIBRARY " ${LIBR_CORE_LIBRARY}) file(GLOB_RECURSE R_SOURCES ${CMAKE_CURRENT_LIST_DIR}/src/*.cc ${CMAKE_CURRENT_LIST_DIR}/src/*.c) # Use object library to expose symbols add_library(xgboost-r OBJECT ${R_SOURCES}) if (ENABLE_ALL_WARNINGS) target_compile_options(xgboost-r PRIVATE -Wall -Wextra) endif (ENABLE_ALL_WARNINGS) target_compile_definitions(xgboost-r PUBLIC -DXGBOOST_STRICT_R_MODE=1 -DXGBOOST_CUSTOMIZE_GLOBAL_PRNG=1 -DDMLC_LOG_BEFORE_THROW=0 -DDMLC_DISABLE_STDIN=1 -DDMLC_LOG_CUSTOMIZE=1 -DRABIT_CUSTOMIZE_MSG_ -DRABIT_STRICT_CXX98_) target_include_directories(xgboost-r PRIVATE ${LIBR_INCLUDE_DIRS} ${PROJECT_SOURCE_DIR}/include ${PROJECT_SOURCE_DIR}/dmlc-core/include ${PROJECT_SOURCE_DIR}/rabit/include) target_link_libraries(xgboost-r PUBLIC ${LIBR_CORE_LIBRARY}) if (USE_OPENMP) find_package(OpenMP REQUIRED) target_link_libraries(xgboost-r PUBLIC OpenMP::OpenMP_CXX OpenMP::OpenMP_C) endif (USE_OPENMP) set_target_properties( xgboost-r PROPERTIES CXX_STANDARD 14 CXX_STANDARD_REQUIRED ON POSITION_INDEPENDENT_CODE ON) # Get compilation and link flags of xgboost-r and propagate to objxgboost target_link_libraries(objxgboost PUBLIC xgboost-r) # Add all objects of xgboost-r to objxgboost target_sources(objxgboost INTERFACE $) set(LIBR_HOME "${LIBR_HOME}" PARENT_SCOPE) set(LIBR_EXECUTABLE "${LIBR_EXECUTABLE}" PARENT_SCOPE) xgboost-1.5.2/R-package/DESCRIPTION000066400000000000000000000046201417122711700165110ustar00rootroot00000000000000Package: xgboost Type: Package Title: Extreme Gradient Boosting Version: 1.5.2.1 Date: 2022-1-17 Authors@R: c( person("Tianqi", "Chen", role = c("aut"), email = "tianqi.tchen@gmail.com"), person("Tong", "He", role = c("aut", "cre"), email = "hetong007@gmail.com"), person("Michael", "Benesty", role = c("aut"), email = "michael@benesty.fr"), person("Vadim", "Khotilovich", role = c("aut"), email = "khotilovich@gmail.com"), person("Yuan", "Tang", role = c("aut"), email = "terrytangyuan@gmail.com", comment = c(ORCID = "0000-0001-5243-233X")), person("Hyunsu", "Cho", role = c("aut"), email = "chohyu01@cs.washington.edu"), person("Kailong", "Chen", role = c("aut")), person("Rory", "Mitchell", role = c("aut")), person("Ignacio", "Cano", role = c("aut")), person("Tianyi", "Zhou", role = c("aut")), person("Mu", "Li", role = c("aut")), person("Junyuan", "Xie", role = c("aut")), person("Min", "Lin", role = c("aut")), person("Yifeng", "Geng", role = c("aut")), person("Yutian", "Li", role = c("aut")), person("XGBoost contributors", role = c("cph"), comment = "base XGBoost implementation") ) Description: Extreme Gradient Boosting, which is an efficient implementation of the gradient boosting framework from Chen & Guestrin (2016) . This package is its R interface. The package includes efficient linear model solver and tree learning algorithms. The package can automatically do parallel computation on a single machine which could be more than 10 times faster than existing gradient boosting packages. It supports various objective functions, including regression, classification and ranking. The package is made to be extensible, so that users are also allowed to define their own objectives easily. License: Apache License (== 2.0) | file LICENSE URL: https://github.com/dmlc/xgboost BugReports: https://github.com/dmlc/xgboost/issues NeedsCompilation: yes VignetteBuilder: knitr Suggests: knitr, rmarkdown, ggplot2 (>= 1.0.1), DiagrammeR (>= 0.9.0), Ckmeans.1d.dp (>= 3.3.1), vcd (>= 1.3), testthat, lintr, igraph (>= 1.0.1), float, crayon, titanic Depends: R (>= 3.3.0) Imports: Matrix (>= 1.1-0), methods, data.table (>= 1.9.6), jsonlite (>= 1.0), RoxygenNote: 7.1.1 SystemRequirements: GNU make, C++14 xgboost-1.5.2/R-package/LICENSE000066400000000000000000000011041417122711700160020ustar00rootroot00000000000000Copyright (c) 2014 by Tianqi Chen and Contributors Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. xgboost-1.5.2/R-package/NAMESPACE000066400000000000000000000045231417122711700162240ustar00rootroot00000000000000# Generated by roxygen2: do not edit by hand S3method("[",xgb.DMatrix) S3method("dimnames<-",xgb.DMatrix) S3method(dim,xgb.DMatrix) S3method(dimnames,xgb.DMatrix) S3method(getinfo,xgb.DMatrix) S3method(predict,xgb.Booster) S3method(predict,xgb.Booster.handle) S3method(print,xgb.Booster) S3method(print,xgb.DMatrix) S3method(print,xgb.cv.synchronous) S3method(setinfo,xgb.DMatrix) S3method(slice,xgb.DMatrix) export("xgb.attr<-") export("xgb.attributes<-") export("xgb.config<-") export("xgb.parameters<-") export(cb.cv.predict) export(cb.early.stop) export(cb.evaluation.log) export(cb.gblinear.history) export(cb.print.evaluation) export(cb.reset.parameters) export(cb.save.model) export(getinfo) export(setinfo) export(slice) export(xgb.Booster.complete) export(xgb.DMatrix) export(xgb.DMatrix.save) export(xgb.attr) export(xgb.attributes) export(xgb.config) export(xgb.create.features) export(xgb.cv) export(xgb.dump) export(xgb.gblinear.history) export(xgb.get.config) export(xgb.ggplot.deepness) export(xgb.ggplot.importance) export(xgb.ggplot.shap.summary) export(xgb.importance) export(xgb.load) export(xgb.load.raw) export(xgb.model.dt.tree) export(xgb.plot.deepness) export(xgb.plot.importance) export(xgb.plot.multi.trees) export(xgb.plot.shap) export(xgb.plot.shap.summary) export(xgb.plot.tree) export(xgb.save) export(xgb.save.raw) export(xgb.serialize) export(xgb.set.config) export(xgb.train) export(xgb.unserialize) export(xgboost) import(methods) importClassesFrom(Matrix,dgCMatrix) importClassesFrom(Matrix,dgeMatrix) importFrom(Matrix,colSums) importFrom(Matrix,sparse.model.matrix) importFrom(Matrix,sparseMatrix) importFrom(Matrix,sparseVector) importFrom(Matrix,t) importFrom(data.table,":=") importFrom(data.table,as.data.table) importFrom(data.table,data.table) importFrom(data.table,is.data.table) importFrom(data.table,rbindlist) importFrom(data.table,setkey) importFrom(data.table,setkeyv) importFrom(data.table,setnames) importFrom(grDevices,rgb) importFrom(graphics,barplot) importFrom(graphics,grid) importFrom(graphics,lines) importFrom(graphics,par) importFrom(graphics,points) importFrom(graphics,title) importFrom(jsonlite,fromJSON) importFrom(jsonlite,toJSON) importFrom(stats,median) importFrom(stats,predict) importFrom(utils,head) importFrom(utils,object.size) importFrom(utils,str) importFrom(utils,tail) useDynLib(xgboost, .registration = TRUE) xgboost-1.5.2/R-package/R/000077500000000000000000000000001417122711700152025ustar00rootroot00000000000000xgboost-1.5.2/R-package/R/callbacks.R000066400000000000000000000747541417122711700172650ustar00rootroot00000000000000#' Callback closures for booster training. #' #' These are used to perform various service tasks either during boosting iterations or at the end. #' This approach helps to modularize many of such tasks without bloating the main training methods, #' and it offers . #' #' @details #' By default, a callback function is run after each boosting iteration. #' An R-attribute \code{is_pre_iteration} could be set for a callback to define a pre-iteration function. #' #' When a callback function has \code{finalize} parameter, its finalizer part will also be run after #' the boosting is completed. #' #' WARNING: side-effects!!! Be aware that these callback functions access and modify things in #' the environment from which they are called from, which is a fairly uncommon thing to do in R. #' #' To write a custom callback closure, make sure you first understand the main concepts about R environments. #' Check either R documentation on \code{\link[base]{environment}} or the #' \href{http://adv-r.had.co.nz/Environments.html}{Environments chapter} from the "Advanced R" #' book by Hadley Wickham. Further, the best option is to read the code of some of the existing callbacks - #' choose ones that do something similar to what you want to achieve. Also, you would need to get familiar #' with the objects available inside of the \code{xgb.train} and \code{xgb.cv} internal environments. #' #' @seealso #' \code{\link{cb.print.evaluation}}, #' \code{\link{cb.evaluation.log}}, #' \code{\link{cb.reset.parameters}}, #' \code{\link{cb.early.stop}}, #' \code{\link{cb.save.model}}, #' \code{\link{cb.cv.predict}}, #' \code{\link{xgb.train}}, #' \code{\link{xgb.cv}} #' #' @name callbacks NULL # # Callbacks ------------------------------------------------------------------- # #' Callback closure for printing the result of evaluation #' #' @param period results would be printed every number of periods #' @param showsd whether standard deviations should be printed (when available) #' #' @details #' The callback function prints the result of evaluation at every \code{period} iterations. #' The initial and the last iteration's evaluations are always printed. #' #' Callback function expects the following values to be set in its calling frame: #' \code{bst_evaluation} (also \code{bst_evaluation_err} when available), #' \code{iteration}, #' \code{begin_iteration}, #' \code{end_iteration}. #' #' @seealso #' \code{\link{callbacks}} #' #' @export cb.print.evaluation <- function(period = 1, showsd = TRUE) { callback <- function(env = parent.frame()) { if (length(env$bst_evaluation) == 0 || period == 0 || NVL(env$rank, 0) != 0) return() i <- env$iteration if ((i - 1) %% period == 0 || i == env$begin_iteration || i == env$end_iteration) { stdev <- if (showsd) env$bst_evaluation_err else NULL msg <- format.eval.string(i, env$bst_evaluation, stdev) cat(msg, '\n') } } attr(callback, 'call') <- match.call() attr(callback, 'name') <- 'cb.print.evaluation' callback } #' Callback closure for logging the evaluation history #' #' @details #' This callback function appends the current iteration evaluation results \code{bst_evaluation} #' available in the calling parent frame to the \code{evaluation_log} list in a calling frame. #' #' The finalizer callback (called with \code{finalize = TURE} in the end) converts #' the \code{evaluation_log} list into a final data.table. #' #' The iteration evaluation result \code{bst_evaluation} must be a named numeric vector. #' #' Note: in the column names of the final data.table, the dash '-' character is replaced with #' the underscore '_' in order to make the column names more like regular R identifiers. #' #' Callback function expects the following values to be set in its calling frame: #' \code{evaluation_log}, #' \code{bst_evaluation}, #' \code{iteration}. #' #' @seealso #' \code{\link{callbacks}} #' #' @export cb.evaluation.log <- function() { mnames <- NULL init <- function(env) { if (!is.list(env$evaluation_log)) stop("'evaluation_log' has to be a list") mnames <<- names(env$bst_evaluation) if (is.null(mnames) || any(mnames == "")) stop("bst_evaluation must have non-empty names") mnames <<- gsub('-', '_', names(env$bst_evaluation)) if (!is.null(env$bst_evaluation_err)) mnames <<- c(paste0(mnames, '_mean'), paste0(mnames, '_std')) } finalizer <- function(env) { env$evaluation_log <- as.data.table(t(simplify2array(env$evaluation_log))) setnames(env$evaluation_log, c('iter', mnames)) if (!is.null(env$bst_evaluation_err)) { # rearrange col order from _mean,_mean,...,_std,_std,... # to be _mean,_std,_mean,_std,... len <- length(mnames) means <- mnames[seq_len(len / 2)] stds <- mnames[(len / 2 + 1):len] cnames <- numeric(len) cnames[c(TRUE, FALSE)] <- means cnames[c(FALSE, TRUE)] <- stds env$evaluation_log <- env$evaluation_log[, c('iter', cnames), with = FALSE] } } callback <- function(env = parent.frame(), finalize = FALSE) { if (is.null(mnames)) init(env) if (finalize) return(finalizer(env)) ev <- env$bst_evaluation if (!is.null(env$bst_evaluation_err)) ev <- c(ev, env$bst_evaluation_err) env$evaluation_log <- c(env$evaluation_log, list(c(iter = env$iteration, ev))) } attr(callback, 'call') <- match.call() attr(callback, 'name') <- 'cb.evaluation.log' callback } #' Callback closure for resetting the booster's parameters at each iteration. #' #' @param new_params a list where each element corresponds to a parameter that needs to be reset. #' Each element's value must be either a vector of values of length \code{nrounds} #' to be set at each iteration, #' or a function of two parameters \code{learning_rates(iteration, nrounds)} #' which returns a new parameter value by using the current iteration number #' and the total number of boosting rounds. #' #' @details #' This is a "pre-iteration" callback function used to reset booster's parameters #' at the beginning of each iteration. #' #' Note that when training is resumed from some previous model, and a function is used to #' reset a parameter value, the \code{nrounds} argument in this function would be the #' the number of boosting rounds in the current training. #' #' Callback function expects the following values to be set in its calling frame: #' \code{bst} or \code{bst_folds}, #' \code{iteration}, #' \code{begin_iteration}, #' \code{end_iteration}. #' #' @seealso #' \code{\link{callbacks}} #' #' @export cb.reset.parameters <- function(new_params) { if (typeof(new_params) != "list") stop("'new_params' must be a list") pnames <- gsub("\\.", "_", names(new_params)) nrounds <- NULL # run some checks in the beginning init <- function(env) { nrounds <<- env$end_iteration - env$begin_iteration + 1 if (is.null(env$bst) && is.null(env$bst_folds)) stop("Parent frame has neither 'bst' nor 'bst_folds'") # Some parameters are not allowed to be changed, # since changing them would simply wreck some chaos not_allowed <- pnames %in% c('num_class', 'num_output_group', 'size_leaf_vector', 'updater_seq') if (any(not_allowed)) stop('Parameters ', paste(pnames[not_allowed]), " cannot be changed during boosting.") for (n in pnames) { p <- new_params[[n]] if (is.function(p)) { if (length(formals(p)) != 2) stop("Parameter '", n, "' is a function but not of two arguments") } else if (is.numeric(p) || is.character(p)) { if (length(p) != nrounds) stop("Length of '", n, "' has to be equal to 'nrounds'") } else { stop("Parameter '", n, "' is not a function or a vector") } } } callback <- function(env = parent.frame()) { if (is.null(nrounds)) init(env) i <- env$iteration pars <- lapply(new_params, function(p) { if (is.function(p)) return(p(i, nrounds)) p[i] }) if (!is.null(env$bst)) { xgb.parameters(env$bst$handle) <- pars } else { for (fd in env$bst_folds) xgb.parameters(fd$bst) <- pars } } attr(callback, 'is_pre_iteration') <- TRUE attr(callback, 'call') <- match.call() attr(callback, 'name') <- 'cb.reset.parameters' callback } #' Callback closure to activate the early stopping. #' #' @param stopping_rounds The number of rounds with no improvement in #' the evaluation metric in order to stop the training. #' @param maximize whether to maximize the evaluation metric #' @param metric_name the name of an evaluation column to use as a criteria for early #' stopping. If not set, the last column would be used. #' Let's say the test data in \code{watchlist} was labelled as \code{dtest}, #' and one wants to use the AUC in test data for early stopping regardless of where #' it is in the \code{watchlist}, then one of the following would need to be set: #' \code{metric_name='dtest-auc'} or \code{metric_name='dtest_auc'}. #' All dash '-' characters in metric names are considered equivalent to '_'. #' @param verbose whether to print the early stopping information. #' #' @details #' This callback function determines the condition for early stopping #' by setting the \code{stop_condition = TRUE} flag in its calling frame. #' #' The following additional fields are assigned to the model's R object: #' \itemize{ #' \item \code{best_score} the evaluation score at the best iteration #' \item \code{best_iteration} at which boosting iteration the best score has occurred (1-based index) #' } #' The Same values are also stored as xgb-attributes: #' \itemize{ #' \item \code{best_iteration} is stored as a 0-based iteration index (for interoperability of binary models) #' \item \code{best_msg} message string is also stored. #' } #' #' At least one data element is required in the evaluation watchlist for early stopping to work. #' #' Callback function expects the following values to be set in its calling frame: #' \code{stop_condition}, #' \code{bst_evaluation}, #' \code{rank}, #' \code{bst} (or \code{bst_folds} and \code{basket}), #' \code{iteration}, #' \code{begin_iteration}, #' \code{end_iteration}, #' \code{num_parallel_tree}. #' #' @seealso #' \code{\link{callbacks}}, #' \code{\link{xgb.attr}} #' #' @export cb.early.stop <- function(stopping_rounds, maximize = FALSE, metric_name = NULL, verbose = TRUE) { # state variables best_iteration <- -1 best_ntreelimit <- -1 best_score <- Inf best_msg <- NULL metric_idx <- 1 init <- function(env) { if (length(env$bst_evaluation) == 0) stop("For early stopping, watchlist must have at least one element") eval_names <- gsub('-', '_', names(env$bst_evaluation)) if (!is.null(metric_name)) { metric_idx <<- which(gsub('-', '_', metric_name) == eval_names) if (length(metric_idx) == 0) stop("'metric_name' for early stopping is not one of the following:\n", paste(eval_names, collapse = ' '), '\n') } if (is.null(metric_name) && length(env$bst_evaluation) > 1) { metric_idx <<- length(eval_names) if (verbose) cat('Multiple eval metrics are present. Will use ', eval_names[metric_idx], ' for early stopping.\n', sep = '') } metric_name <<- eval_names[metric_idx] # maximize is usually NULL when not set in xgb.train and built-in metrics if (is.null(maximize)) maximize <<- grepl('(_auc|_map|_ndcg)', metric_name) if (verbose && NVL(env$rank, 0) == 0) cat("Will train until ", metric_name, " hasn't improved in ", stopping_rounds, " rounds.\n\n", sep = '') best_iteration <<- 1 if (maximize) best_score <<- -Inf env$stop_condition <- FALSE if (!is.null(env$bst)) { if (!inherits(env$bst, 'xgb.Booster')) stop("'bst' in the parent frame must be an 'xgb.Booster'") if (!is.null(best_score <- xgb.attr(env$bst$handle, 'best_score'))) { best_score <<- as.numeric(best_score) best_iteration <<- as.numeric(xgb.attr(env$bst$handle, 'best_iteration')) + 1 best_msg <<- as.numeric(xgb.attr(env$bst$handle, 'best_msg')) } else { xgb.attributes(env$bst$handle) <- list(best_iteration = best_iteration - 1, best_score = best_score) } } else if (is.null(env$bst_folds) || is.null(env$basket)) { stop("Parent frame has neither 'bst' nor ('bst_folds' and 'basket')") } } finalizer <- function(env) { if (!is.null(env$bst)) { attr_best_score <- as.numeric(xgb.attr(env$bst$handle, 'best_score')) if (best_score != attr_best_score) { # If the difference is too big, throw an error if (abs(best_score - attr_best_score) >= 1e-14) { stop("Inconsistent 'best_score' values between the closure state: ", best_score, " and the xgb.attr: ", attr_best_score) } # If the difference is due to floating-point truncation, update best_score best_score <- attr_best_score } env$bst$best_iteration <- best_iteration env$bst$best_ntreelimit <- best_ntreelimit env$bst$best_score <- best_score } else { env$basket$best_iteration <- best_iteration env$basket$best_ntreelimit <- best_ntreelimit } } callback <- function(env = parent.frame(), finalize = FALSE) { if (best_iteration < 0) init(env) if (finalize) return(finalizer(env)) i <- env$iteration score <- env$bst_evaluation[metric_idx] if ((maximize && score > best_score) || (!maximize && score < best_score)) { best_msg <<- format.eval.string(i, env$bst_evaluation, env$bst_evaluation_err) best_score <<- score best_iteration <<- i best_ntreelimit <<- best_iteration * env$num_parallel_tree # save the property to attributes, so they will occur in checkpoint if (!is.null(env$bst)) { xgb.attributes(env$bst) <- list( best_iteration = best_iteration - 1, # convert to 0-based index best_score = best_score, best_msg = best_msg, best_ntreelimit = best_ntreelimit) } } else if (i - best_iteration >= stopping_rounds) { env$stop_condition <- TRUE env$end_iteration <- i if (verbose && NVL(env$rank, 0) == 0) cat("Stopping. Best iteration:\n", best_msg, "\n\n", sep = '') } } attr(callback, 'call') <- match.call() attr(callback, 'name') <- 'cb.early.stop' callback } #' Callback closure for saving a model file. #' #' @param save_period save the model to disk after every #' \code{save_period} iterations; 0 means save the model at the end. #' @param save_name the name or path for the saved model file. #' It can contain a \code{\link[base]{sprintf}} formatting specifier #' to include the integer iteration number in the file name. #' E.g., with \code{save_name} = 'xgboost_%04d.model', #' the file saved at iteration 50 would be named "xgboost_0050.model". #' #' @details #' This callback function allows to save an xgb-model file, either periodically after each \code{save_period}'s or at the end. #' #' Callback function expects the following values to be set in its calling frame: #' \code{bst}, #' \code{iteration}, #' \code{begin_iteration}, #' \code{end_iteration}. #' #' @seealso #' \code{\link{callbacks}} #' #' @export cb.save.model <- function(save_period = 0, save_name = "xgboost.model") { if (save_period < 0) stop("'save_period' cannot be negative") callback <- function(env = parent.frame()) { if (is.null(env$bst)) stop("'save_model' callback requires the 'bst' booster object in its calling frame") if ((save_period > 0 && (env$iteration - env$begin_iteration) %% save_period == 0) || (save_period == 0 && env$iteration == env$end_iteration)) xgb.save(env$bst, sprintf(save_name, env$iteration)) } attr(callback, 'call') <- match.call() attr(callback, 'name') <- 'cb.save.model' callback } #' Callback closure for returning cross-validation based predictions. #' #' @param save_models a flag for whether to save the folds' models. #' #' @details #' This callback function saves predictions for all of the test folds, #' and also allows to save the folds' models. #' #' It is a "finalizer" callback and it uses early stopping information whenever it is available, #' thus it must be run after the early stopping callback if the early stopping is used. #' #' Callback function expects the following values to be set in its calling frame: #' \code{bst_folds}, #' \code{basket}, #' \code{data}, #' \code{end_iteration}, #' \code{params}, #' \code{num_parallel_tree}, #' \code{num_class}. #' #' @return #' Predictions are returned inside of the \code{pred} element, which is either a vector or a matrix, #' depending on the number of prediction outputs per data row. The order of predictions corresponds #' to the order of rows in the original dataset. Note that when a custom \code{folds} list is #' provided in \code{xgb.cv}, the predictions would only be returned properly when this list is a #' non-overlapping list of k sets of indices, as in a standard k-fold CV. The predictions would not be #' meaningful when user-provided folds have overlapping indices as in, e.g., random sampling splits. #' When some of the indices in the training dataset are not included into user-provided \code{folds}, #' their prediction value would be \code{NA}. #' #' @seealso #' \code{\link{callbacks}} #' #' @export cb.cv.predict <- function(save_models = FALSE) { finalizer <- function(env) { if (is.null(env$basket) || is.null(env$bst_folds)) stop("'cb.cv.predict' callback requires 'basket' and 'bst_folds' lists in its calling frame") N <- nrow(env$data) pred <- if (env$num_class > 1) { matrix(NA_real_, N, env$num_class) } else { rep(NA_real_, N) } iterationrange <- c(1, NVL(env$basket$best_iteration, env$end_iteration) + 1) if (NVL(env$params[['booster']], '') == 'gblinear') { iterationrange <- c(1, 1) # must be 0 for gblinear } for (fd in env$bst_folds) { pr <- predict(fd$bst, fd$watchlist[[2]], iterationrange = iterationrange, reshape = TRUE) if (is.matrix(pred)) { pred[fd$index, ] <- pr } else { pred[fd$index] <- pr } } env$basket$pred <- pred if (save_models) { env$basket$models <- lapply(env$bst_folds, function(fd) { xgb.attr(fd$bst, 'niter') <- env$end_iteration - 1 xgb.Booster.complete(xgb.handleToBooster(fd$bst), saveraw = TRUE) }) } } callback <- function(env = parent.frame(), finalize = FALSE) { if (finalize) return(finalizer(env)) } attr(callback, 'call') <- match.call() attr(callback, 'name') <- 'cb.cv.predict' callback } #' Callback closure for collecting the model coefficients history of a gblinear booster #' during its training. #' #' @param sparse when set to FALSE/TRUE, a dense/sparse matrix is used to store the result. #' Sparse format is useful when one expects only a subset of coefficients to be non-zero, #' when using the "thrifty" feature selector with fairly small number of top features #' selected per iteration. #' #' @details #' To keep things fast and simple, gblinear booster does not internally store the history of linear #' model coefficients at each boosting iteration. This callback provides a workaround for storing #' the coefficients' path, by extracting them after each training iteration. #' #' Callback function expects the following values to be set in its calling frame: #' \code{bst} (or \code{bst_folds}). #' #' @return #' Results are stored in the \code{coefs} element of the closure. #' The \code{\link{xgb.gblinear.history}} convenience function provides an easy way to access it. #' With \code{xgb.train}, it is either a dense of a sparse matrix. #' While with \code{xgb.cv}, it is a list (an element per each fold) of such matrices. #' #' @seealso #' \code{\link{callbacks}}, \code{\link{xgb.gblinear.history}}. #' #' @examples #' #### Binary classification: #' # #' # In the iris dataset, it is hard to linearly separate Versicolor class from the rest #' # without considering the 2nd order interactions: #' x <- model.matrix(Species ~ .^2, iris)[,-1] #' colnames(x) #' dtrain <- xgb.DMatrix(scale(x), label = 1*(iris$Species == "versicolor")) #' param <- list(booster = "gblinear", objective = "reg:logistic", eval_metric = "auc", #' lambda = 0.0003, alpha = 0.0003, nthread = 2) #' # For 'shotgun', which is a default linear updater, using high eta values may result in #' # unstable behaviour in some datasets. With this simple dataset, however, the high learning #' # rate does not break the convergence, but allows us to illustrate the typical pattern of #' # "stochastic explosion" behaviour of this lock-free algorithm at early boosting iterations. #' bst <- xgb.train(param, dtrain, list(tr=dtrain), nrounds = 200, eta = 1., #' callbacks = list(cb.gblinear.history())) #' # Extract the coefficients' path and plot them vs boosting iteration number: #' coef_path <- xgb.gblinear.history(bst) #' matplot(coef_path, type = 'l') #' #' # With the deterministic coordinate descent updater, it is safer to use higher learning rates. #' # Will try the classical componentwise boosting which selects a single best feature per round: #' bst <- xgb.train(param, dtrain, list(tr=dtrain), nrounds = 200, eta = 0.8, #' updater = 'coord_descent', feature_selector = 'thrifty', top_k = 1, #' callbacks = list(cb.gblinear.history())) #' matplot(xgb.gblinear.history(bst), type = 'l') #' # Componentwise boosting is known to have similar effect to Lasso regularization. #' # Try experimenting with various values of top_k, eta, nrounds, #' # as well as different feature_selectors. #' #' # For xgb.cv: #' bst <- xgb.cv(param, dtrain, nfold = 5, nrounds = 100, eta = 0.8, #' callbacks = list(cb.gblinear.history())) #' # coefficients in the CV fold #3 #' matplot(xgb.gblinear.history(bst)[[3]], type = 'l') #' #' #' #### Multiclass classification: #' # #' dtrain <- xgb.DMatrix(scale(x), label = as.numeric(iris$Species) - 1) #' param <- list(booster = "gblinear", objective = "multi:softprob", num_class = 3, #' lambda = 0.0003, alpha = 0.0003, nthread = 2) #' # For the default linear updater 'shotgun' it sometimes is helpful #' # to use smaller eta to reduce instability #' bst <- xgb.train(param, dtrain, list(tr=dtrain), nrounds = 70, eta = 0.5, #' callbacks = list(cb.gblinear.history())) #' # Will plot the coefficient paths separately for each class: #' matplot(xgb.gblinear.history(bst, class_index = 0), type = 'l') #' matplot(xgb.gblinear.history(bst, class_index = 1), type = 'l') #' matplot(xgb.gblinear.history(bst, class_index = 2), type = 'l') #' #' # CV: #' bst <- xgb.cv(param, dtrain, nfold = 5, nrounds = 70, eta = 0.5, #' callbacks = list(cb.gblinear.history(FALSE))) #' # 1st fold of 1st class #' matplot(xgb.gblinear.history(bst, class_index = 0)[[1]], type = 'l') #' #' @export cb.gblinear.history <- function(sparse=FALSE) { coefs <- NULL init <- function(env) { if (!is.null(env$bst)) { # xgb.train: } else if (!is.null(env$bst_folds)) { # xgb.cv: } else stop("Parent frame has neither 'bst' nor 'bst_folds'") } # convert from list to (sparse) matrix list2mat <- function(coef_list) { if (sparse) { coef_mat <- sparseMatrix(x = unlist(lapply(coef_list, slot, "x")), i = unlist(lapply(coef_list, slot, "i")), p = c(0, cumsum(sapply(coef_list, function(x) length(x@x)))), dims = c(length(coef_list[[1]]), length(coef_list))) return(t(coef_mat)) } else { return(do.call(rbind, coef_list)) } } finalizer <- function(env) { if (length(coefs) == 0) return() if (!is.null(env$bst)) { # # xgb.train: coefs <<- list2mat(coefs) } else { # xgb.cv: # second lapply transposes the list coefs <<- lapply( X = lapply( X = seq_along(coefs[[1]]), FUN = function(i) lapply(coefs, "[[", i) ), FUN = list2mat ) } } extract.coef <- function(env) { if (!is.null(env$bst)) { # # xgb.train: cf <- as.numeric(grep('(booster|bias|weigh)', xgb.dump(env$bst), invert = TRUE, value = TRUE)) if (sparse) cf <- as(cf, "sparseVector") } else { # xgb.cv: cf <- vector("list", length(env$bst_folds)) for (i in seq_along(env$bst_folds)) { dmp <- xgb.dump(xgb.handleToBooster(env$bst_folds[[i]]$bst)) cf[[i]] <- as.numeric(grep('(booster|bias|weigh)', dmp, invert = TRUE, value = TRUE)) if (sparse) cf[[i]] <- as(cf[[i]], "sparseVector") } } cf } callback <- function(env = parent.frame(), finalize = FALSE) { if (is.null(coefs)) init(env) if (finalize) return(finalizer(env)) cf <- extract.coef(env) coefs <<- c(coefs, list(cf)) } attr(callback, 'call') <- match.call() attr(callback, 'name') <- 'cb.gblinear.history' callback } #' Extract gblinear coefficients history. #' #' A helper function to extract the matrix of linear coefficients' history #' from a gblinear model created while using the \code{cb.gblinear.history()} #' callback. #' #' @param model either an \code{xgb.Booster} or a result of \code{xgb.cv()}, trained #' using the \code{cb.gblinear.history()} callback. #' @param class_index zero-based class index to extract the coefficients for only that #' specific class in a multinomial multiclass model. When it is NULL, all the #' coefficients are returned. Has no effect in non-multiclass models. #' #' @return #' For an \code{xgb.train} result, a matrix (either dense or sparse) with the columns #' corresponding to iteration's coefficients (in the order as \code{xgb.dump()} would #' return) and the rows corresponding to boosting iterations. #' #' For an \code{xgb.cv} result, a list of such matrices is returned with the elements #' corresponding to CV folds. #' #' @export xgb.gblinear.history <- function(model, class_index = NULL) { if (!(inherits(model, "xgb.Booster") || inherits(model, "xgb.cv.synchronous"))) stop("model must be an object of either xgb.Booster or xgb.cv.synchronous class") is_cv <- inherits(model, "xgb.cv.synchronous") if (is.null(model[["callbacks"]]) || is.null(model$callbacks[["cb.gblinear.history"]])) stop("model must be trained while using the cb.gblinear.history() callback") if (!is_cv) { # extract num_class & num_feat from the internal model dmp <- xgb.dump(model) if (length(dmp) < 2 || dmp[2] != "bias:") stop("It does not appear to be a gblinear model") dmp <- dmp[-c(1, 2)] n <- which(dmp == 'weight:') if (length(n) != 1) stop("It does not appear to be a gblinear model") num_class <- n - 1 num_feat <- (length(dmp) - 4) / num_class } else { # in case of CV, the object is expected to have this info if (model$params$booster != "gblinear") stop("It does not appear to be a gblinear model") num_class <- NVL(model$params$num_class, 1) num_feat <- model$nfeatures if (is.null(num_feat)) stop("This xgb.cv result does not have nfeatures info") } if (!is.null(class_index) && num_class > 1 && (class_index[1] < 0 || class_index[1] >= num_class)) stop("class_index has to be within [0,", num_class - 1, "]") coef_path <- environment(model$callbacks$cb.gblinear.history)[["coefs"]] if (!is.null(class_index) && num_class > 1) { coef_path <- if (is.list(coef_path)) { lapply(coef_path, function(x) x[, seq(1 + class_index, by = num_class, length.out = num_feat)]) } else { coef_path <- coef_path[, seq(1 + class_index, by = num_class, length.out = num_feat)] } } coef_path } # # Internal utility functions for callbacks ------------------------------------ # # Format the evaluation metric string format.eval.string <- function(iter, eval_res, eval_err = NULL) { if (length(eval_res) == 0) stop('no evaluation results') enames <- names(eval_res) if (is.null(enames)) stop('evaluation results must have names') iter <- sprintf('[%d]\t', iter) if (!is.null(eval_err)) { if (length(eval_res) != length(eval_err)) stop('eval_res & eval_err lengths mismatch') res <- paste0(sprintf("%s:%f+%f", enames, eval_res, eval_err), collapse = '\t') } else { res <- paste0(sprintf("%s:%f", enames, eval_res), collapse = '\t') } return(paste0(iter, res)) } # Extract callback names from the list of callbacks callback.names <- function(cb_list) { unlist(lapply(cb_list, function(x) attr(x, 'name'))) } # Extract callback calls from the list of callbacks callback.calls <- function(cb_list) { unlist(lapply(cb_list, function(x) attr(x, 'call'))) } # Add a callback cb to the list and make sure that # cb.early.stop and cb.cv.predict are at the end of the list # with cb.cv.predict being the last (when present) add.cb <- function(cb_list, cb) { cb_list <- c(cb_list, cb) names(cb_list) <- callback.names(cb_list) if ('cb.early.stop' %in% names(cb_list)) { cb_list <- c(cb_list, cb_list['cb.early.stop']) # this removes only the first one cb_list['cb.early.stop'] <- NULL } if ('cb.cv.predict' %in% names(cb_list)) { cb_list <- c(cb_list, cb_list['cb.cv.predict']) cb_list['cb.cv.predict'] <- NULL } cb_list } # Sort callbacks list into categories categorize.callbacks <- function(cb_list) { list( pre_iter = Filter(function(x) { pre <- attr(x, 'is_pre_iteration') !is.null(pre) && pre }, cb_list), post_iter = Filter(function(x) { pre <- attr(x, 'is_pre_iteration') is.null(pre) || !pre }, cb_list), finalize = Filter(function(x) { 'finalize' %in% names(formals(x)) }, cb_list) ) } # Check whether all callback functions with names given by 'query_names' are present in the 'cb_list'. has.callbacks <- function(cb_list, query_names) { if (length(cb_list) < length(query_names)) return(FALSE) if (!is.list(cb_list) || any(sapply(cb_list, class) != 'function')) { stop('`cb_list` must be a list of callback functions') } cb_names <- callback.names(cb_list) if (!is.character(cb_names) || length(cb_names) != length(cb_list) || any(cb_names == "")) { stop('All callbacks in the `cb_list` must have a non-empty `name` attribute') } if (!is.character(query_names) || length(query_names) == 0 || any(query_names == "")) { stop('query_names must be a non-empty vector of non-empty character names') } return(all(query_names %in% cb_names)) } xgboost-1.5.2/R-package/R/utils.R000066400000000000000000000413511417122711700164710ustar00rootroot00000000000000# # This file is for the low level reusable utility functions # that are not supposed to be visible to a user. # # # General helper utilities ---------------------------------------------------- # # SQL-style NVL shortcut. NVL <- function(x, val) { if (is.null(x)) return(val) if (is.vector(x)) { x[is.na(x)] <- val return(x) } if (typeof(x) == 'closure') return(x) stop("typeof(x) == ", typeof(x), " is not supported by NVL") } # List of classification and ranking objectives .CLASSIFICATION_OBJECTIVES <- function() { return(c('binary:logistic', 'binary:logitraw', 'binary:hinge', 'multi:softmax', 'multi:softprob', 'rank:pairwise', 'rank:ndcg', 'rank:map')) } # # Low-level functions for boosting -------------------------------------------- # # Merges booster params with whatever is provided in ... # plus runs some checks check.booster.params <- function(params, ...) { if (!identical(class(params), "list")) stop("params must be a list") # in R interface, allow for '.' instead of '_' in parameter names names(params) <- gsub("\\.", "_", names(params)) # merge parameters from the params and the dots-expansion dot_params <- list(...) names(dot_params) <- gsub("\\.", "_", names(dot_params)) if (length(intersect(names(params), names(dot_params))) > 0) stop("Same parameters in 'params' and in the call are not allowed. Please check your 'params' list.") params <- c(params, dot_params) # providing a parameter multiple times makes sense only for 'eval_metric' name_freqs <- table(names(params)) multi_names <- setdiff(names(name_freqs[name_freqs > 1]), 'eval_metric') if (length(multi_names) > 0) { warning("The following parameters were provided multiple times:\n\t", paste(multi_names, collapse = ', '), "\n Only the last value for each of them will be used.\n") # While xgboost internals would choose the last value for a multiple-times parameter, # enforce it here in R as well (b/c multi-parameters might be used further in R code, # and R takes the 1st value when multiple elements with the same name are present in a list). for (n in multi_names) { del_idx <- which(n == names(params)) del_idx <- del_idx[-length(del_idx)] params[[del_idx]] <- NULL } } # for multiclass, expect num_class to be set if (typeof(params[['objective']]) == "character" && substr(NVL(params[['objective']], 'x'), 1, 6) == 'multi:' && as.numeric(NVL(params[['num_class']], 0)) < 2) { stop("'num_class' > 1 parameter must be set for multiclass classification") } # monotone_constraints parser if (!is.null(params[['monotone_constraints']]) && typeof(params[['monotone_constraints']]) != "character") { vec2str <- paste(params[['monotone_constraints']], collapse = ',') vec2str <- paste0('(', vec2str, ')') params[['monotone_constraints']] <- vec2str } # interaction constraints parser (convert from list of column indices to string) if (!is.null(params[['interaction_constraints']]) && typeof(params[['interaction_constraints']]) != "character"){ # check input class if (!identical(class(params[['interaction_constraints']]), 'list')) stop('interaction_constraints should be class list') if (!all(unique(sapply(params[['interaction_constraints']], class)) %in% c('numeric', 'integer'))) { stop('interaction_constraints should be a list of numeric/integer vectors') } # recast parameter as string interaction_constraints <- sapply(params[['interaction_constraints']], function(x) paste0('[', paste(x, collapse = ','), ']')) params[['interaction_constraints']] <- paste0('[', paste(interaction_constraints, collapse = ','), ']') } return(params) } # Performs some checks related to custom objective function. # WARNING: has side-effects and can modify 'params' and 'obj' in its calling frame check.custom.obj <- function(env = parent.frame()) { if (!is.null(env$params[['objective']]) && !is.null(env$obj)) stop("Setting objectives in 'params' and 'obj' at the same time is not allowed") if (!is.null(env$obj) && typeof(env$obj) != 'closure') stop("'obj' must be a function") # handle the case when custom objective function was provided through params if (!is.null(env$params[['objective']]) && typeof(env$params$objective) == 'closure') { env$obj <- env$params$objective env$params$objective <- NULL } } # Performs some checks related to custom evaluation function. # WARNING: has side-effects and can modify 'params' and 'feval' in its calling frame check.custom.eval <- function(env = parent.frame()) { if (!is.null(env$params[['eval_metric']]) && !is.null(env$feval)) stop("Setting evaluation metrics in 'params' and 'feval' at the same time is not allowed") if (!is.null(env$feval) && typeof(env$feval) != 'closure') stop("'feval' must be a function") # handle a situation when custom eval function was provided through params if (!is.null(env$params[['eval_metric']]) && typeof(env$params$eval_metric) == 'closure') { env$feval <- env$params$eval_metric env$params$eval_metric <- NULL } # require maximize to be set when custom feval and early stopping are used together if (!is.null(env$feval) && is.null(env$maximize) && ( !is.null(env$early_stopping_rounds) || has.callbacks(env$callbacks, 'cb.early.stop'))) stop("Please set 'maximize' to indicate whether the evaluation metric needs to be maximized or not") } # Update a booster handle for an iteration with dtrain data xgb.iter.update <- function(booster_handle, dtrain, iter, obj = NULL) { if (!identical(class(booster_handle), "xgb.Booster.handle")) { stop("booster_handle must be of xgb.Booster.handle class") } if (!inherits(dtrain, "xgb.DMatrix")) { stop("dtrain must be of xgb.DMatrix class") } if (is.null(obj)) { .Call(XGBoosterUpdateOneIter_R, booster_handle, as.integer(iter), dtrain) } else { pred <- predict(booster_handle, dtrain, outputmargin = TRUE, training = TRUE, ntreelimit = 0) gpair <- obj(pred, dtrain) .Call(XGBoosterBoostOneIter_R, booster_handle, dtrain, gpair$grad, gpair$hess) } return(TRUE) } # Evaluate one iteration. # Returns a named vector of evaluation metrics # with the names in a 'datasetname-metricname' format. xgb.iter.eval <- function(booster_handle, watchlist, iter, feval = NULL) { if (!identical(class(booster_handle), "xgb.Booster.handle")) stop("class of booster_handle must be xgb.Booster.handle") if (length(watchlist) == 0) return(NULL) evnames <- names(watchlist) if (is.null(feval)) { msg <- .Call(XGBoosterEvalOneIter_R, booster_handle, as.integer(iter), watchlist, as.list(evnames)) mat <- matrix(strsplit(msg, '\\s+|:')[[1]][-1], nrow = 2) res <- structure(as.numeric(mat[2, ]), names = mat[1, ]) } else { res <- sapply(seq_along(watchlist), function(j) { w <- watchlist[[j]] ## predict using all trees preds <- predict(booster_handle, w, outputmargin = TRUE, iterationrange = c(1, 1)) eval_res <- feval(preds, w) out <- eval_res$value names(out) <- paste0(evnames[j], "-", eval_res$metric) out }) } return(res) } # # Helper functions for cross validation --------------------------------------- # # Possibly convert the labels into factors, depending on the objective. # The labels are converted into factors only when the given objective refers to the classification # or ranking tasks. convert.labels <- function(labels, objective_name) { if (objective_name %in% .CLASSIFICATION_OBJECTIVES()) { return(as.factor(labels)) } else { return(labels) } } # Generates random (stratified if needed) CV folds generate.cv.folds <- function(nfold, nrows, stratified, label, params) { # cannot do it for rank objective <- params$objective if (is.character(objective) && strtrim(objective, 5) == 'rank:') { stop("\n\tAutomatic generation of CV-folds is not implemented for ranking!\n", "\tConsider providing pre-computed CV-folds through the 'folds=' parameter.\n") } # shuffle rnd_idx <- sample.int(nrows) if (stratified && length(label) == length(rnd_idx)) { y <- label[rnd_idx] # WARNING: some heuristic logic is employed to identify classification setting! # - For classification, need to convert y labels to factor before making the folds, # and then do stratification by factor levels. # - For regression, leave y numeric and do stratification by quantiles. if (is.character(objective)) { y <- convert.labels(y, params$objective) } else { # If no 'objective' given in params, it means that user either wants to # use the default 'reg:squarederror' objective or has provided a custom # obj function. Here, assume classification setting when y has 5 or less # unique values: if (length(unique(y)) <= 5) { y <- factor(y) } } folds <- xgb.createFolds(y, nfold) } else { # make simple non-stratified folds kstep <- length(rnd_idx) %/% nfold folds <- list() for (i in seq_len(nfold - 1)) { folds[[i]] <- rnd_idx[seq_len(kstep)] rnd_idx <- rnd_idx[-seq_len(kstep)] } folds[[nfold]] <- rnd_idx } return(folds) } # Creates CV folds stratified by the values of y. # It was borrowed from caret::createFolds and simplified # by always returning an unnamed list of fold indices. xgb.createFolds <- function(y, k = 10) { if (is.numeric(y)) { ## Group the numeric data based on their magnitudes ## and sample within those groups. ## When the number of samples is low, we may have ## issues further slicing the numeric data into ## groups. The number of groups will depend on the ## ratio of the number of folds to the sample size. ## At most, we will use quantiles. If the sample ## is too small, we just do regular unstratified ## CV cuts <- floor(length(y) / k) if (cuts < 2) cuts <- 2 if (cuts > 5) cuts <- 5 y <- cut(y, unique(stats::quantile(y, probs = seq(0, 1, length = cuts))), include.lowest = TRUE) } if (k < length(y)) { ## reset levels so that the possible levels and ## the levels in the vector are the same y <- factor(as.character(y)) numInClass <- table(y) foldVector <- vector(mode = "integer", length(y)) ## For each class, balance the fold allocation as far ## as possible, then resample the remainder. ## The final assignment of folds is also randomized. for (i in seq_along(numInClass)) { ## create a vector of integers from 1:k as many times as possible without ## going over the number of samples in the class. Note that if the number ## of samples in a class is less than k, nothing is produced here. seqVector <- rep(seq_len(k), numInClass[i] %/% k) ## add enough random integers to get length(seqVector) == numInClass[i] if (numInClass[i] %% k > 0) seqVector <- c(seqVector, sample.int(k, numInClass[i] %% k)) ## shuffle the integers for fold assignment and assign to this classes's data ## seqVector[sample.int(length(seqVector))] is used to handle length(seqVector) == 1 foldVector[y == dimnames(numInClass)$y[i]] <- seqVector[sample.int(length(seqVector))] } } else { foldVector <- seq(along = y) } out <- split(seq(along = y), foldVector) names(out) <- NULL out } # # Deprectaion notice utilities ------------------------------------------------ # #' Deprecation notices. #' #' At this time, some of the parameter names were changed in order to make the code style more uniform. #' The deprecated parameters would be removed in the next release. #' #' To see all the current deprecated and new parameters, check the \code{xgboost:::depr_par_lut} table. #' #' A deprecation warning is shown when any of the deprecated parameters is used in a call. #' An additional warning is shown when there was a partial match to a deprecated parameter #' (as R is able to partially match parameter names). #' #' @name xgboost-deprecated NULL #' Do not use \code{\link[base]{saveRDS}} or \code{\link[base]{save}} for long-term archival of #' models. Instead, use \code{\link{xgb.save}} or \code{\link{xgb.save.raw}}. #' #' It is a common practice to use the built-in \code{\link[base]{saveRDS}} function (or #' \code{\link[base]{save}}) to persist R objects to the disk. While it is possible to persist #' \code{xgb.Booster} objects using \code{\link[base]{saveRDS}}, it is not advisable to do so if #' the model is to be accessed in the future. If you train a model with the current version of #' XGBoost and persist it with \code{\link[base]{saveRDS}}, the model is not guaranteed to be #' accessible in later releases of XGBoost. To ensure that your model can be accessed in future #' releases of XGBoost, use \code{\link{xgb.save}} or \code{\link{xgb.save.raw}} instead. #' #' @details #' Use \code{\link{xgb.save}} to save the XGBoost model as a stand-alone file. You may opt into #' the JSON format by specifying the JSON extension. To read the model back, use #' \code{\link{xgb.load}}. #' #' Use \code{\link{xgb.save.raw}} to save the XGBoost model as a sequence (vector) of raw bytes #' in a future-proof manner. Future releases of XGBoost will be able to read the raw bytes and #' re-construct the corresponding model. To read the model back, use \code{\link{xgb.load.raw}}. #' The \code{\link{xgb.save.raw}} function is useful if you'd like to persist the XGBoost model #' as part of another R object. #' #' Note: Do not use \code{\link{xgb.serialize}} to store models long-term. It persists not only the #' model but also internal configurations and parameters, and its format is not stable across #' multiple XGBoost versions. Use \code{\link{xgb.serialize}} only for checkpointing. #' #' For more details and explanation about model persistence and archival, consult the page #' \url{https://xgboost.readthedocs.io/en/latest/tutorials/saving_model.html}. #' #' @examples #' data(agaricus.train, package='xgboost') #' bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 2, #' eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") #' #' # Save as a stand-alone file; load it with xgb.load() #' xgb.save(bst, 'xgb.model') #' bst2 <- xgb.load('xgb.model') #' #' # Save as a stand-alone file (JSON); load it with xgb.load() #' xgb.save(bst, 'xgb.model.json') #' bst2 <- xgb.load('xgb.model.json') #' if (file.exists('xgb.model.json')) file.remove('xgb.model.json') #' #' # Save as a raw byte vector; load it with xgb.load.raw() #' xgb_bytes <- xgb.save.raw(bst) #' bst2 <- xgb.load.raw(xgb_bytes) #' #' # Persist XGBoost model as part of another R object #' obj <- list(xgb_model_bytes = xgb.save.raw(bst), description = "My first XGBoost model") #' # Persist the R object. Here, saveRDS() is okay, since it doesn't persist #' # xgb.Booster directly. What's being persisted is the future-proof byte representation #' # as given by xgb.save.raw(). #' saveRDS(obj, 'my_object.rds') #' # Read back the R object #' obj2 <- readRDS('my_object.rds') #' # Re-construct xgb.Booster object from the bytes #' bst2 <- xgb.load.raw(obj2$xgb_model_bytes) #' if (file.exists('my_object.rds')) file.remove('my_object.rds') #' #' @name a-compatibility-note-for-saveRDS-save NULL # Lookup table for the deprecated parameters bookkeeping depr_par_lut <- matrix(c( 'print.every.n', 'print_every_n', 'early.stop.round', 'early_stopping_rounds', 'training.data', 'data', 'with.stats', 'with_stats', 'numberOfClusters', 'n_clusters', 'features.keep', 'features_keep', 'plot.height', 'plot_height', 'plot.width', 'plot_width', 'n_first_tree', 'trees', 'dummy', 'DUMMY' ), ncol = 2, byrow = TRUE) colnames(depr_par_lut) <- c('old', 'new') # Checks the dot-parameters for deprecated names # (including partial matching), gives a deprecation warning, # and sets new parameters to the old parameters' values within its parent frame. # WARNING: has side-effects check.deprecation <- function(..., env = parent.frame()) { pars <- list(...) # exact and partial matches all_match <- pmatch(names(pars), depr_par_lut[, 1]) # indices of matched pars' names idx_pars <- which(!is.na(all_match)) if (length(idx_pars) == 0) return() # indices of matched LUT rows idx_lut <- all_match[idx_pars] # which of idx_lut were the exact matches? ex_match <- depr_par_lut[idx_lut, 1] %in% names(pars) for (i in seq_along(idx_pars)) { pars_par <- names(pars)[idx_pars[i]] old_par <- depr_par_lut[idx_lut[i], 1] new_par <- depr_par_lut[idx_lut[i], 2] if (!ex_match[i]) { warning("'", pars_par, "' was partially matched to '", old_par, "'") } .Deprecated(new_par, old = old_par, package = 'xgboost') if (new_par != 'NULL') { eval(parse(text = paste(new_par, '<-', pars[[pars_par]])), envir = env) } } } xgboost-1.5.2/R-package/R/xgb.Booster.R000066400000000000000000000724021417122711700175260ustar00rootroot00000000000000# Construct an internal xgboost Booster and return a handle to it. # internal utility function xgb.Booster.handle <- function(params = list(), cachelist = list(), modelfile = NULL, handle = NULL) { if (typeof(cachelist) != "list" || !all(vapply(cachelist, inherits, logical(1), what = 'xgb.DMatrix'))) { stop("cachelist must be a list of xgb.DMatrix objects") } ## Load existing model, dispatch for on disk model file and in memory buffer if (!is.null(modelfile)) { if (typeof(modelfile) == "character") { ## A filename handle <- .Call(XGBoosterCreate_R, cachelist) modelfile <- path.expand(modelfile) .Call(XGBoosterLoadModel_R, handle, modelfile[1]) class(handle) <- "xgb.Booster.handle" if (length(params) > 0) { xgb.parameters(handle) <- params } return(handle) } else if (typeof(modelfile) == "raw") { ## A memory buffer bst <- xgb.unserialize(modelfile, handle) xgb.parameters(bst) <- params return (bst) } else if (inherits(modelfile, "xgb.Booster")) { ## A booster object bst <- xgb.Booster.complete(modelfile, saveraw = TRUE) bst <- xgb.unserialize(bst$raw) xgb.parameters(bst) <- params return (bst) } else { stop("modelfile must be either character filename, or raw booster dump, or xgb.Booster object") } } ## Create new model handle <- .Call(XGBoosterCreate_R, cachelist) class(handle) <- "xgb.Booster.handle" if (length(params) > 0) { xgb.parameters(handle) <- params } return(handle) } # Convert xgb.Booster.handle to xgb.Booster # internal utility function xgb.handleToBooster <- function(handle, raw = NULL) { bst <- list(handle = handle, raw = raw) class(bst) <- "xgb.Booster" return(bst) } # Check whether xgb.Booster.handle is null # internal utility function is.null.handle <- function(handle) { if (is.null(handle)) return(TRUE) if (!identical(class(handle), "xgb.Booster.handle")) stop("argument type must be xgb.Booster.handle") if (.Call(XGCheckNullPtr_R, handle)) return(TRUE) return(FALSE) } # Return a verified to be valid handle out of either xgb.Booster.handle or # xgb.Booster internal utility function xgb.get.handle <- function(object) { if (inherits(object, "xgb.Booster")) { handle <- object$handle } else if (inherits(object, "xgb.Booster.handle")) { handle <- object } else { stop("argument must be of either xgb.Booster or xgb.Booster.handle class") } if (is.null.handle(handle)) { stop("invalid xgb.Booster.handle") } handle } #' Restore missing parts of an incomplete xgb.Booster object. #' #' It attempts to complete an \code{xgb.Booster} object by restoring either its missing #' raw model memory dump (when it has no \code{raw} data but its \code{xgb.Booster.handle} is valid) #' or its missing internal handle (when its \code{xgb.Booster.handle} is not valid #' but it has a raw Booster memory dump). #' #' @param object object of class \code{xgb.Booster} #' @param saveraw a flag indicating whether to append \code{raw} Booster memory dump data #' when it doesn't already exist. #' #' @details #' #' While this method is primarily for internal use, it might be useful in some practical situations. #' #' E.g., when an \code{xgb.Booster} model is saved as an R object and then is loaded as an R object, #' its handle (pointer) to an internal xgboost model would be invalid. The majority of xgboost methods #' should still work for such a model object since those methods would be using #' \code{xgb.Booster.complete} internally. However, one might find it to be more efficient to call the #' \code{xgb.Booster.complete} function explicitly once after loading a model as an R-object. #' That would prevent further repeated implicit reconstruction of an internal booster model. #' #' @return #' An object of \code{xgb.Booster} class. #' #' @examples #' #' data(agaricus.train, package='xgboost') #' bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 2, #' eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") #' saveRDS(bst, "xgb.model.rds") #' #' # Warning: The resulting RDS file is only compatible with the current XGBoost version. #' # Refer to the section titled "a-compatibility-note-for-saveRDS-save". #' bst1 <- readRDS("xgb.model.rds") #' if (file.exists("xgb.model.rds")) file.remove("xgb.model.rds") #' # the handle is invalid: #' print(bst1$handle) #' #' bst1 <- xgb.Booster.complete(bst1) #' # now the handle points to a valid internal booster model: #' print(bst1$handle) #' #' @export xgb.Booster.complete <- function(object, saveraw = TRUE) { if (!inherits(object, "xgb.Booster")) stop("argument type must be xgb.Booster") if (is.null.handle(object$handle)) { object$handle <- xgb.Booster.handle(modelfile = object$raw, handle = object$handle) } else { if (is.null(object$raw) && saveraw) { object$raw <- xgb.serialize(object$handle) } } attrs <- xgb.attributes(object) if (!is.null(attrs$best_ntreelimit)) { object$best_ntreelimit <- as.integer(attrs$best_ntreelimit) } if (!is.null(attrs$best_iteration)) { ## Convert from 0 based back to 1 based. object$best_iteration <- as.integer(attrs$best_iteration) + 1 } if (!is.null(attrs$best_score)) { object$best_score <- as.numeric(attrs$best_score) } if (!is.null(attrs$best_msg)) { object$best_msg <- attrs$best_msg } if (!is.null(attrs$niter)) { object$niter <- as.integer(attrs$niter) } return(object) } #' Predict method for eXtreme Gradient Boosting model #' #' Predicted values based on either xgboost model or model handle object. #' #' @param object Object of class \code{xgb.Booster} or \code{xgb.Booster.handle} #' @param newdata takes \code{matrix}, \code{dgCMatrix}, local data file or \code{xgb.DMatrix}. #' @param missing Missing is only used when input is dense matrix. Pick a float value that represents #' missing values in data (e.g., sometimes 0 or some other extreme value is used). #' @param outputmargin whether the prediction should be returned in the for of original untransformed #' sum of predictions from boosting iterations' results. E.g., setting \code{outputmargin=TRUE} for #' logistic regression would result in predictions for log-odds instead of probabilities. #' @param ntreelimit Deprecated, use \code{iterationrange} instead. #' @param predleaf whether predict leaf index. #' @param predcontrib whether to return feature contributions to individual predictions (see Details). #' @param approxcontrib whether to use a fast approximation for feature contributions (see Details). #' @param predinteraction whether to return contributions of feature interactions to individual predictions (see Details). #' @param reshape whether to reshape the vector of predictions to a matrix form when there are several #' prediction outputs per case. This option has no effect when either of predleaf, predcontrib, #' or predinteraction flags is TRUE. #' @param training whether is the prediction result used for training. For dart booster, #' training predicting will perform dropout. #' @param iterationrange Specifies which layer of trees are used in prediction. For #' example, if a random forest is trained with 100 rounds. Specifying #' `iteration_range=(1, 21)`, then only the forests built during [1, 21) (half open set) #' rounds are used in this prediction. It's 1-based index just like R vector. When set #' to \code{c(1, 1)} XGBoost will use all trees. #' @param strict_shape Default is \code{FALSE}. When it's set to \code{TRUE}, output #' type and shape of prediction are invariant to model type. #' #' @param ... Parameters passed to \code{predict.xgb.Booster} #' #' @details #' #' Note that \code{iterationrange} would currently do nothing for predictions from gblinear, #' since gblinear doesn't keep its boosting history. #' #' One possible practical applications of the \code{predleaf} option is to use the model #' as a generator of new features which capture non-linearity and interactions, #' e.g., as implemented in \code{\link{xgb.create.features}}. #' #' Setting \code{predcontrib = TRUE} allows to calculate contributions of each feature to #' individual predictions. For "gblinear" booster, feature contributions are simply linear terms #' (feature_beta * feature_value). For "gbtree" booster, feature contributions are SHAP #' values (Lundberg 2017) that sum to the difference between the expected output #' of the model and the current prediction (where the hessian weights are used to compute the expectations). #' Setting \code{approxcontrib = TRUE} approximates these values following the idea explained #' in \url{http://blog.datadive.net/interpreting-random-forests/}. #' #' With \code{predinteraction = TRUE}, SHAP values of contributions of interaction of each pair of features #' are computed. Note that this operation might be rather expensive in terms of compute and memory. #' Since it quadratically depends on the number of features, it is recommended to perform selection #' of the most important features first. See below about the format of the returned results. #' #' @return #' The return type is different depending whether \code{strict_shape} is set to \code{TRUE}. By default, #' for regression or binary classification, it returns a vector of length \code{nrows(newdata)}. #' For multiclass classification, either a \code{num_class * nrows(newdata)} vector or #' a \code{(nrows(newdata), num_class)} dimension matrix is returned, depending on #' the \code{reshape} value. #' #' When \code{predleaf = TRUE}, the output is a matrix object with the #' number of columns corresponding to the number of trees. #' #' When \code{predcontrib = TRUE} and it is not a multiclass setting, the output is a matrix object with #' \code{num_features + 1} columns. The last "+ 1" column in a matrix corresponds to bias. #' For a multiclass case, a list of \code{num_class} elements is returned, where each element is #' such a matrix. The contribution values are on the scale of untransformed margin #' (e.g., for binary classification would mean that the contributions are log-odds deviations from bias). #' #' When \code{predinteraction = TRUE} and it is not a multiclass setting, the output is a 3d array with #' dimensions \code{c(nrow, num_features + 1, num_features + 1)}. The off-diagonal (in the last two dimensions) #' elements represent different features interaction contributions. The array is symmetric WRT the last #' two dimensions. The "+ 1" columns corresponds to bias. Summing this array along the last dimension should #' produce practically the same result as predict with \code{predcontrib = TRUE}. #' For a multiclass case, a list of \code{num_class} elements is returned, where each element is #' such an array. #' #' When \code{strict_shape} is set to \code{TRUE}, the output is always an array. For #' normal prediction, the output is a 2-dimension array \code{(num_class, nrow(newdata))}. #' #' For \code{predcontrib = TRUE}, output is \code{(ncol(newdata) + 1, num_class, nrow(newdata))} #' For \code{predinteraction = TRUE}, output is \code{(ncol(newdata) + 1, ncol(newdata) + 1, num_class, nrow(newdata))} #' For \code{predleaf = TRUE}, output is \code{(n_trees_in_forest, num_class, n_iterations, nrow(newdata))} #' #' @seealso #' \code{\link{xgb.train}}. #' #' @references #' #' Scott M. Lundberg, Su-In Lee, "A Unified Approach to Interpreting Model Predictions", NIPS Proceedings 2017, \url{https://arxiv.org/abs/1705.07874} #' #' Scott M. Lundberg, Su-In Lee, "Consistent feature attribution for tree ensembles", \url{https://arxiv.org/abs/1706.06060} #' #' @examples #' ## binary classification: #' #' data(agaricus.train, package='xgboost') #' data(agaricus.test, package='xgboost') #' train <- agaricus.train #' test <- agaricus.test #' #' bst <- xgboost(data = train$data, label = train$label, max_depth = 2, #' eta = 0.5, nthread = 2, nrounds = 5, objective = "binary:logistic") #' # use all trees by default #' pred <- predict(bst, test$data) #' # use only the 1st tree #' pred1 <- predict(bst, test$data, iterationrange = c(1, 2)) #' #' # Predicting tree leafs: #' # the result is an nsamples X ntrees matrix #' pred_leaf <- predict(bst, test$data, predleaf = TRUE) #' str(pred_leaf) #' #' # Predicting feature contributions to predictions: #' # the result is an nsamples X (nfeatures + 1) matrix #' pred_contr <- predict(bst, test$data, predcontrib = TRUE) #' str(pred_contr) #' # verify that contributions' sums are equal to log-odds of predictions (up to float precision): #' summary(rowSums(pred_contr) - qlogis(pred)) #' # for the 1st record, let's inspect its features that had non-zero contribution to prediction: #' contr1 <- pred_contr[1,] #' contr1 <- contr1[-length(contr1)] # drop BIAS #' contr1 <- contr1[contr1 != 0] # drop non-contributing features #' contr1 <- contr1[order(abs(contr1))] # order by contribution magnitude #' old_mar <- par("mar") #' par(mar = old_mar + c(0,7,0,0)) #' barplot(contr1, horiz = TRUE, las = 2, xlab = "contribution to prediction in log-odds") #' par(mar = old_mar) #' #' #' ## multiclass classification in iris dataset: #' #' lb <- as.numeric(iris$Species) - 1 #' num_class <- 3 #' set.seed(11) #' bst <- xgboost(data = as.matrix(iris[, -5]), label = lb, #' max_depth = 4, eta = 0.5, nthread = 2, nrounds = 10, subsample = 0.5, #' objective = "multi:softprob", num_class = num_class) #' # predict for softmax returns num_class probability numbers per case: #' pred <- predict(bst, as.matrix(iris[, -5])) #' str(pred) #' # reshape it to a num_class-columns matrix #' pred <- matrix(pred, ncol=num_class, byrow=TRUE) #' # convert the probabilities to softmax labels #' pred_labels <- max.col(pred) - 1 #' # the following should result in the same error as seen in the last iteration #' sum(pred_labels != lb)/length(lb) #' #' # compare that to the predictions from softmax: #' set.seed(11) #' bst <- xgboost(data = as.matrix(iris[, -5]), label = lb, #' max_depth = 4, eta = 0.5, nthread = 2, nrounds = 10, subsample = 0.5, #' objective = "multi:softmax", num_class = num_class) #' pred <- predict(bst, as.matrix(iris[, -5])) #' str(pred) #' all.equal(pred, pred_labels) #' # prediction from using only 5 iterations should result #' # in the same error as seen in iteration 5: #' pred5 <- predict(bst, as.matrix(iris[, -5]), iterationrange=c(1, 6)) #' sum(pred5 != lb)/length(lb) #' #' @rdname predict.xgb.Booster #' @export predict.xgb.Booster <- function(object, newdata, missing = NA, outputmargin = FALSE, ntreelimit = NULL, predleaf = FALSE, predcontrib = FALSE, approxcontrib = FALSE, predinteraction = FALSE, reshape = FALSE, training = FALSE, iterationrange = NULL, strict_shape = FALSE, ...) { object <- xgb.Booster.complete(object, saveraw = FALSE) if (!inherits(newdata, "xgb.DMatrix")) newdata <- xgb.DMatrix(newdata, missing = missing) if (!is.null(object[["feature_names"]]) && !is.null(colnames(newdata)) && !identical(object[["feature_names"]], colnames(newdata))) stop("Feature names stored in `object` and `newdata` are different!") if (NVL(object$params[['booster']], '') == 'gblinear' || is.null(ntreelimit)) ntreelimit <- 0 if (ntreelimit != 0 && is.null(iterationrange)) { ## only ntreelimit, initialize iteration range iterationrange <- c(0, 0) } else if (ntreelimit == 0 && !is.null(iterationrange)) { ## only iteration range, handle 1-based indexing iterationrange <- c(iterationrange[1] - 1, iterationrange[2] - 1) } else if (ntreelimit != 0 && !is.null(iterationrange)) { ## both are specified, let libgxgboost throw an error } else { ## no limit is supplied, use best if (is.null(object$best_iteration)) { iterationrange <- c(0, 0) } else { ## We don't need to + 1 as R is 1-based index. iterationrange <- c(0, as.integer(object$best_iteration)) } } ## Handle the 0 length values. box <- function(val) { if (length(val) == 0) { cval <- vector(, 1) cval[0] <- val return(cval) } return (val) } ## We set strict_shape to TRUE then drop the dimensions conditionally args <- list( training = box(training), strict_shape = box(TRUE), iteration_begin = box(as.integer(iterationrange[1])), iteration_end = box(as.integer(iterationrange[2])), ntree_limit = box(as.integer(ntreelimit)), type = box(as.integer(0)) ) set_type <- function(type) { if (args$type != 0) { stop("One type of prediction at a time.") } return(box(as.integer(type))) } if (outputmargin) { args$type <- set_type(1) } if (predcontrib) { args$type <- set_type(if (approxcontrib) 3 else 2) } if (predinteraction) { args$type <- set_type(if (approxcontrib) 5 else 4) } if (predleaf) { args$type <- set_type(6) } predts <- .Call( XGBoosterPredictFromDMatrix_R, object$handle, newdata, jsonlite::toJSON(args, auto_unbox = TRUE) ) names(predts) <- c("shape", "results") shape <- predts$shape ret <- predts$results n_ret <- length(ret) n_row <- nrow(newdata) if (n_row != shape[1]) { stop("Incorrect predict shape.") } arr <- array(data = ret, dim = rev(shape)) cnames <- if (!is.null(colnames(newdata))) c(colnames(newdata), "BIAS") else NULL n_groups <- shape[2] ## Needed regardless of whether strict shape is being used. if (predcontrib) { dimnames(arr) <- list(cnames, NULL, NULL) } else if (predinteraction) { dimnames(arr) <- list(cnames, cnames, NULL, NULL) } if (strict_shape) { return(arr) # strict shape is calculated by libxgboost uniformly. } if (predleaf) { ## Predict leaf arr <- if (n_ret == n_row) { matrix(arr, ncol = 1) } else { matrix(arr, nrow = n_row, byrow = TRUE) } } else if (predcontrib) { ## Predict contribution arr <- aperm(a = arr, perm = c(2, 3, 1)) # [group, row, col] arr <- if (n_ret == n_row) { matrix(arr, ncol = 1, dimnames = list(NULL, cnames)) } else if (n_groups != 1) { ## turns array into list of matrices lapply(seq_len(n_groups), function(g) arr[g, , ]) } else { ## remove the first axis (group) dn <- dimnames(arr) matrix(arr[1, , ], nrow = dim(arr)[2], ncol = dim(arr)[3], dimnames = c(dn[2], dn[3])) } } else if (predinteraction) { ## Predict interaction arr <- aperm(a = arr, perm = c(3, 4, 1, 2)) # [group, row, col, col] arr <- if (n_ret == n_row) { matrix(arr, ncol = 1, dimnames = list(NULL, cnames)) } else if (n_groups != 1) { ## turns array into list of matrices lapply(seq_len(n_groups), function(g) arr[g, , , ]) } else { ## remove the first axis (group) arr <- arr[1, , , , drop = FALSE] array(arr, dim = dim(arr)[2:4], dimnames(arr)[2:4]) } } else { ## Normal prediction arr <- if (reshape && n_groups != 1) { matrix(arr, ncol = n_groups, byrow = TRUE) } else { as.vector(ret) } } return(arr) } #' @rdname predict.xgb.Booster #' @export predict.xgb.Booster.handle <- function(object, ...) { bst <- xgb.handleToBooster(object) ret <- predict(bst, ...) return(ret) } #' Accessors for serializable attributes of a model. #' #' These methods allow to manipulate the key-value attribute strings of an xgboost model. #' #' @param object Object of class \code{xgb.Booster} or \code{xgb.Booster.handle}. #' @param name a non-empty character string specifying which attribute is to be accessed. #' @param value a value of an attribute for \code{xgb.attr<-}; for \code{xgb.attributes<-} #' it's a list (or an object coercible to a list) with the names of attributes to set #' and the elements corresponding to attribute values. #' Non-character values are converted to character. #' When attribute value is not a scalar, only the first index is used. #' Use \code{NULL} to remove an attribute. #' #' @details #' The primary purpose of xgboost model attributes is to store some meta-data about the model. #' Note that they are a separate concept from the object attributes in R. #' Specifically, they refer to key-value strings that can be attached to an xgboost model, #' stored together with the model's binary representation, and accessed later #' (from R or any other interface). #' In contrast, any R-attribute assigned to an R-object of \code{xgb.Booster} class #' would not be saved by \code{xgb.save} because an xgboost model is an external memory object #' and its serialization is handled externally. #' Also, setting an attribute that has the same name as one of xgboost's parameters wouldn't #' change the value of that parameter for a model. #' Use \code{\link{xgb.parameters<-}} to set or change model parameters. #' #' The attribute setters would usually work more efficiently for \code{xgb.Booster.handle} #' than for \code{xgb.Booster}, since only just a handle (pointer) would need to be copied. #' That would only matter if attributes need to be set many times. #' Note, however, that when feeding a handle of an \code{xgb.Booster} object to the attribute setters, #' the raw model cache of an \code{xgb.Booster} object would not be automatically updated, #' and it would be user's responsibility to call \code{xgb.serialize} to update it. #' #' The \code{xgb.attributes<-} setter either updates the existing or adds one or several attributes, #' but it doesn't delete the other existing attributes. #' #' @return #' \code{xgb.attr} returns either a string value of an attribute #' or \code{NULL} if an attribute wasn't stored in a model. #' #' \code{xgb.attributes} returns a list of all attribute stored in a model #' or \code{NULL} if a model has no stored attributes. #' #' @examples #' data(agaricus.train, package='xgboost') #' train <- agaricus.train #' #' bst <- xgboost(data = train$data, label = train$label, max_depth = 2, #' eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") #' #' xgb.attr(bst, "my_attribute") <- "my attribute value" #' print(xgb.attr(bst, "my_attribute")) #' xgb.attributes(bst) <- list(a = 123, b = "abc") #' #' xgb.save(bst, 'xgb.model') #' bst1 <- xgb.load('xgb.model') #' if (file.exists('xgb.model')) file.remove('xgb.model') #' print(xgb.attr(bst1, "my_attribute")) #' print(xgb.attributes(bst1)) #' #' # deletion: #' xgb.attr(bst1, "my_attribute") <- NULL #' print(xgb.attributes(bst1)) #' xgb.attributes(bst1) <- list(a = NULL, b = NULL) #' print(xgb.attributes(bst1)) #' #' @rdname xgb.attr #' @export xgb.attr <- function(object, name) { if (is.null(name) || nchar(as.character(name[1])) == 0) stop("invalid attribute name") handle <- xgb.get.handle(object) .Call(XGBoosterGetAttr_R, handle, as.character(name[1])) } #' @rdname xgb.attr #' @export `xgb.attr<-` <- function(object, name, value) { if (is.null(name) || nchar(as.character(name[1])) == 0) stop("invalid attribute name") handle <- xgb.get.handle(object) if (!is.null(value)) { # Coerce the elements to be scalar strings. # Q: should we warn user about non-scalar elements? if (is.numeric(value[1])) { value <- format(value[1], digits = 17) } else { value <- as.character(value[1]) } } .Call(XGBoosterSetAttr_R, handle, as.character(name[1]), value) if (is(object, 'xgb.Booster') && !is.null(object$raw)) { object$raw <- xgb.serialize(object$handle) } object } #' @rdname xgb.attr #' @export xgb.attributes <- function(object) { handle <- xgb.get.handle(object) attr_names <- .Call(XGBoosterGetAttrNames_R, handle) if (is.null(attr_names)) return(NULL) res <- lapply(attr_names, function(x) { .Call(XGBoosterGetAttr_R, handle, x) }) names(res) <- attr_names res } #' @rdname xgb.attr #' @export `xgb.attributes<-` <- function(object, value) { a <- as.list(value) if (is.null(names(a)) || any(nchar(names(a)) == 0)) { stop("attribute names cannot be empty strings") } # Coerce the elements to be scalar strings. # Q: should we warn a user about non-scalar elements? a <- lapply(a, function(x) { if (is.null(x)) return(NULL) if (is.numeric(x[1])) { format(x[1], digits = 17) } else { as.character(x[1]) } }) handle <- xgb.get.handle(object) for (i in seq_along(a)) { .Call(XGBoosterSetAttr_R, handle, names(a[i]), a[[i]]) } if (is(object, 'xgb.Booster') && !is.null(object$raw)) { object$raw <- xgb.serialize(object$handle) } object } #' Accessors for model parameters as JSON string. #' #' @param object Object of class \code{xgb.Booster} #' @param value A JSON string. #' #' @examples #' data(agaricus.train, package='xgboost') #' train <- agaricus.train #' #' bst <- xgboost(data = train$data, label = train$label, max_depth = 2, #' eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") #' config <- xgb.config(bst) #' #' @rdname xgb.config #' @export xgb.config <- function(object) { handle <- xgb.get.handle(object) .Call(XGBoosterSaveJsonConfig_R, handle); } #' @rdname xgb.config #' @export `xgb.config<-` <- function(object, value) { handle <- xgb.get.handle(object) .Call(XGBoosterLoadJsonConfig_R, handle, value) object$raw <- NULL # force renew the raw buffer object <- xgb.Booster.complete(object) object } #' Accessors for model parameters. #' #' Only the setter for xgboost parameters is currently implemented. #' #' @param object Object of class \code{xgb.Booster} or \code{xgb.Booster.handle}. #' @param value a list (or an object coercible to a list) with the names of parameters to set #' and the elements corresponding to parameter values. #' #' @details #' Note that the setter would usually work more efficiently for \code{xgb.Booster.handle} #' than for \code{xgb.Booster}, since only just a handle would need to be copied. #' #' @examples #' data(agaricus.train, package='xgboost') #' train <- agaricus.train #' #' bst <- xgboost(data = train$data, label = train$label, max_depth = 2, #' eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") #' #' xgb.parameters(bst) <- list(eta = 0.1) #' #' @rdname xgb.parameters #' @export `xgb.parameters<-` <- function(object, value) { if (length(value) == 0) return(object) p <- as.list(value) if (is.null(names(p)) || any(nchar(names(p)) == 0)) { stop("parameter names cannot be empty strings") } names(p) <- gsub("\\.", "_", names(p)) p <- lapply(p, function(x) as.character(x)[1]) handle <- xgb.get.handle(object) for (i in seq_along(p)) { .Call(XGBoosterSetParam_R, handle, names(p[i]), p[[i]]) } if (is(object, 'xgb.Booster') && !is.null(object$raw)) { object$raw <- xgb.serialize(object$handle) } object } # Extract the number of trees in a model. # TODO: either add a getter to C-interface, or simply set an 'ntree' attribute after each iteration. # internal utility function xgb.ntree <- function(bst) { length(grep('^booster', xgb.dump(bst))) } #' Print xgb.Booster #' #' Print information about xgb.Booster. #' #' @param x an xgb.Booster object #' @param verbose whether to print detailed data (e.g., attribute values) #' @param ... not currently used #' #' @examples #' data(agaricus.train, package='xgboost') #' train <- agaricus.train #' bst <- xgboost(data = train$data, label = train$label, max_depth = 2, #' eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") #' attr(bst, 'myattr') <- 'memo' #' #' print(bst) #' print(bst, verbose=TRUE) #' #' @method print xgb.Booster #' @export print.xgb.Booster <- function(x, verbose = FALSE, ...) { cat('##### xgb.Booster\n') valid_handle <- !is.null.handle(x$handle) if (!valid_handle) cat("Handle is invalid! Suggest using xgb.Booster.complete\n") cat('raw: ') if (!is.null(x$raw)) { cat(format(object.size(x$raw), units = "auto"), '\n') } else { cat('NULL\n') } if (!is.null(x$call)) { cat('call:\n ') print(x$call) } if (!is.null(x$params)) { cat('params (as set within xgb.train):\n') cat(' ', paste(names(x$params), paste0('"', unlist(x$params), '"'), sep = ' = ', collapse = ', '), '\n', sep = '') } # TODO: need an interface to access all the xgboosts parameters attrs <- character(0) if (valid_handle) attrs <- xgb.attributes(x) if (length(attrs) > 0) { cat('xgb.attributes:\n') if (verbose) { cat(paste(paste0(' ', names(attrs)), paste0('"', unlist(attrs), '"'), sep = ' = ', collapse = '\n'), '\n', sep = '') } else { cat(' ', paste(names(attrs), collapse = ', '), '\n', sep = '') } } if (!is.null(x$callbacks) && length(x$callbacks) > 0) { cat('callbacks:\n') lapply(callback.calls(x$callbacks), function(x) { cat(' ') print(x) }) } if (!is.null(x$feature_names)) cat('# of features:', length(x$feature_names), '\n') cat('niter: ', x$niter, '\n', sep = '') # TODO: uncomment when faster xgb.ntree is implemented #cat('ntree: ', xgb.ntree(x), '\n', sep='') for (n in setdiff(names(x), c('handle', 'raw', 'call', 'params', 'callbacks', 'evaluation_log', 'niter', 'feature_names'))) { if (is.atomic(x[[n]])) { cat(n, ':', x[[n]], '\n', sep = ' ') } else { cat(n, ':\n\t', sep = ' ') print(x[[n]]) } } if (!is.null(x$evaluation_log)) { cat('evaluation_log:\n') print(x$evaluation_log, row.names = FALSE, topn = 2) } invisible(x) } xgboost-1.5.2/R-package/R/xgb.DMatrix.R000066400000000000000000000302611417122711700174560ustar00rootroot00000000000000#' Construct xgb.DMatrix object #' #' Construct xgb.DMatrix object from either a dense matrix, a sparse matrix, or a local file. #' Supported input file formats are either a LIBSVM text file or a binary file that was created previously by #' \code{\link{xgb.DMatrix.save}}). #' #' @param data a \code{matrix} object (either numeric or integer), a \code{dgCMatrix} object, or a character #' string representing a filename. #' @param info a named list of additional information to store in the \code{xgb.DMatrix} object. #' See \code{\link{setinfo}} for the specific allowed kinds of #' @param missing a float value to represents missing values in data (used only when input is a dense matrix). #' It is useful when a 0 or some other extreme value represents missing values in data. #' @param silent whether to suppress printing an informational message after loading from a file. #' @param nthread Number of threads used for creating DMatrix. #' @param ... the \code{info} data could be passed directly as parameters, without creating an \code{info} list. #' #' @examples #' data(agaricus.train, package='xgboost') #' dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) #' xgb.DMatrix.save(dtrain, 'xgb.DMatrix.data') #' dtrain <- xgb.DMatrix('xgb.DMatrix.data') #' if (file.exists('xgb.DMatrix.data')) file.remove('xgb.DMatrix.data') #' @export xgb.DMatrix <- function(data, info = list(), missing = NA, silent = FALSE, nthread = NULL, ...) { cnames <- NULL if (typeof(data) == "character") { if (length(data) > 1) stop("'data' has class 'character' and length ", length(data), ".\n 'data' accepts either a numeric matrix or a single filename.") data <- path.expand(data) handle <- .Call(XGDMatrixCreateFromFile_R, data, as.integer(silent)) } else if (is.matrix(data)) { handle <- .Call(XGDMatrixCreateFromMat_R, data, missing, as.integer(NVL(nthread, -1))) cnames <- colnames(data) } else if (inherits(data, "dgCMatrix")) { handle <- .Call(XGDMatrixCreateFromCSC_R, data@p, data@i, data@x, nrow(data)) cnames <- colnames(data) } else { stop("xgb.DMatrix does not support construction from ", typeof(data)) } dmat <- handle attributes(dmat) <- list(.Dimnames = list(NULL, cnames), class = "xgb.DMatrix") info <- append(info, list(...)) for (i in seq_along(info)) { p <- info[i] setinfo(dmat, names(p), p[[1]]) } return(dmat) } # get dmatrix from data, label # internal helper method xgb.get.DMatrix <- function(data, label = NULL, missing = NA, weight = NULL, nthread = NULL) { if (inherits(data, "dgCMatrix") || is.matrix(data)) { if (is.null(label)) { stop("label must be provided when data is a matrix") } dtrain <- xgb.DMatrix(data, label = label, missing = missing, nthread = nthread) if (!is.null(weight)){ setinfo(dtrain, "weight", weight) } } else { if (!is.null(label)) { warning("xgboost: label will be ignored.") } if (is.character(data)) { data <- path.expand(data) dtrain <- xgb.DMatrix(data[1]) } else if (inherits(data, "xgb.DMatrix")) { dtrain <- data } else if (inherits(data, "data.frame")) { stop("xgboost doesn't support data.frame as input. Convert it to matrix first.") } else { stop("xgboost: invalid input data") } } return (dtrain) } #' Dimensions of xgb.DMatrix #' #' Returns a vector of numbers of rows and of columns in an \code{xgb.DMatrix}. #' @param x Object of class \code{xgb.DMatrix} #' #' @details #' Note: since \code{nrow} and \code{ncol} internally use \code{dim}, they can also #' be directly used with an \code{xgb.DMatrix} object. #' #' @examples #' data(agaricus.train, package='xgboost') #' train <- agaricus.train #' dtrain <- xgb.DMatrix(train$data, label=train$label) #' #' stopifnot(nrow(dtrain) == nrow(train$data)) #' stopifnot(ncol(dtrain) == ncol(train$data)) #' stopifnot(all(dim(dtrain) == dim(train$data))) #' #' @export dim.xgb.DMatrix <- function(x) { c(.Call(XGDMatrixNumRow_R, x), .Call(XGDMatrixNumCol_R, x)) } #' Handling of column names of \code{xgb.DMatrix} #' #' Only column names are supported for \code{xgb.DMatrix}, thus setting of #' row names would have no effect and returned row names would be NULL. #' #' @param x object of class \code{xgb.DMatrix} #' @param value a list of two elements: the first one is ignored #' and the second one is column names #' #' @details #' Generic \code{dimnames} methods are used by \code{colnames}. #' Since row names are irrelevant, it is recommended to use \code{colnames} directly. #' #' @examples #' data(agaricus.train, package='xgboost') #' train <- agaricus.train #' dtrain <- xgb.DMatrix(train$data, label=train$label) #' dimnames(dtrain) #' colnames(dtrain) #' colnames(dtrain) <- make.names(1:ncol(train$data)) #' print(dtrain, verbose=TRUE) #' #' @rdname dimnames.xgb.DMatrix #' @export dimnames.xgb.DMatrix <- function(x) { attr(x, '.Dimnames') } #' @rdname dimnames.xgb.DMatrix #' @export `dimnames<-.xgb.DMatrix` <- function(x, value) { if (!is.list(value) || length(value) != 2L) stop("invalid 'dimnames' given: must be a list of two elements") if (!is.null(value[[1L]])) stop("xgb.DMatrix does not have rownames") if (is.null(value[[2]])) { attr(x, '.Dimnames') <- NULL return(x) } if (ncol(x) != length(value[[2]])) stop("can't assign ", length(value[[2]]), " colnames to a ", ncol(x), " column xgb.DMatrix") attr(x, '.Dimnames') <- value x } #' Get information of an xgb.DMatrix object #' #' Get information of an xgb.DMatrix object #' @param object Object of class \code{xgb.DMatrix} #' @param name the name of the information field to get (see details) #' @param ... other parameters #' #' @details #' The \code{name} field can be one of the following: #' #' \itemize{ #' \item \code{label}: label XGBoost learn from ; #' \item \code{weight}: to do a weight rescale ; #' \item \code{base_margin}: base margin is the base prediction XGBoost will boost from ; #' \item \code{nrow}: number of rows of the \code{xgb.DMatrix}. #' #' } #' #' \code{group} can be setup by \code{setinfo} but can't be retrieved by \code{getinfo}. #' #' @examples #' data(agaricus.train, package='xgboost') #' dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) #' #' labels <- getinfo(dtrain, 'label') #' setinfo(dtrain, 'label', 1-labels) #' #' labels2 <- getinfo(dtrain, 'label') #' stopifnot(all(labels2 == 1-labels)) #' @rdname getinfo #' @export getinfo <- function(object, ...) UseMethod("getinfo") #' @rdname getinfo #' @export getinfo.xgb.DMatrix <- function(object, name, ...) { if (typeof(name) != "character" || length(name) != 1 || !name %in% c('label', 'weight', 'base_margin', 'nrow', 'label_lower_bound', 'label_upper_bound')) { stop("getinfo: name must be one of the following\n", " 'label', 'weight', 'base_margin', 'nrow', 'label_lower_bound', 'label_upper_bound'") } if (name != "nrow"){ ret <- .Call(XGDMatrixGetInfo_R, object, name) } else { ret <- nrow(object) } if (length(ret) == 0) return(NULL) return(ret) } #' Set information of an xgb.DMatrix object #' #' Set information of an xgb.DMatrix object #' #' @param object Object of class "xgb.DMatrix" #' @param name the name of the field to get #' @param info the specific field of information to set #' @param ... other parameters #' #' @details #' The \code{name} field can be one of the following: #' #' \itemize{ #' \item \code{label}: label XGBoost learn from ; #' \item \code{weight}: to do a weight rescale ; #' \item \code{base_margin}: base margin is the base prediction XGBoost will boost from ; #' \item \code{group}: number of rows in each group (to use with \code{rank:pairwise} objective). #' } #' #' @examples #' data(agaricus.train, package='xgboost') #' dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) #' #' labels <- getinfo(dtrain, 'label') #' setinfo(dtrain, 'label', 1-labels) #' labels2 <- getinfo(dtrain, 'label') #' stopifnot(all.equal(labels2, 1-labels)) #' @rdname setinfo #' @export setinfo <- function(object, ...) UseMethod("setinfo") #' @rdname setinfo #' @export setinfo.xgb.DMatrix <- function(object, name, info, ...) { if (name == "label") { if (length(info) != nrow(object)) stop("The length of labels must equal to the number of rows in the input data") .Call(XGDMatrixSetInfo_R, object, name, as.numeric(info)) return(TRUE) } if (name == "label_lower_bound") { if (length(info) != nrow(object)) stop("The length of lower-bound labels must equal to the number of rows in the input data") .Call(XGDMatrixSetInfo_R, object, name, as.numeric(info)) return(TRUE) } if (name == "label_upper_bound") { if (length(info) != nrow(object)) stop("The length of upper-bound labels must equal to the number of rows in the input data") .Call(XGDMatrixSetInfo_R, object, name, as.numeric(info)) return(TRUE) } if (name == "weight") { .Call(XGDMatrixSetInfo_R, object, name, as.numeric(info)) return(TRUE) } if (name == "base_margin") { # if (length(info)!=nrow(object)) # stop("The length of base margin must equal to the number of rows in the input data") .Call(XGDMatrixSetInfo_R, object, name, as.numeric(info)) return(TRUE) } if (name == "group") { if (sum(info) != nrow(object)) stop("The sum of groups must equal to the number of rows in the input data") .Call(XGDMatrixSetInfo_R, object, name, as.integer(info)) return(TRUE) } stop("setinfo: unknown info name ", name) return(FALSE) } #' Get a new DMatrix containing the specified rows of #' original xgb.DMatrix object #' #' Get a new DMatrix containing the specified rows of #' original xgb.DMatrix object #' #' @param object Object of class "xgb.DMatrix" #' @param idxset a integer vector of indices of rows needed #' @param colset currently not used (columns subsetting is not available) #' @param ... other parameters (currently not used) #' #' @examples #' data(agaricus.train, package='xgboost') #' dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) #' #' dsub <- slice(dtrain, 1:42) #' labels1 <- getinfo(dsub, 'label') #' dsub <- dtrain[1:42, ] #' labels2 <- getinfo(dsub, 'label') #' all.equal(labels1, labels2) #' #' @rdname slice.xgb.DMatrix #' @export slice <- function(object, ...) UseMethod("slice") #' @rdname slice.xgb.DMatrix #' @export slice.xgb.DMatrix <- function(object, idxset, ...) { if (!inherits(object, "xgb.DMatrix")) { stop("object must be xgb.DMatrix") } ret <- .Call(XGDMatrixSliceDMatrix_R, object, idxset) attr_list <- attributes(object) nr <- nrow(object) len <- sapply(attr_list, NROW) ind <- which(len == nr) if (length(ind) > 0) { nms <- names(attr_list)[ind] for (i in seq_along(ind)) { obj_attr <- attr(object, nms[i]) if (NCOL(obj_attr) > 1) { attr(ret, nms[i]) <- obj_attr[idxset, ] } else { attr(ret, nms[i]) <- obj_attr[idxset] } } } return(structure(ret, class = "xgb.DMatrix")) } #' @rdname slice.xgb.DMatrix #' @export `[.xgb.DMatrix` <- function(object, idxset, colset = NULL) { slice(object, idxset) } #' Print xgb.DMatrix #' #' Print information about xgb.DMatrix. #' Currently it displays dimensions and presence of info-fields and colnames. #' #' @param x an xgb.DMatrix object #' @param verbose whether to print colnames (when present) #' @param ... not currently used #' #' @examples #' data(agaricus.train, package='xgboost') #' dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) #' #' dtrain #' print(dtrain, verbose=TRUE) #' #' @method print xgb.DMatrix #' @export print.xgb.DMatrix <- function(x, verbose = FALSE, ...) { cat('xgb.DMatrix dim:', nrow(x), 'x', ncol(x), ' info: ') infos <- character(0) if (length(getinfo(x, 'label')) > 0) infos <- 'label' if (length(getinfo(x, 'weight')) > 0) infos <- c(infos, 'weight') if (length(getinfo(x, 'base_margin')) > 0) infos <- c(infos, 'base_margin') if (length(infos) == 0) infos <- 'NA' cat(infos) cnames <- colnames(x) cat(' colnames:') if (verbose & !is.null(cnames)) { cat("\n'") cat(cnames, sep = "','") cat("'") } else { if (is.null(cnames)) cat(' no') else cat(' yes') } cat("\n") invisible(x) } xgboost-1.5.2/R-package/R/xgb.DMatrix.save.R000066400000000000000000000014261417122711700204140ustar00rootroot00000000000000#' Save xgb.DMatrix object to binary file #' #' Save xgb.DMatrix object to binary file #' #' @param dmatrix the \code{xgb.DMatrix} object #' @param fname the name of the file to write. #' #' @examples #' data(agaricus.train, package='xgboost') #' dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) #' xgb.DMatrix.save(dtrain, 'xgb.DMatrix.data') #' dtrain <- xgb.DMatrix('xgb.DMatrix.data') #' if (file.exists('xgb.DMatrix.data')) file.remove('xgb.DMatrix.data') #' @export xgb.DMatrix.save <- function(dmatrix, fname) { if (typeof(fname) != "character") stop("fname must be character") if (!inherits(dmatrix, "xgb.DMatrix")) stop("dmatrix must be xgb.DMatrix") fname <- path.expand(fname) .Call(XGDMatrixSaveBinary_R, dmatrix, fname[1], 0L) return(TRUE) } xgboost-1.5.2/R-package/R/xgb.config.R000066400000000000000000000027651417122711700173630ustar00rootroot00000000000000#' Global configuration consists of a collection of parameters that can be applied in the global #' scope. See \url{https://xgboost.readthedocs.io/en/stable/parameter.html} for the full list of #' parameters supported in the global configuration. Use \code{xgb.set.config} to update the #' values of one or more global-scope parameters. Use \code{xgb.get.config} to fetch the current #' values of all global-scope parameters (listed in #' \url{https://xgboost.readthedocs.io/en/stable/parameter.html}). #' #' @rdname xgbConfig #' @title Set and get global configuration #' @name xgb.set.config, xgb.get.config #' @export xgb.set.config xgb.get.config #' @param ... List of parameters to be set, as keyword arguments #' @return #' \code{xgb.set.config} returns \code{TRUE} to signal success. \code{xgb.get.config} returns #' a list containing all global-scope parameters and their values. #' #' @examples #' # Set verbosity level to silent (0) #' xgb.set.config(verbosity = 0) #' # Now global verbosity level is 0 #' config <- xgb.get.config() #' print(config$verbosity) #' # Set verbosity level to warning (1) #' xgb.set.config(verbosity = 1) #' # Now global verbosity level is 1 #' config <- xgb.get.config() #' print(config$verbosity) xgb.set.config <- function(...) { new_config <- list(...) .Call(XGBSetGlobalConfig_R, jsonlite::toJSON(new_config, auto_unbox = TRUE)) return(TRUE) } #' @rdname xgbConfig xgb.get.config <- function() { config <- .Call(XGBGetGlobalConfig_R) return(jsonlite::fromJSON(config)) } xgboost-1.5.2/R-package/R/xgb.create.features.R000066400000000000000000000074721417122711700211760ustar00rootroot00000000000000#' Create new features from a previously learned model #' #' May improve the learning by adding new features to the training data based on the decision trees from a previously learned model. #' #' @param model decision tree boosting model learned on the original data #' @param data original data (usually provided as a \code{dgCMatrix} matrix) #' @param ... currently not used #' #' @return \code{dgCMatrix} matrix including both the original data and the new features. #' #' @details #' This is the function inspired from the paragraph 3.1 of the paper: #' #' \strong{Practical Lessons from Predicting Clicks on Ads at Facebook} #' #' \emph{(Xinran He, Junfeng Pan, Ou Jin, Tianbing Xu, Bo Liu, Tao Xu, Yan, xin Shi, Antoine Atallah, Ralf Herbrich, Stuart Bowers, #' Joaquin Quinonero Candela)} #' #' International Workshop on Data Mining for Online Advertising (ADKDD) - August 24, 2014 #' #' \url{https://research.fb.com/publications/practical-lessons-from-predicting-clicks-on-ads-at-facebook/}. #' #' Extract explaining the method: #' #' "We found that boosted decision trees are a powerful and very #' convenient way to implement non-linear and tuple transformations #' of the kind we just described. We treat each individual #' tree as a categorical feature that takes as value the #' index of the leaf an instance ends up falling in. We use #' 1-of-K coding of this type of features. #' #' For example, consider the boosted tree model in Figure 1 with 2 subtrees, #' where the first subtree has 3 leafs and the second 2 leafs. If an #' instance ends up in leaf 2 in the first subtree and leaf 1 in #' second subtree, the overall input to the linear classifier will #' be the binary vector \code{[0, 1, 0, 1, 0]}, where the first 3 entries #' correspond to the leaves of the first subtree and last 2 to #' those of the second subtree. #' #' [...] #' #' We can understand boosted decision tree #' based transformation as a supervised feature encoding that #' converts a real-valued vector into a compact binary-valued #' vector. A traversal from root node to a leaf node represents #' a rule on certain features." #' #' @examples #' data(agaricus.train, package='xgboost') #' data(agaricus.test, package='xgboost') #' dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) #' dtest <- with(agaricus.test, xgb.DMatrix(data, label = label)) #' #' param <- list(max_depth=2, eta=1, silent=1, objective='binary:logistic') #' nrounds = 4 #' #' bst = xgb.train(params = param, data = dtrain, nrounds = nrounds, nthread = 2) #' #' # Model accuracy without new features #' accuracy.before <- sum((predict(bst, agaricus.test$data) >= 0.5) == agaricus.test$label) / #' length(agaricus.test$label) #' #' # Convert previous features to one hot encoding #' new.features.train <- xgb.create.features(model = bst, agaricus.train$data) #' new.features.test <- xgb.create.features(model = bst, agaricus.test$data) #' #' # learning with new features #' new.dtrain <- xgb.DMatrix(data = new.features.train, label = agaricus.train$label) #' new.dtest <- xgb.DMatrix(data = new.features.test, label = agaricus.test$label) #' watchlist <- list(train = new.dtrain) #' bst <- xgb.train(params = param, data = new.dtrain, nrounds = nrounds, nthread = 2) #' #' # Model accuracy with new features #' accuracy.after <- sum((predict(bst, new.dtest) >= 0.5) == agaricus.test$label) / #' length(agaricus.test$label) #' #' # Here the accuracy was already good and is now perfect. #' cat(paste("The accuracy was", accuracy.before, "before adding leaf features and it is now", #' accuracy.after, "!\n")) #' #' @export xgb.create.features <- function(model, data, ...){ check.deprecation(...) pred_with_leaf <- predict(model, data, predleaf = TRUE) cols <- lapply(as.data.frame(pred_with_leaf), factor) cbind(data, sparse.model.matrix(~ . -1, cols)) # nolint } xgboost-1.5.2/R-package/R/xgb.cv.R000066400000000000000000000330731417122711700165220ustar00rootroot00000000000000#' Cross Validation #' #' The cross validation function of xgboost #' #' @param params the list of parameters. The complete list of parameters is #' available in the \href{http://xgboost.readthedocs.io/en/latest/parameter.html}{online documentation}. Below #' is a shorter summary: #' \itemize{ #' \item \code{objective} objective function, common ones are #' \itemize{ #' \item \code{reg:squarederror} Regression with squared loss. #' \item \code{binary:logistic} logistic regression for classification. #' \item See \code{\link[=xgb.train]{xgb.train}()} for complete list of objectives. #' } #' \item \code{eta} step size of each boosting step #' \item \code{max_depth} maximum depth of the tree #' \item \code{nthread} number of thread used in training, if not set, all threads are used #' } #' #' See \code{\link{xgb.train}} for further details. #' See also demo/ for walkthrough example in R. #' @param data takes an \code{xgb.DMatrix}, \code{matrix}, or \code{dgCMatrix} as the input. #' @param nrounds the max number of iterations #' @param nfold the original dataset is randomly partitioned into \code{nfold} equal size subsamples. #' @param label vector of response values. Should be provided only when data is an R-matrix. #' @param missing is only used when input is a dense matrix. By default is set to NA, which means #' that NA values should be considered as 'missing' by the algorithm. #' Sometimes, 0 or other extreme value might be used to represent missing values. #' @param prediction A logical value indicating whether to return the test fold predictions #' from each CV model. This parameter engages the \code{\link{cb.cv.predict}} callback. #' @param showsd \code{boolean}, whether to show standard deviation of cross validation #' @param metrics, list of evaluation metrics to be used in cross validation, #' when it is not specified, the evaluation metric is chosen according to objective function. #' Possible options are: #' \itemize{ #' \item \code{error} binary classification error rate #' \item \code{rmse} Rooted mean square error #' \item \code{logloss} negative log-likelihood function #' \item \code{mae} Mean absolute error #' \item \code{mape} Mean absolute percentage error #' \item \code{auc} Area under curve #' \item \code{aucpr} Area under PR curve #' \item \code{merror} Exact matching error, used to evaluate multi-class classification #' } #' @param obj customized objective function. Returns gradient and second order #' gradient with given prediction and dtrain. #' @param feval customized evaluation function. Returns #' \code{list(metric='metric-name', value='metric-value')} with given #' prediction and dtrain. #' @param stratified a \code{boolean} indicating whether sampling of folds should be stratified #' by the values of outcome labels. #' @param folds \code{list} provides a possibility to use a list of pre-defined CV folds #' (each element must be a vector of test fold's indices). When folds are supplied, #' the \code{nfold} and \code{stratified} parameters are ignored. #' @param train_folds \code{list} list specifying which indicies to use for training. If \code{NULL} #' (the default) all indices not specified in \code{folds} will be used for training. #' @param verbose \code{boolean}, print the statistics during the process #' @param print_every_n Print each n-th iteration evaluation messages when \code{verbose>0}. #' Default is 1 which means all messages are printed. This parameter is passed to the #' \code{\link{cb.print.evaluation}} callback. #' @param early_stopping_rounds If \code{NULL}, the early stopping function is not triggered. #' If set to an integer \code{k}, training with a validation set will stop if the performance #' doesn't improve for \code{k} rounds. #' Setting this parameter engages the \code{\link{cb.early.stop}} callback. #' @param maximize If \code{feval} and \code{early_stopping_rounds} are set, #' then this parameter must be set as well. #' When it is \code{TRUE}, it means the larger the evaluation score the better. #' This parameter is passed to the \code{\link{cb.early.stop}} callback. #' @param callbacks a list of callback functions to perform various task during boosting. #' See \code{\link{callbacks}}. Some of the callbacks are automatically created depending on the #' parameters' values. User can provide either existing or their own callback methods in order #' to customize the training process. #' @param ... other parameters to pass to \code{params}. #' #' @details #' The original sample is randomly partitioned into \code{nfold} equal size subsamples. #' #' Of the \code{nfold} subsamples, a single subsample is retained as the validation data for testing the model, and the remaining \code{nfold - 1} subsamples are used as training data. #' #' The cross-validation process is then repeated \code{nrounds} times, with each of the \code{nfold} subsamples used exactly once as the validation data. #' #' All observations are used for both training and validation. #' #' Adapted from \url{https://en.wikipedia.org/wiki/Cross-validation_\%28statistics\%29} #' #' @return #' An object of class \code{xgb.cv.synchronous} with the following elements: #' \itemize{ #' \item \code{call} a function call. #' \item \code{params} parameters that were passed to the xgboost library. Note that it does not #' capture parameters changed by the \code{\link{cb.reset.parameters}} callback. #' \item \code{callbacks} callback functions that were either automatically assigned or #' explicitly passed. #' \item \code{evaluation_log} evaluation history stored as a \code{data.table} with the #' first column corresponding to iteration number and the rest corresponding to the #' CV-based evaluation means and standard deviations for the training and test CV-sets. #' It is created by the \code{\link{cb.evaluation.log}} callback. #' \item \code{niter} number of boosting iterations. #' \item \code{nfeatures} number of features in training data. #' \item \code{folds} the list of CV folds' indices - either those passed through the \code{folds} #' parameter or randomly generated. #' \item \code{best_iteration} iteration number with the best evaluation metric value #' (only available with early stopping). #' \item \code{best_ntreelimit} and the \code{ntreelimit} Deprecated attributes, use \code{best_iteration} instead. #' \item \code{pred} CV prediction values available when \code{prediction} is set. #' It is either vector or matrix (see \code{\link{cb.cv.predict}}). #' \item \code{models} a list of the CV folds' models. It is only available with the explicit #' setting of the \code{cb.cv.predict(save_models = TRUE)} callback. #' } #' #' @examples #' data(agaricus.train, package='xgboost') #' dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) #' cv <- xgb.cv(data = dtrain, nrounds = 3, nthread = 2, nfold = 5, metrics = list("rmse","auc"), #' max_depth = 3, eta = 1, objective = "binary:logistic") #' print(cv) #' print(cv, verbose=TRUE) #' #' @export xgb.cv <- function(params=list(), data, nrounds, nfold, label = NULL, missing = NA, prediction = FALSE, showsd = TRUE, metrics=list(), obj = NULL, feval = NULL, stratified = TRUE, folds = NULL, train_folds = NULL, verbose = TRUE, print_every_n=1L, early_stopping_rounds = NULL, maximize = NULL, callbacks = list(), ...) { check.deprecation(...) params <- check.booster.params(params, ...) # TODO: should we deprecate the redundant 'metrics' parameter? for (m in metrics) params <- c(params, list("eval_metric" = m)) check.custom.obj() check.custom.eval() #if (is.null(params[['eval_metric']]) && is.null(feval)) # stop("Either 'eval_metric' or 'feval' must be provided for CV") # Check the labels if ((inherits(data, 'xgb.DMatrix') && is.null(getinfo(data, 'label'))) || (!inherits(data, 'xgb.DMatrix') && is.null(label))) { stop("Labels must be provided for CV either through xgb.DMatrix, or through 'label=' when 'data' is matrix") } else if (inherits(data, 'xgb.DMatrix')) { if (!is.null(label)) warning("xgb.cv: label will be ignored, since data is of type xgb.DMatrix") cv_label <- getinfo(data, 'label') } else { cv_label <- label } # CV folds if (!is.null(folds)) { if (!is.list(folds) || length(folds) < 2) stop("'folds' must be a list with 2 or more elements that are vectors of indices for each CV-fold") nfold <- length(folds) } else { if (nfold <= 1) stop("'nfold' must be > 1") folds <- generate.cv.folds(nfold, nrow(data), stratified, cv_label, params) } # Potential TODO: sequential CV #if (strategy == 'sequential') # stop('Sequential CV strategy is not yet implemented') # verbosity & evaluation printing callback: params <- c(params, list(silent = 1)) print_every_n <- max(as.integer(print_every_n), 1L) if (!has.callbacks(callbacks, 'cb.print.evaluation') && verbose) { callbacks <- add.cb(callbacks, cb.print.evaluation(print_every_n, showsd = showsd)) } # evaluation log callback: always is on in CV evaluation_log <- list() if (!has.callbacks(callbacks, 'cb.evaluation.log')) { callbacks <- add.cb(callbacks, cb.evaluation.log()) } # Early stopping callback stop_condition <- FALSE if (!is.null(early_stopping_rounds) && !has.callbacks(callbacks, 'cb.early.stop')) { callbacks <- add.cb(callbacks, cb.early.stop(early_stopping_rounds, maximize = maximize, verbose = verbose)) } # CV-predictions callback if (prediction && !has.callbacks(callbacks, 'cb.cv.predict')) { callbacks <- add.cb(callbacks, cb.cv.predict(save_models = FALSE)) } # Sort the callbacks into categories cb <- categorize.callbacks(callbacks) # create the booster-folds # train_folds dall <- xgb.get.DMatrix(data, label, missing) bst_folds <- lapply(seq_along(folds), function(k) { dtest <- slice(dall, folds[[k]]) # code originally contributed by @RolandASc on stackoverflow if (is.null(train_folds)) dtrain <- slice(dall, unlist(folds[-k])) else dtrain <- slice(dall, train_folds[[k]]) handle <- xgb.Booster.handle(params, list(dtrain, dtest)) list(dtrain = dtrain, bst = handle, watchlist = list(train = dtrain, test = dtest), index = folds[[k]]) }) rm(dall) # a "basket" to collect some results from callbacks basket <- list() # extract parameters that can affect the relationship b/w #trees and #iterations num_class <- max(as.numeric(NVL(params[['num_class']], 1)), 1) # nolint num_parallel_tree <- max(as.numeric(NVL(params[['num_parallel_tree']], 1)), 1) # nolint # those are fixed for CV (no training continuation) begin_iteration <- 1 end_iteration <- nrounds # synchronous CV boosting: run CV folds' models within each iteration for (iteration in begin_iteration:end_iteration) { for (f in cb$pre_iter) f() msg <- lapply(bst_folds, function(fd) { xgb.iter.update(fd$bst, fd$dtrain, iteration - 1, obj) xgb.iter.eval(fd$bst, fd$watchlist, iteration - 1, feval) }) msg <- simplify2array(msg) bst_evaluation <- rowMeans(msg) bst_evaluation_err <- sqrt(rowMeans(msg^2) - bst_evaluation^2) # nolint for (f in cb$post_iter) f() if (stop_condition) break } for (f in cb$finalize) f(finalize = TRUE) # the CV result ret <- list( call = match.call(), params = params, callbacks = callbacks, evaluation_log = evaluation_log, niter = end_iteration, nfeatures = ncol(data), folds = folds ) ret <- c(ret, basket) class(ret) <- 'xgb.cv.synchronous' invisible(ret) } #' Print xgb.cv result #' #' Prints formatted results of \code{xgb.cv}. #' #' @param x an \code{xgb.cv.synchronous} object #' @param verbose whether to print detailed data #' @param ... passed to \code{data.table.print} #' #' @details #' When not verbose, it would only print the evaluation results, #' including the best iteration (when available). #' #' @examples #' data(agaricus.train, package='xgboost') #' train <- agaricus.train #' cv <- xgb.cv(data = train$data, label = train$label, nfold = 5, max_depth = 2, #' eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") #' print(cv) #' print(cv, verbose=TRUE) #' #' @rdname print.xgb.cv #' @method print xgb.cv.synchronous #' @export print.xgb.cv.synchronous <- function(x, verbose = FALSE, ...) { cat('##### xgb.cv ', length(x$folds), '-folds\n', sep = '') if (verbose) { if (!is.null(x$call)) { cat('call:\n ') print(x$call) } if (!is.null(x$params)) { cat('params (as set within xgb.cv):\n') cat(' ', paste(names(x$params), paste0('"', unlist(x$params), '"'), sep = ' = ', collapse = ', '), '\n', sep = '') } if (!is.null(x$callbacks) && length(x$callbacks) > 0) { cat('callbacks:\n') lapply(callback.calls(x$callbacks), function(x) { cat(' ') print(x) }) } for (n in c('niter', 'best_iteration', 'best_ntreelimit')) { if (is.null(x[[n]])) next cat(n, ': ', x[[n]], '\n', sep = '') } if (!is.null(x$pred)) { cat('pred:\n') str(x$pred) } } if (verbose) cat('evaluation_log:\n') print(x$evaluation_log, row.names = FALSE, ...) if (!is.null(x$best_iteration)) { cat('Best iteration:\n') print(x$evaluation_log[x$best_iteration], row.names = FALSE, ...) } invisible(x) } xgboost-1.5.2/R-package/R/xgb.dump.R000066400000000000000000000057051417122711700170600ustar00rootroot00000000000000#' Dump an xgboost model in text format. #' #' Dump an xgboost model in text format. #' #' @param model the model object. #' @param fname the name of the text file where to save the model text dump. #' If not provided or set to \code{NULL}, the model is returned as a \code{character} vector. #' @param fmap feature map file representing feature types. #' Detailed description could be found at #' \url{https://github.com/dmlc/xgboost/wiki/Binary-Classification#dump-model}. #' See demo/ for walkthrough example in R, and #' \url{https://github.com/dmlc/xgboost/blob/master/demo/data/featmap.txt} #' for example Format. #' @param with_stats whether to dump some additional statistics about the splits. #' When this option is on, the model dump contains two additional values: #' gain is the approximate loss function gain we get in each split; #' cover is the sum of second order gradient in each node. #' @param dump_format either 'text' or 'json' format could be specified. #' @param ... currently not used #' #' @return #' If fname is not provided or set to \code{NULL} the function will return the model #' as a \code{character} vector. Otherwise it will return \code{TRUE}. #' #' @examples #' data(agaricus.train, package='xgboost') #' data(agaricus.test, package='xgboost') #' train <- agaricus.train #' test <- agaricus.test #' bst <- xgboost(data = train$data, label = train$label, max_depth = 2, #' eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") #' # save the model in file 'xgb.model.dump' #' dump_path = file.path(tempdir(), 'model.dump') #' xgb.dump(bst, dump_path, with_stats = TRUE) #' #' # print the model without saving it to a file #' print(xgb.dump(bst, with_stats = TRUE)) #' #' # print in JSON format: #' cat(xgb.dump(bst, with_stats = TRUE, dump_format='json')) #' #' @export xgb.dump <- function(model, fname = NULL, fmap = "", with_stats=FALSE, dump_format = c("text", "json"), ...) { check.deprecation(...) dump_format <- match.arg(dump_format) if (!inherits(model, "xgb.Booster")) stop("model: argument must be of type xgb.Booster") if (!(is.null(fname) || is.character(fname))) stop("fname: argument must be a character string (when provided)") if (!(is.null(fmap) || is.character(fmap))) stop("fmap: argument must be a character string (when provided)") model <- xgb.Booster.complete(model) model_dump <- .Call(XGBoosterDumpModel_R, model$handle, NVL(fmap, "")[1], as.integer(with_stats), as.character(dump_format)) if (is.null(fname)) model_dump <- gsub('\t', '', model_dump, fixed = TRUE) if (dump_format == "text") model_dump <- unlist(strsplit(model_dump, '\n', fixed = TRUE)) model_dump <- grep('^\\s*$', model_dump, invert = TRUE, value = TRUE) if (is.null(fname)) { return(model_dump) } else { fname <- path.expand(fname) writeLines(model_dump, fname[1]) return(TRUE) } } xgboost-1.5.2/R-package/R/xgb.ggplot.R000066400000000000000000000170411417122711700174030ustar00rootroot00000000000000# ggplot backend for the xgboost plotting facilities #' @rdname xgb.plot.importance #' @export xgb.ggplot.importance <- function(importance_matrix = NULL, top_n = NULL, measure = NULL, rel_to_first = FALSE, n_clusters = c(1:10), ...) { importance_matrix <- xgb.plot.importance(importance_matrix, top_n = top_n, measure = measure, rel_to_first = rel_to_first, plot = FALSE, ...) if (!requireNamespace("ggplot2", quietly = TRUE)) { stop("ggplot2 package is required", call. = FALSE) } if (!requireNamespace("Ckmeans.1d.dp", quietly = TRUE)) { stop("Ckmeans.1d.dp package is required", call. = FALSE) } clusters <- suppressWarnings( Ckmeans.1d.dp::Ckmeans.1d.dp(importance_matrix$Importance, n_clusters) ) importance_matrix[, Cluster := as.character(clusters$cluster)] plot <- ggplot2::ggplot(importance_matrix, ggplot2::aes(x = factor(Feature, levels = rev(Feature)), y = Importance, width = 0.5), environment = environment()) + ggplot2::geom_bar(ggplot2::aes(fill = Cluster), stat = "identity", position = "identity") + ggplot2::coord_flip() + ggplot2::xlab("Features") + ggplot2::ggtitle("Feature importance") + ggplot2::theme(plot.title = ggplot2::element_text(lineheight = .9, face = "bold"), panel.grid.major.y = ggplot2::element_blank()) return(plot) } #' @rdname xgb.plot.deepness #' @export xgb.ggplot.deepness <- function(model = NULL, which = c("2x1", "max.depth", "med.depth", "med.weight")) { if (!requireNamespace("ggplot2", quietly = TRUE)) stop("ggplot2 package is required for plotting the graph deepness.", call. = FALSE) which <- match.arg(which) dt_depths <- xgb.plot.deepness(model = model, plot = FALSE) dt_summaries <- dt_depths[, .(.N, Cover = mean(Cover)), Depth] setkey(dt_summaries, 'Depth') if (which == "2x1") { p1 <- ggplot2::ggplot(dt_summaries) + ggplot2::geom_bar(ggplot2::aes(x = Depth, y = N), stat = "Identity") + ggplot2::xlab("") + ggplot2::ylab("Number of leafs") + ggplot2::ggtitle("Model complexity") + ggplot2::theme( plot.title = ggplot2::element_text(lineheight = 0.9, face = "bold"), panel.grid.major.y = ggplot2::element_blank(), axis.ticks = ggplot2::element_blank(), axis.text.x = ggplot2::element_blank() ) p2 <- ggplot2::ggplot(dt_summaries) + ggplot2::geom_bar(ggplot2::aes(x = Depth, y = Cover), stat = "Identity") + ggplot2::xlab("Leaf depth") + ggplot2::ylab("Weighted cover") multiplot(p1, p2, cols = 1) return(invisible(list(p1, p2))) } else if (which == "max.depth") { p <- ggplot2::ggplot(dt_depths[, max(Depth), Tree]) + ggplot2::geom_jitter(ggplot2::aes(x = Tree, y = V1), height = 0.15, alpha = 0.4, size = 3, stroke = 0) + ggplot2::xlab("tree #") + ggplot2::ylab("Max tree leaf depth") return(p) } else if (which == "med.depth") { p <- ggplot2::ggplot(dt_depths[, median(as.numeric(Depth)), Tree]) + ggplot2::geom_jitter(ggplot2::aes(x = Tree, y = V1), height = 0.15, alpha = 0.4, size = 3, stroke = 0) + ggplot2::xlab("tree #") + ggplot2::ylab("Median tree leaf depth") return(p) } else if (which == "med.weight") { p <- ggplot2::ggplot(dt_depths[, median(abs(Weight)), Tree]) + ggplot2::geom_point(ggplot2::aes(x = Tree, y = V1), alpha = 0.4, size = 3, stroke = 0) + ggplot2::xlab("tree #") + ggplot2::ylab("Median absolute leaf weight") return(p) } } #' @rdname xgb.plot.shap.summary #' @export xgb.ggplot.shap.summary <- function(data, shap_contrib = NULL, features = NULL, top_n = 10, model = NULL, trees = NULL, target_class = NULL, approxcontrib = FALSE, subsample = NULL) { data_list <- xgb.shap.data( data = data, shap_contrib = shap_contrib, features = features, top_n = top_n, model = model, trees = trees, target_class = target_class, approxcontrib = approxcontrib, subsample = subsample, max_observations = 10000 # 10,000 samples per feature. ) p_data <- prepare.ggplot.shap.data(data_list, normalize = TRUE) # Reverse factor levels so that the first level is at the top of the plot p_data[, "feature" := factor(feature, rev(levels(feature)))] p <- ggplot2::ggplot(p_data, ggplot2::aes(x = feature, y = p_data$shap_value, colour = p_data$feature_value)) + ggplot2::geom_jitter(alpha = 0.5, width = 0.1) + ggplot2::scale_colour_viridis_c(limits = c(-3, 3), option = "plasma", direction = -1) + ggplot2::geom_abline(slope = 0, intercept = 0, colour = "darkgrey") + ggplot2::coord_flip() p } #' Combine and melt feature values and SHAP contributions for sample #' observations. #' #' Conforms to data format required for ggplot functions. #' #' Internal utility function. #' #' @param data_list List containing 'data' and 'shap_contrib' returned by #' \code{xgb.shap.data()}. #' @param normalize Whether to standardize feature values to have mean 0 and #' standard deviation 1 (useful for comparing multiple features on the same #' plot). Default \code{FALSE}. #' #' @return A data.table containing the observation ID, the feature name, the #' feature value (normalized if specified), and the SHAP contribution value. prepare.ggplot.shap.data <- function(data_list, normalize = FALSE) { data <- data_list[["data"]] shap_contrib <- data_list[["shap_contrib"]] data <- data.table::as.data.table(as.matrix(data)) if (normalize) { data[, (names(data)) := lapply(.SD, normalize)] } data[, "id" := seq_len(nrow(data))] data_m <- data.table::melt.data.table(data, id.vars = "id", variable.name = "feature", value.name = "feature_value") shap_contrib <- data.table::as.data.table(as.matrix(shap_contrib)) shap_contrib[, "id" := seq_len(nrow(shap_contrib))] shap_contrib_m <- data.table::melt.data.table(shap_contrib, id.vars = "id", variable.name = "feature", value.name = "shap_value") p_data <- data.table::merge.data.table(data_m, shap_contrib_m, by = c("id", "feature")) p_data } #' Scale feature value to have mean 0, standard deviation 1 #' #' This is used to compare multiple features on the same plot. #' Internal utility function #' #' @param x Numeric vector #' #' @return Numeric vector with mean 0 and sd 1. normalize <- function(x) { loc <- mean(x, na.rm = TRUE) scale <- stats::sd(x, na.rm = TRUE) (x - loc) / scale } # Plot multiple ggplot graph aligned by rows and columns. # ... the plots # cols number of columns # internal utility function multiplot <- function(..., cols = 1) { plots <- list(...) num_plots <- length(plots) layout <- matrix(seq(1, cols * ceiling(num_plots / cols)), ncol = cols, nrow = ceiling(num_plots / cols)) if (num_plots == 1) { print(plots[[1]]) } else { grid::grid.newpage() grid::pushViewport(grid::viewport(layout = grid::grid.layout(nrow(layout), ncol(layout)))) for (i in 1:num_plots) { # Get the i,j matrix positions of the regions that contain this subplot matchidx <- as.data.table(which(layout == i, arr.ind = TRUE)) print( plots[[i]], vp = grid::viewport( layout.pos.row = matchidx$row, layout.pos.col = matchidx$col ) ) } } } globalVariables(c( "Cluster", "ggplot", "aes", "geom_bar", "coord_flip", "xlab", "ylab", "ggtitle", "theme", "element_blank", "element_text", "V1", "Weight", "feature" )) xgboost-1.5.2/R-package/R/xgb.importance.R000066400000000000000000000151521417122711700202510ustar00rootroot00000000000000#' Importance of features in a model. #' #' Creates a \code{data.table} of feature importances in a model. #' #' @param feature_names character vector of feature names. If the model already #' contains feature names, those would be used when \code{feature_names=NULL} (default value). #' Non-null \code{feature_names} could be provided to override those in the model. #' @param model object of class \code{xgb.Booster}. #' @param trees (only for the gbtree booster) an integer vector of tree indices that should be included #' into the importance calculation. If set to \code{NULL}, all trees of the model are parsed. #' It could be useful, e.g., in multiclass classification to get feature importances #' for each class separately. IMPORTANT: the tree index in xgboost models #' is zero-based (e.g., use \code{trees = 0:4} for first 5 trees). #' @param data deprecated. #' @param label deprecated. #' @param target deprecated. #' #' @details #' #' This function works for both linear and tree models. #' #' For linear models, the importance is the absolute magnitude of linear coefficients. #' For that reason, in order to obtain a meaningful ranking by importance for a linear model, #' the features need to be on the same scale (which you also would want to do when using either #' L1 or L2 regularization). #' #' @return #' #' For a tree model, a \code{data.table} with the following columns: #' \itemize{ #' \item \code{Features} names of the features used in the model; #' \item \code{Gain} represents fractional contribution of each feature to the model based on #' the total gain of this feature's splits. Higher percentage means a more important #' predictive feature. #' \item \code{Cover} metric of the number of observation related to this feature; #' \item \code{Frequency} percentage representing the relative number of times #' a feature have been used in trees. #' } #' #' A linear model's importance \code{data.table} has the following columns: #' \itemize{ #' \item \code{Features} names of the features used in the model; #' \item \code{Weight} the linear coefficient of this feature; #' \item \code{Class} (only for multiclass models) class label. #' } #' #' If \code{feature_names} is not provided and \code{model} doesn't have \code{feature_names}, #' index of the features will be used instead. Because the index is extracted from the model dump #' (based on C++ code), it starts at 0 (as in C/C++ or Python) instead of 1 (usual in R). #' #' @examples #' #' # binomial classification using gbtree: #' data(agaricus.train, package='xgboost') #' bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 2, #' eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") #' xgb.importance(model = bst) #' #' # binomial classification using gblinear: #' bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, booster = "gblinear", #' eta = 0.3, nthread = 1, nrounds = 20, objective = "binary:logistic") #' xgb.importance(model = bst) #' #' # multiclass classification using gbtree: #' nclass <- 3 #' nrounds <- 10 #' mbst <- xgboost(data = as.matrix(iris[, -5]), label = as.numeric(iris$Species) - 1, #' max_depth = 3, eta = 0.2, nthread = 2, nrounds = nrounds, #' objective = "multi:softprob", num_class = nclass) #' # all classes clumped together: #' xgb.importance(model = mbst) #' # inspect importances separately for each class: #' xgb.importance(model = mbst, trees = seq(from=0, by=nclass, length.out=nrounds)) #' xgb.importance(model = mbst, trees = seq(from=1, by=nclass, length.out=nrounds)) #' xgb.importance(model = mbst, trees = seq(from=2, by=nclass, length.out=nrounds)) #' #' # multiclass classification using gblinear: #' mbst <- xgboost(data = scale(as.matrix(iris[, -5])), label = as.numeric(iris$Species) - 1, #' booster = "gblinear", eta = 0.2, nthread = 1, nrounds = 15, #' objective = "multi:softprob", num_class = nclass) #' xgb.importance(model = mbst) #' #' @export xgb.importance <- function(feature_names = NULL, model = NULL, trees = NULL, data = NULL, label = NULL, target = NULL){ if (!(is.null(data) && is.null(label) && is.null(target))) warning("xgb.importance: parameters 'data', 'label' and 'target' are deprecated") if (!inherits(model, "xgb.Booster")) stop("model: must be an object of class xgb.Booster") if (is.null(feature_names) && !is.null(model$feature_names)) feature_names <- model$feature_names if (!(is.null(feature_names) || is.character(feature_names))) stop("feature_names: Has to be a character vector") model <- xgb.Booster.complete(model) config <- jsonlite::fromJSON(xgb.config(model)) if (config$learner$gradient_booster$name == "gblinear") { args <- list(importance_type = "weight", feature_names = feature_names) results <- .Call( XGBoosterFeatureScore_R, model$handle, jsonlite::toJSON(args, auto_unbox = TRUE, null = "null") ) names(results) <- c("features", "shape", "weight") n_classes <- if (length(results$shape) == 2) { results$shape[2] } else { 0 } importance <- if (n_classes == 0) { data.table(Feature = results$features, Weight = results$weight)[order(-abs(Weight))] } else { data.table( Feature = rep(results$features, each = n_classes), Weight = results$weight, Class = seq_len(n_classes) - 1 )[order(Class, -abs(Weight))] } } else { concatenated <- list() output_names <- vector() for (importance_type in c("weight", "total_gain", "total_cover")) { args <- list(importance_type = importance_type, feature_names = feature_names, tree_idx = trees) results <- .Call( XGBoosterFeatureScore_R, model$handle, jsonlite::toJSON(args, auto_unbox = TRUE, null = "null") ) names(results) <- c("features", "shape", importance_type) concatenated[ switch(importance_type, "weight" = "Frequency", "total_gain" = "Gain", "total_cover" = "Cover") ] <- results[importance_type] output_names <- results$features } importance <- data.table( Feature = output_names, Gain = concatenated$Gain / sum(concatenated$Gain), Cover = concatenated$Cover / sum(concatenated$Cover), Frequency = concatenated$Frequency / sum(concatenated$Frequency) )[order(Gain, decreasing = TRUE)] } importance } # Avoid error messages during CRAN check. # The reason is that these variables are never declared # They are mainly column names inferred by Data.table... globalVariables(c(".", ".N", "Gain", "Cover", "Frequency", "Feature", "Class")) xgboost-1.5.2/R-package/R/xgb.load.R000066400000000000000000000031771417122711700170330ustar00rootroot00000000000000#' Load xgboost model from binary file #' #' Load xgboost model from the binary model file. #' #' @param modelfile the name of the binary input file. #' #' @details #' The input file is expected to contain a model saved in an xgboost-internal binary format #' using either \code{\link{xgb.save}} or \code{\link{cb.save.model}} in R, or using some #' appropriate methods from other xgboost interfaces. E.g., a model trained in Python and #' saved from there in xgboost format, could be loaded from R. #' #' Note: a model saved as an R-object, has to be loaded using corresponding R-methods, #' not \code{xgb.load}. #' #' @return #' An object of \code{xgb.Booster} class. #' #' @seealso #' \code{\link{xgb.save}}, \code{\link{xgb.Booster.complete}}. #' #' @examples #' data(agaricus.train, package='xgboost') #' data(agaricus.test, package='xgboost') #' train <- agaricus.train #' test <- agaricus.test #' bst <- xgboost(data = train$data, label = train$label, max_depth = 2, #' eta = 1, nthread = 2, nrounds = 2,objective = "binary:logistic") #' xgb.save(bst, 'xgb.model') #' bst <- xgb.load('xgb.model') #' if (file.exists('xgb.model')) file.remove('xgb.model') #' pred <- predict(bst, test$data) #' @export xgb.load <- function(modelfile) { if (is.null(modelfile)) stop("xgb.load: modelfile cannot be NULL") handle <- xgb.Booster.handle(modelfile = modelfile) # re-use modelfile if it is raw so we do not need to serialize if (typeof(modelfile) == "raw") { bst <- xgb.handleToBooster(handle, modelfile) } else { bst <- xgb.handleToBooster(handle, NULL) } bst <- xgb.Booster.complete(bst, saveraw = TRUE) return(bst) } xgboost-1.5.2/R-package/R/xgb.load.raw.R000066400000000000000000000006271417122711700176200ustar00rootroot00000000000000#' Load serialised xgboost model from R's raw vector #' #' User can generate raw memory buffer by calling xgb.save.raw #' #' @param buffer the buffer returned by xgb.save.raw #' #' @export xgb.load.raw <- function(buffer) { cachelist <- list() handle <- .Call(XGBoosterCreate_R, cachelist) .Call(XGBoosterLoadModelFromRaw_R, handle, buffer) class(handle) <- "xgb.Booster.handle" return (handle) } xgboost-1.5.2/R-package/R/xgb.model.dt.tree.R000066400000000000000000000155121417122711700205540ustar00rootroot00000000000000#' Parse a boosted tree model text dump #' #' Parse a boosted tree model text dump into a \code{data.table} structure. #' #' @param feature_names character vector of feature names. If the model already #' contains feature names, those would be used when \code{feature_names=NULL} (default value). #' Non-null \code{feature_names} could be provided to override those in the model. #' @param model object of class \code{xgb.Booster} #' @param text \code{character} vector previously generated by the \code{xgb.dump} #' function (where parameter \code{with_stats = TRUE} should have been set). #' \code{text} takes precedence over \code{model}. #' @param trees an integer vector of tree indices that should be parsed. #' If set to \code{NULL}, all trees of the model are parsed. #' It could be useful, e.g., in multiclass classification to get only #' the trees of one certain class. IMPORTANT: the tree index in xgboost models #' is zero-based (e.g., use \code{trees = 0:4} for first 5 trees). #' @param use_int_id a logical flag indicating whether nodes in columns "Yes", "No", "Missing" should be #' represented as integers (when FALSE) or as "Tree-Node" character strings (when FALSE). #' @param ... currently not used. #' #' @return #' A \code{data.table} with detailed information about model trees' nodes. #' #' The columns of the \code{data.table} are: #' #' \itemize{ #' \item \code{Tree}: integer ID of a tree in a model (zero-based index) #' \item \code{Node}: integer ID of a node in a tree (zero-based index) #' \item \code{ID}: character identifier of a node in a model (only when \code{use_int_id=FALSE}) #' \item \code{Feature}: for a branch node, it's a feature id or name (when available); #' for a leaf note, it simply labels it as \code{'Leaf'} #' \item \code{Split}: location of the split for a branch node (split condition is always "less than") #' \item \code{Yes}: ID of the next node when the split condition is met #' \item \code{No}: ID of the next node when the split condition is not met #' \item \code{Missing}: ID of the next node when branch value is missing #' \item \code{Quality}: either the split gain (change in loss) or the leaf value #' \item \code{Cover}: metric related to the number of observation either seen by a split #' or collected by a leaf during training. #' } #' #' When \code{use_int_id=FALSE}, columns "Yes", "No", and "Missing" point to model-wide node identifiers #' in the "ID" column. When \code{use_int_id=TRUE}, those columns point to node identifiers from #' the corresponding trees in the "Node" column. #' #' @examples #' # Basic use: #' #' data(agaricus.train, package='xgboost') #' #' bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 2, #' eta = 1, nthread = 2, nrounds = 2,objective = "binary:logistic") #' #' (dt <- xgb.model.dt.tree(colnames(agaricus.train$data), bst)) #' #' # This bst model already has feature_names stored with it, so those would be used when #' # feature_names is not set: #' (dt <- xgb.model.dt.tree(model = bst)) #' #' # How to match feature names of splits that are following a current 'Yes' branch: #' #' merge(dt, dt[, .(ID, Y.Feature=Feature)], by.x='Yes', by.y='ID', all.x=TRUE)[order(Tree,Node)] #' #' @export xgb.model.dt.tree <- function(feature_names = NULL, model = NULL, text = NULL, trees = NULL, use_int_id = FALSE, ...){ check.deprecation(...) if (!inherits(model, "xgb.Booster") && !is.character(text)) { stop("Either 'model' must be an object of class xgb.Booster\n", " or 'text' must be a character vector with the result of xgb.dump\n", " (or NULL if 'model' was provided).") } if (is.null(feature_names) && !is.null(model) && !is.null(model$feature_names)) feature_names <- model$feature_names if (!(is.null(feature_names) || is.character(feature_names))) { stop("feature_names: must be a character vector") } if (!(is.null(trees) || is.numeric(trees))) { stop("trees: must be a vector of integers.") } if (is.null(text)){ text <- xgb.dump(model = model, with_stats = TRUE) } if (length(text) < 2 || sum(grepl('yes=(\\d+),no=(\\d+)', text)) < 1) { stop("Non-tree model detected! This function can only be used with tree models.") } position <- which(grepl("booster", text, fixed = TRUE)) add.tree.id <- function(node, tree) if (use_int_id) node else paste(tree, node, sep = "-") anynumber_regex <- "[-+]?[0-9]*\\.?[0-9]+([eE][-+]?[0-9]+)?" td <- data.table(t = text) td[position, Tree := 1L] td[, Tree := cumsum(ifelse(is.na(Tree), 0L, Tree)) - 1L] if (is.null(trees)) { trees <- 0:max(td$Tree) } else { trees <- trees[trees >= 0 & trees <= max(td$Tree)] } td <- td[Tree %in% trees & !grepl('^booster', t)] td[, Node := as.integer(sub("^([0-9]+):.*", "\\1", t))] if (!use_int_id) td[, ID := add.tree.id(Node, Tree)] td[, isLeaf := grepl("leaf", t, fixed = TRUE)] # parse branch lines branch_rx <- paste0("f(\\d+)<(", anynumber_regex, ")\\] yes=(\\d+),no=(\\d+),missing=(\\d+),", "gain=(", anynumber_regex, "),cover=(", anynumber_regex, ")") branch_cols <- c("Feature", "Split", "Yes", "No", "Missing", "Quality", "Cover") td[isLeaf == FALSE, (branch_cols) := { matches <- regmatches(t, regexec(branch_rx, t)) # skip some indices with spurious capture groups from anynumber_regex xtr <- do.call(rbind, matches)[, c(2, 3, 5, 6, 7, 8, 10), drop = FALSE] xtr[, 3:5] <- add.tree.id(xtr[, 3:5], Tree) as.data.table(xtr) }] # assign feature_names when available if (!is.null(feature_names)) { if (length(feature_names) <= max(as.numeric(td$Feature), na.rm = TRUE)) stop("feature_names has less elements than there are features used in the model") td[isLeaf == FALSE, Feature := feature_names[as.numeric(Feature) + 1]] } # parse leaf lines leaf_rx <- paste0("leaf=(", anynumber_regex, "),cover=(", anynumber_regex, ")") leaf_cols <- c("Feature", "Quality", "Cover") td[isLeaf == TRUE, (leaf_cols) := { matches <- regmatches(t, regexec(leaf_rx, t)) xtr <- do.call(rbind, matches)[, c(2, 4)] c("Leaf", as.data.table(xtr)) }] # convert some columns to numeric numeric_cols <- c("Split", "Quality", "Cover") td[, (numeric_cols) := lapply(.SD, as.numeric), .SDcols = numeric_cols] if (use_int_id) { int_cols <- c("Yes", "No", "Missing") td[, (int_cols) := lapply(.SD, as.integer), .SDcols = int_cols] } td[, t := NULL] td[, isLeaf := NULL] td[order(Tree, Node)] } # Avoid error messages during CRAN check. # The reason is that these variables are never declared # They are mainly column names inferred by Data.table... globalVariables(c("Tree", "Node", "ID", "Feature", "t", "isLeaf", ".SD", ".SDcols")) xgboost-1.5.2/R-package/R/xgb.plot.deepness.R000066400000000000000000000141231417122711700206700ustar00rootroot00000000000000#' Plot model trees deepness #' #' Visualizes distributions related to depth of tree leafs. #' \code{xgb.plot.deepness} uses base R graphics, while \code{xgb.ggplot.deepness} uses the ggplot backend. #' #' @param model either an \code{xgb.Booster} model generated by the \code{xgb.train} function #' or a data.table result of the \code{xgb.model.dt.tree} function. #' @param plot (base R barplot) whether a barplot should be produced. #' If FALSE, only a data.table is returned. #' @param which which distribution to plot (see details). #' @param ... other parameters passed to \code{barplot} or \code{plot}. #' #' @details #' #' When \code{which="2x1"}, two distributions with respect to the leaf depth #' are plotted on top of each other: #' \itemize{ #' \item the distribution of the number of leafs in a tree model at a certain depth; #' \item the distribution of average weighted number of observations ("cover") #' ending up in leafs at certain depth. #' } #' Those could be helpful in determining sensible ranges of the \code{max_depth} #' and \code{min_child_weight} parameters. #' #' When \code{which="max.depth"} or \code{which="med.depth"}, plots of either maximum or median depth #' per tree with respect to tree number are created. And \code{which="med.weight"} allows to see how #' a tree's median absolute leaf weight changes through the iterations. #' #' This function was inspired by the blog post #' \url{https://github.com/aysent/random-forest-leaf-visualization}. #' #' @return #' #' Other than producing plots (when \code{plot=TRUE}), the \code{xgb.plot.deepness} function #' silently returns a processed data.table where each row corresponds to a terminal leaf in a tree model, #' and contains information about leaf's depth, cover, and weight (which is used in calculating predictions). #' #' The \code{xgb.ggplot.deepness} silently returns either a list of two ggplot graphs when \code{which="2x1"} #' or a single ggplot graph for the other \code{which} options. #' #' @seealso #' #' \code{\link{xgb.train}}, \code{\link{xgb.model.dt.tree}}. #' #' @examples #' #' data(agaricus.train, package='xgboost') #' #' # Change max_depth to a higher number to get a more significant result #' bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 6, #' eta = 0.1, nthread = 2, nrounds = 50, objective = "binary:logistic", #' subsample = 0.5, min_child_weight = 2) #' #' xgb.plot.deepness(bst) #' xgb.ggplot.deepness(bst) #' #' xgb.plot.deepness(bst, which='max.depth', pch=16, col=rgb(0,0,1,0.3), cex=2) #' #' xgb.plot.deepness(bst, which='med.weight', pch=16, col=rgb(0,0,1,0.3), cex=2) #' #' @rdname xgb.plot.deepness #' @export xgb.plot.deepness <- function(model = NULL, which = c("2x1", "max.depth", "med.depth", "med.weight"), plot = TRUE, ...) { if (!(inherits(model, "xgb.Booster") || is.data.table(model))) stop("model: Has to be either an xgb.Booster model generaged by the xgb.train function\n", "or a data.table result of the xgb.importance function") if (!requireNamespace("igraph", quietly = TRUE)) stop("igraph package is required for plotting the graph deepness.", call. = FALSE) which <- match.arg(which) dt_tree <- model if (inherits(model, "xgb.Booster")) dt_tree <- xgb.model.dt.tree(model = model) if (!all(c("Feature", "Tree", "ID", "Yes", "No", "Cover") %in% colnames(dt_tree))) stop("Model tree columns are not as expected!\n", " Note that this function works only for tree models.") dt_depths <- merge(get.leaf.depth(dt_tree), dt_tree[, .(ID, Cover, Weight = Quality)], by = "ID") setkeyv(dt_depths, c("Tree", "ID")) # count by depth levels, and also calculate average cover at a depth dt_summaries <- dt_depths[, .(.N, Cover = mean(Cover)), Depth] setkey(dt_summaries, "Depth") if (plot) { if (which == "2x1") { op <- par(no.readonly = TRUE) par(mfrow = c(2, 1), oma = c(3, 1, 3, 1) + 0.1, mar = c(1, 4, 1, 0) + 0.1) dt_summaries[, barplot(N, border = NA, ylab = 'Number of leafs', ...)] dt_summaries[, barplot(Cover, border = NA, ylab = "Weighted cover", names.arg = Depth, ...)] title("Model complexity", xlab = "Leaf depth", outer = TRUE, line = 1) par(op) } else if (which == "max.depth") { dt_depths[, max(Depth), Tree][ , plot(jitter(V1, amount = 0.1) ~ Tree, ylab = 'Max tree leaf depth', xlab = "tree #", ...)] } else if (which == "med.depth") { dt_depths[, median(as.numeric(Depth)), Tree][ , plot(jitter(V1, amount = 0.1) ~ Tree, ylab = 'Median tree leaf depth', xlab = "tree #", ...)] } else if (which == "med.weight") { dt_depths[, median(abs(Weight)), Tree][ , plot(V1 ~ Tree, ylab = 'Median absolute leaf weight', xlab = "tree #", ...)] } } invisible(dt_depths) } # Extract path depths from root to leaf # from data.table containing the nodes and edges of the trees. # internal utility function get.leaf.depth <- function(dt_tree) { # extract tree graph's edges dt_edges <- rbindlist(list( dt_tree[Feature != "Leaf", .(ID, To = Yes, Tree)], dt_tree[Feature != "Leaf", .(ID, To = No, Tree)] )) # whether "To" is a leaf: dt_edges <- merge(dt_edges, dt_tree[Feature == "Leaf", .(ID, Leaf = TRUE)], all.x = TRUE, by.x = "To", by.y = "ID") dt_edges[is.na(Leaf), Leaf := FALSE] dt_edges[, { graph <- igraph::graph_from_data_frame(.SD[, .(ID, To)]) # min(ID) in a tree is a root node paths_tmp <- igraph::shortest_paths(graph, from = min(ID), to = To[Leaf == TRUE]) # list of paths to each leaf in a tree paths <- lapply(paths_tmp$vpath, names) # combine into a resulting path lengths table for a tree data.table(Depth = sapply(paths, length), ID = To[Leaf == TRUE]) }, by = Tree] } # Avoid error messages during CRAN check. # The reason is that these variables are never declared # They are mainly column names inferred by Data.table... globalVariables( c( ".N", "N", "Depth", "Quality", "Cover", "Tree", "ID", "Yes", "No", "Feature", "Leaf", "Weight" ) ) xgboost-1.5.2/R-package/R/xgb.plot.importance.R000066400000000000000000000126161417122711700212300ustar00rootroot00000000000000#' Plot feature importance as a bar graph #' #' Represents previously calculated feature importance as a bar graph. #' \code{xgb.plot.importance} uses base R graphics, while \code{xgb.ggplot.importance} uses the ggplot backend. #' #' @param importance_matrix a \code{data.table} returned by \code{\link{xgb.importance}}. #' @param top_n maximal number of top features to include into the plot. #' @param measure the name of importance measure to plot. #' When \code{NULL}, 'Gain' would be used for trees and 'Weight' would be used for gblinear. #' @param rel_to_first whether importance values should be represented as relative to the highest ranked feature. #' See Details. #' @param left_margin (base R barplot) allows to adjust the left margin size to fit feature names. #' When it is NULL, the existing \code{par('mar')} is used. #' @param cex (base R barplot) passed as \code{cex.names} parameter to \code{barplot}. #' @param plot (base R barplot) whether a barplot should be produced. #' If FALSE, only a data.table is returned. #' @param n_clusters (ggplot only) a \code{numeric} vector containing the min and the max range #' of the possible number of clusters of bars. #' @param ... other parameters passed to \code{barplot} (except horiz, border, cex.names, names.arg, and las). #' #' @details #' The graph represents each feature as a horizontal bar of length proportional to the importance of a feature. #' Features are shown ranked in a decreasing importance order. #' It works for importances from both \code{gblinear} and \code{gbtree} models. #' #' When \code{rel_to_first = FALSE}, the values would be plotted as they were in \code{importance_matrix}. #' For gbtree model, that would mean being normalized to the total of 1 #' ("what is feature's importance contribution relative to the whole model?"). #' For linear models, \code{rel_to_first = FALSE} would show actual values of the coefficients. #' Setting \code{rel_to_first = TRUE} allows to see the picture from the perspective of #' "what is feature's importance contribution relative to the most important feature?" #' #' The ggplot-backend method also performs 1-D clustering of the importance values, #' with bar colors corresponding to different clusters that have somewhat similar importance values. #' #' @return #' The \code{xgb.plot.importance} function creates a \code{barplot} (when \code{plot=TRUE}) #' and silently returns a processed data.table with \code{n_top} features sorted by importance. #' #' The \code{xgb.ggplot.importance} function returns a ggplot graph which could be customized afterwards. #' E.g., to change the title of the graph, add \code{+ ggtitle("A GRAPH NAME")} to the result. #' #' @seealso #' \code{\link[graphics]{barplot}}. #' #' @examples #' data(agaricus.train) #' #' bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 3, #' eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") #' #' importance_matrix <- xgb.importance(colnames(agaricus.train$data), model = bst) #' #' xgb.plot.importance(importance_matrix, rel_to_first = TRUE, xlab = "Relative importance") #' #' (gg <- xgb.ggplot.importance(importance_matrix, measure = "Frequency", rel_to_first = TRUE)) #' gg + ggplot2::ylab("Frequency") #' #' @rdname xgb.plot.importance #' @export xgb.plot.importance <- function(importance_matrix = NULL, top_n = NULL, measure = NULL, rel_to_first = FALSE, left_margin = 10, cex = NULL, plot = TRUE, ...) { check.deprecation(...) if (!is.data.table(importance_matrix)) { stop("importance_matrix: must be a data.table") } imp_names <- colnames(importance_matrix) if (is.null(measure)) { if (all(c("Feature", "Gain") %in% imp_names)) { measure <- "Gain" } else if (all(c("Feature", "Weight") %in% imp_names)) { measure <- "Weight" } else { stop("Importance matrix column names are not as expected!") } } else { if (!measure %in% imp_names) stop("Invalid `measure`") if (!"Feature" %in% imp_names) stop("Importance matrix column names are not as expected!") } # also aggregate, just in case when the values were not yet summed up by feature importance_matrix <- importance_matrix[, Importance := sum(get(measure)), by = Feature] # make sure it's ordered importance_matrix <- importance_matrix[order(-abs(Importance))] if (!is.null(top_n)) { top_n <- min(top_n, nrow(importance_matrix)) importance_matrix <- head(importance_matrix, top_n) } if (rel_to_first) { importance_matrix[, Importance := Importance / max(abs(Importance))] } if (is.null(cex)) { cex <- 2.5 / log2(1 + nrow(importance_matrix)) } if (plot) { original_mar <- par()$mar # reset margins so this function doesn't have side effects on.exit({par(mar = original_mar)}) mar <- original_mar if (!is.null(left_margin)) mar[2] <- left_margin par(mar = mar) # reverse the order of rows to have the highest ranked at the top importance_matrix[rev(seq_len(nrow(importance_matrix))), barplot(Importance, horiz = TRUE, border = NA, cex.names = cex, names.arg = Feature, las = 1, ...)] } invisible(importance_matrix) } # Avoid error messages during CRAN check. # The reason is that these variables are never declared # They are mainly column names inferred by Data.table... globalVariables(c("Feature", "Importance")) xgboost-1.5.2/R-package/R/xgb.plot.multi.trees.R000066400000000000000000000141311417122711700213340ustar00rootroot00000000000000#' Project all trees on one tree and plot it #' #' Visualization of the ensemble of trees as a single collective unit. #' #' @param model produced by the \code{xgb.train} function. #' @param feature_names names of each feature as a \code{character} vector. #' @param features_keep number of features to keep in each position of the multi trees. #' @param plot_width width in pixels of the graph to produce #' @param plot_height height in pixels of the graph to produce #' @param render a logical flag for whether the graph should be rendered (see Value). #' @param ... currently not used #' #' @details #' #' This function tries to capture the complexity of a gradient boosted tree model #' in a cohesive way by compressing an ensemble of trees into a single tree-graph representation. #' The goal is to improve the interpretability of a model generally seen as black box. #' #' Note: this function is applicable to tree booster-based models only. #' #' It takes advantage of the fact that the shape of a binary tree is only defined by #' its depth (therefore, in a boosting model, all trees have similar shape). #' #' Moreover, the trees tend to reuse the same features. #' #' The function projects each tree onto one, and keeps for each position the #' \code{features_keep} first features (based on the Gain per feature measure). #' #' This function is inspired by this blog post: #' \url{https://wellecks.wordpress.com/2015/02/21/peering-into-the-black-box-visualizing-lambdamart/} #' #' @return #' #' When \code{render = TRUE}: #' returns a rendered graph object which is an \code{htmlwidget} of class \code{grViz}. #' Similar to ggplot objects, it needs to be printed to see it when not running from command line. #' #' When \code{render = FALSE}: #' silently returns a graph object which is of DiagrammeR's class \code{dgr_graph}. #' This could be useful if one wants to modify some of the graph attributes #' before rendering the graph with \code{\link[DiagrammeR]{render_graph}}. #' #' @examples #' #' data(agaricus.train, package='xgboost') #' #' bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 15, #' eta = 1, nthread = 2, nrounds = 30, objective = "binary:logistic", #' min_child_weight = 50, verbose = 0) #' #' p <- xgb.plot.multi.trees(model = bst, features_keep = 3) #' print(p) #' #' \dontrun{ #' # Below is an example of how to save this plot to a file. #' # Note that for `export_graph` to work, the DiagrammeRsvg and rsvg packages must also be installed. #' library(DiagrammeR) #' gr <- xgb.plot.multi.trees(model=bst, features_keep = 3, render=FALSE) #' export_graph(gr, 'tree.pdf', width=1500, height=600) #' } #' #' @export xgb.plot.multi.trees <- function(model, feature_names = NULL, features_keep = 5, plot_width = NULL, plot_height = NULL, render = TRUE, ...){ check.deprecation(...) tree.matrix <- xgb.model.dt.tree(feature_names = feature_names, model = model) # first number of the path represents the tree, then the following numbers are related to the path to follow # root init root.nodes <- tree.matrix[Node == 0, ID] tree.matrix[ID %in% root.nodes, abs.node.position := root.nodes] precedent.nodes <- root.nodes while (tree.matrix[, sum(is.na(abs.node.position))] > 0) { yes.row.nodes <- tree.matrix[abs.node.position %in% precedent.nodes & !is.na(Yes)] no.row.nodes <- tree.matrix[abs.node.position %in% precedent.nodes & !is.na(No)] yes.nodes.abs.pos <- paste0(yes.row.nodes[, abs.node.position], "_0") no.nodes.abs.pos <- paste0(no.row.nodes[, abs.node.position], "_1") tree.matrix[ID %in% yes.row.nodes[, Yes], abs.node.position := yes.nodes.abs.pos] tree.matrix[ID %in% no.row.nodes[, No], abs.node.position := no.nodes.abs.pos] precedent.nodes <- c(yes.nodes.abs.pos, no.nodes.abs.pos) } tree.matrix[!is.na(Yes), Yes := paste0(abs.node.position, "_0")] tree.matrix[!is.na(No), No := paste0(abs.node.position, "_1")] for (nm in c("abs.node.position", "Yes", "No")) data.table::set(tree.matrix, j = nm, value = sub("^\\d+-", "", tree.matrix[[nm]])) nodes.dt <- tree.matrix[ , .(Quality = sum(Quality)) , by = .(abs.node.position, Feature) ][, .(Text = paste0( paste0( Feature[1:min(length(Feature), features_keep)], " (", format(Quality[1:min(length(Quality), features_keep)], digits = 5), ")" ), collapse = "\n" ) ) , by = abs.node.position ] edges.dt <- data.table::rbindlist( l = list( tree.matrix[Feature != "Leaf", .(abs.node.position, Yes)], tree.matrix[Feature != "Leaf", .(abs.node.position, No)] ) ) data.table::setnames(edges.dt, c("From", "To")) edges.dt <- edges.dt[, .N, .(From, To)] edges.dt[, N := NULL] nodes <- DiagrammeR::create_node_df( n = nrow(nodes.dt), label = nodes.dt[, Text] ) edges <- DiagrammeR::create_edge_df( from = match(edges.dt[, From], nodes.dt[, abs.node.position]), to = match(edges.dt[, To], nodes.dt[, abs.node.position]), rel = "leading_to") graph <- DiagrammeR::create_graph( nodes_df = nodes, edges_df = edges, attr_theme = NULL ) graph <- DiagrammeR::add_global_graph_attrs( graph = graph, attr_type = "graph", attr = c("layout", "rankdir"), value = c("dot", "LR") ) graph <- DiagrammeR::add_global_graph_attrs( graph = graph, attr_type = "node", attr = c("color", "fillcolor", "style", "shape", "fontname"), value = c("DimGray", "beige", "filled", "rectangle", "Helvetica") ) graph <- DiagrammeR::add_global_graph_attrs( graph = graph, attr_type = "edge", attr = c("color", "arrowsize", "arrowhead", "fontname"), value = c("DimGray", "1.5", "vee", "Helvetica") ) if (!render) return(invisible(graph)) DiagrammeR::render_graph(graph, width = plot_width, height = plot_height) } globalVariables(c(".N", "N", "From", "To", "Text", "Feature", "no.nodes.abs.pos", "ID", "Yes", "No", "Tree", "yes.nodes.abs.pos", "abs.node.position")) xgboost-1.5.2/R-package/R/xgb.plot.shap.R000066400000000000000000000327201417122711700200200ustar00rootroot00000000000000#' SHAP contribution dependency plots #' #' Visualizing the SHAP feature contribution to prediction dependencies on feature value. #' #' @param data data as a \code{matrix} or \code{dgCMatrix}. #' @param shap_contrib a matrix of SHAP contributions that was computed earlier for the above #' \code{data}. When it is NULL, it is computed internally using \code{model} and \code{data}. #' @param features a vector of either column indices or of feature names to plot. When it is NULL, #' feature importance is calculated, and \code{top_n} high ranked features are taken. #' @param top_n when \code{features} is NULL, top_n [1, 100] most important features in a model are taken. #' @param model an \code{xgb.Booster} model. It has to be provided when either \code{shap_contrib} #' or \code{features} is missing. #' @param trees passed to \code{\link{xgb.importance}} when \code{features = NULL}. #' @param target_class is only relevant for multiclass models. When it is set to a 0-based class index, #' only SHAP contributions for that specific class are used. #' If it is not set, SHAP importances are averaged over all classes. #' @param approxcontrib passed to \code{\link{predict.xgb.Booster}} when \code{shap_contrib = NULL}. #' @param subsample a random fraction of data points to use for plotting. When it is NULL, #' it is set so that up to 100K data points are used. #' @param n_col a number of columns in a grid of plots. #' @param col color of the scatterplot markers. #' @param pch scatterplot marker. #' @param discrete_n_uniq a maximal number of unique values in a feature to consider it as discrete. #' @param discrete_jitter an \code{amount} parameter of jitter added to discrete features' positions. #' @param ylab a y-axis label in 1D plots. #' @param plot_NA whether the contributions of cases with missing values should also be plotted. #' @param col_NA a color of marker for missing value contributions. #' @param pch_NA a marker type for NA values. #' @param pos_NA a relative position of the x-location where NA values are shown: #' \code{min(x) + (max(x) - min(x)) * pos_NA}. #' @param plot_loess whether to plot loess-smoothed curves. The smoothing is only done for features with #' more than 5 distinct values. #' @param col_loess a color to use for the loess curves. #' @param span_loess the \code{span} parameter in \code{\link[stats]{loess}}'s call. #' @param which whether to do univariate or bivariate plotting. NOTE: only 1D is implemented so far. #' @param plot whether a plot should be drawn. If FALSE, only a list of matrices is returned. #' @param ... other parameters passed to \code{plot}. #' #' @details #' #' These scatterplots represent how SHAP feature contributions depend of feature values. #' The similarity to partial dependency plots is that they also give an idea for how feature values #' affect predictions. However, in partial dependency plots, we usually see marginal dependencies #' of model prediction on feature value, while SHAP contribution dependency plots display the estimated #' contributions of a feature to model prediction for each individual case. #' #' When \code{plot_loess = TRUE} is set, feature values are rounded to 3 significant digits and #' weighted LOESS is computed and plotted, where weights are the numbers of data points #' at each rounded value. #' #' Note: SHAP contributions are shown on the scale of model margin. E.g., for a logistic binomial objective, #' the margin is prediction before a sigmoidal transform into probability-like values. #' Also, since SHAP stands for "SHapley Additive exPlanation" (model prediction = sum of SHAP #' contributions for all features + bias), depending on the objective used, transforming SHAP #' contributions for a feature from the marginal to the prediction space is not necessarily #' a meaningful thing to do. #' #' @return #' #' In addition to producing plots (when \code{plot=TRUE}), it silently returns a list of two matrices: #' \itemize{ #' \item \code{data} the values of selected features; #' \item \code{shap_contrib} the contributions of selected features. #' } #' #' @references #' #' Scott M. Lundberg, Su-In Lee, "A Unified Approach to Interpreting Model Predictions", NIPS Proceedings 2017, \url{https://arxiv.org/abs/1705.07874} #' #' Scott M. Lundberg, Su-In Lee, "Consistent feature attribution for tree ensembles", \url{https://arxiv.org/abs/1706.06060} #' #' @examples #' #' data(agaricus.train, package='xgboost') #' data(agaricus.test, package='xgboost') #' #' bst <- xgboost(agaricus.train$data, agaricus.train$label, nrounds = 50, #' eta = 0.1, max_depth = 3, subsample = .5, #' method = "hist", objective = "binary:logistic", nthread = 2, verbose = 0) #' #' xgb.plot.shap(agaricus.test$data, model = bst, features = "odor=none") #' contr <- predict(bst, agaricus.test$data, predcontrib = TRUE) #' xgb.plot.shap(agaricus.test$data, contr, model = bst, top_n = 12, n_col = 3) #' xgb.ggplot.shap.summary(agaricus.test$data, contr, model = bst, top_n = 12) # Summary plot #' #' # multiclass example - plots for each class separately: #' nclass <- 3 #' nrounds <- 20 #' x <- as.matrix(iris[, -5]) #' set.seed(123) #' is.na(x[sample(nrow(x) * 4, 30)]) <- TRUE # introduce some missing values #' mbst <- xgboost(data = x, label = as.numeric(iris$Species) - 1, nrounds = nrounds, #' max_depth = 2, eta = 0.3, subsample = .5, nthread = 2, #' objective = "multi:softprob", num_class = nclass, verbose = 0) #' trees0 <- seq(from=0, by=nclass, length.out=nrounds) #' col <- rgb(0, 0, 1, 0.5) #' xgb.plot.shap(x, model = mbst, trees = trees0, target_class = 0, top_n = 4, #' n_col = 2, col = col, pch = 16, pch_NA = 17) #' xgb.plot.shap(x, model = mbst, trees = trees0 + 1, target_class = 1, top_n = 4, #' n_col = 2, col = col, pch = 16, pch_NA = 17) #' xgb.plot.shap(x, model = mbst, trees = trees0 + 2, target_class = 2, top_n = 4, #' n_col = 2, col = col, pch = 16, pch_NA = 17) #' xgb.ggplot.shap.summary(x, model = mbst, target_class = 0, top_n = 4) # Summary plot #' #' @rdname xgb.plot.shap #' @export xgb.plot.shap <- function(data, shap_contrib = NULL, features = NULL, top_n = 1, model = NULL, trees = NULL, target_class = NULL, approxcontrib = FALSE, subsample = NULL, n_col = 1, col = rgb(0, 0, 1, 0.2), pch = '.', discrete_n_uniq = 5, discrete_jitter = 0.01, ylab = "SHAP", plot_NA = TRUE, col_NA = rgb(0.7, 0, 1, 0.6), pch_NA = '.', pos_NA = 1.07, plot_loess = TRUE, col_loess = 2, span_loess = 0.5, which = c("1d", "2d"), plot = TRUE, ...) { data_list <- xgb.shap.data( data = data, shap_contrib = shap_contrib, features = features, top_n = top_n, model = model, trees = trees, target_class = target_class, approxcontrib = approxcontrib, subsample = subsample, max_observations = 100000 ) data <- data_list[["data"]] shap_contrib <- data_list[["shap_contrib"]] features <- colnames(data) which <- match.arg(which) if (which == "2d") stop("2D plots are not implemented yet") if (n_col > length(features)) n_col <- length(features) if (plot && which == "1d") { op <- par(mfrow = c(ceiling(length(features) / n_col), n_col), oma = c(0, 0, 0, 0) + 0.2, mar = c(3.5, 3.5, 0, 0) + 0.1, mgp = c(1.7, 0.6, 0)) for (f in features) { ord <- order(data[, f]) x <- data[, f][ord] y <- shap_contrib[, f][ord] x_lim <- range(x, na.rm = TRUE) y_lim <- range(y, na.rm = TRUE) do_na <- plot_NA && any(is.na(x)) if (do_na) { x_range <- diff(x_lim) loc_na <- min(x, na.rm = TRUE) + x_range * pos_NA x_lim <- range(c(x_lim, loc_na)) } x_uniq <- unique(x) x2plot <- x # add small jitter for discrete features with <= 5 distinct values if (length(x_uniq) <= discrete_n_uniq) x2plot <- jitter(x, amount = discrete_jitter * min(diff(x_uniq), na.rm = TRUE)) plot(x2plot, y, pch = pch, xlab = f, col = col, xlim = x_lim, ylim = y_lim, ylab = ylab, ...) grid() if (plot_loess) { # compress x to 3 digits, and mean-aggregate y zz <- data.table(x = signif(x, 3), y)[, .(.N, y = mean(y)), x] if (nrow(zz) <= 5) { lines(zz$x, zz$y, col = col_loess) } else { lo <- stats::loess(y ~ x, data = zz, weights = zz$N, span = span_loess) zz$y_lo <- predict(lo, zz, type = "link") lines(zz$x, zz$y_lo, col = col_loess) } } if (do_na) { i_na <- which(is.na(x)) x_na <- rep(loc_na, length(i_na)) x_na <- jitter(x_na, amount = x_range * 0.01) points(x_na, y[i_na], pch = pch_NA, col = col_NA) } } par(op) } if (plot && which == "2d") { # TODO warning("Bivariate plotting is currently not available.") } invisible(list(data = data, shap_contrib = shap_contrib)) } #' SHAP contribution dependency summary plot #' #' Compare SHAP contributions of different features. #' #' A point plot (each point representing one sample from \code{data}) is #' produced for each feature, with the points plotted on the SHAP value axis. #' Each point (observation) is coloured based on its feature value. The plot #' hence allows us to see which features have a negative / positive contribution #' on the model prediction, and whether the contribution is different for larger #' or smaller values of the feature. We effectively try to replicate the #' \code{summary_plot} function from https://github.com/slundberg/shap. #' #' @inheritParams xgb.plot.shap #' #' @return A \code{ggplot2} object. #' @export #' #' @examples # See \code{\link{xgb.plot.shap}}. #' @seealso \code{\link{xgb.plot.shap}}, \code{\link{xgb.ggplot.shap.summary}}, #' \url{https://github.com/slundberg/shap} xgb.plot.shap.summary <- function(data, shap_contrib = NULL, features = NULL, top_n = 10, model = NULL, trees = NULL, target_class = NULL, approxcontrib = FALSE, subsample = NULL) { # Only ggplot implementation is available. xgb.ggplot.shap.summary(data, shap_contrib, features, top_n, model, trees, target_class, approxcontrib, subsample) } #' Prepare data for SHAP plots. To be used in xgb.plot.shap, xgb.plot.shap.summary, etc. #' Internal utility function. #' #' @inheritParams xgb.plot.shap #' @keywords internal #' #' @return A list containing: 'data', a matrix containing sample observations #' and their feature values; 'shap_contrib', a matrix containing the SHAP contribution #' values for these observations. xgb.shap.data <- function(data, shap_contrib = NULL, features = NULL, top_n = 1, model = NULL, trees = NULL, target_class = NULL, approxcontrib = FALSE, subsample = NULL, max_observations = 100000) { if (!is.matrix(data) && !inherits(data, "dgCMatrix")) stop("data: must be either matrix or dgCMatrix") if (is.null(shap_contrib) && (is.null(model) || !inherits(model, "xgb.Booster"))) stop("when shap_contrib is not provided, one must provide an xgb.Booster model") if (is.null(features) && (is.null(model) || !inherits(model, "xgb.Booster"))) stop("when features are not provided, one must provide an xgb.Booster model to rank the features") if (!is.null(shap_contrib) && (!is.matrix(shap_contrib) || nrow(shap_contrib) != nrow(data) || ncol(shap_contrib) != ncol(data) + 1)) stop("shap_contrib is not compatible with the provided data") if (is.character(features) && is.null(colnames(data))) stop("either provide `data` with column names or provide `features` as column indices") if (is.null(model$feature_names) && model$nfeatures != ncol(data)) stop("if model has no feature_names, columns in `data` must match features in model") if (!is.null(subsample)) { idx <- sample(x = seq_len(nrow(data)), size = as.integer(subsample * nrow(data)), replace = FALSE) } else { idx <- seq_len(min(nrow(data), max_observations)) } data <- data[idx, ] if (is.null(colnames(data))) { colnames(data) <- paste0("X", seq_len(ncol(data))) } if (!is.null(shap_contrib)) { if (is.list(shap_contrib)) { # multiclass: either choose a class or merge shap_contrib <- if (!is.null(target_class)) shap_contrib[[target_class + 1]] else Reduce("+", lapply(shap_contrib, abs)) } shap_contrib <- shap_contrib[idx, ] if (is.null(colnames(shap_contrib))) { colnames(shap_contrib) <- paste0("X", seq_len(ncol(data))) } } else { shap_contrib <- predict(model, newdata = data, predcontrib = TRUE, approxcontrib = approxcontrib) if (is.list(shap_contrib)) { # multiclass: either choose a class or merge shap_contrib <- if (!is.null(target_class)) shap_contrib[[target_class + 1]] else Reduce("+", lapply(shap_contrib, abs)) } } if (is.null(features)) { if (!is.null(model$feature_names)) { imp <- xgb.importance(model = model, trees = trees) } else { imp <- xgb.importance(model = model, trees = trees, feature_names = colnames(data)) } top_n <- top_n[1] if (top_n < 1 | top_n > 100) stop("top_n: must be an integer within [1, 100]") features <- imp$Feature[1:min(top_n, NROW(imp))] } if (is.character(features)) { features <- match(features, colnames(data)) } shap_contrib <- shap_contrib[, features, drop = FALSE] data <- data[, features, drop = FALSE] list( data = data, shap_contrib = shap_contrib ) } xgboost-1.5.2/R-package/R/xgb.plot.tree.R000066400000000000000000000134431417122711700200250ustar00rootroot00000000000000#' Plot a boosted tree model #' #' Read a tree model text dump and plot the model. #' #' @param feature_names names of each feature as a \code{character} vector. #' @param model produced by the \code{xgb.train} function. #' @param trees an integer vector of tree indices that should be visualized. #' If set to \code{NULL}, all trees of the model are included. #' IMPORTANT: the tree index in xgboost model is zero-based #' (e.g., use \code{trees = 0:2} for the first 3 trees in a model). #' @param plot_width the width of the diagram in pixels. #' @param plot_height the height of the diagram in pixels. #' @param render a logical flag for whether the graph should be rendered (see Value). #' @param show_node_id a logical flag for whether to show node id's in the graph. #' @param ... currently not used. #' #' @details #' #' The content of each node is organised that way: #' #' \itemize{ #' \item Feature name. #' \item \code{Cover}: The sum of second order gradient of training data classified to the leaf. #' If it is square loss, this simply corresponds to the number of instances seen by a split #' or collected by a leaf during training. #' The deeper in the tree a node is, the lower this metric will be. #' \item \code{Gain} (for split nodes): the information gain metric of a split #' (corresponds to the importance of the node in the model). #' \item \code{Value} (for leafs): the margin value that the leaf may contribute to prediction. #' } #' The tree root nodes also indicate the Tree index (0-based). #' #' The "Yes" branches are marked by the "< split_value" label. #' The branches that also used for missing values are marked as bold #' (as in "carrying extra capacity"). #' #' This function uses \href{http://www.graphviz.org/}{GraphViz} as a backend of DiagrammeR. #' #' @return #' #' When \code{render = TRUE}: #' returns a rendered graph object which is an \code{htmlwidget} of class \code{grViz}. #' Similar to ggplot objects, it needs to be printed to see it when not running from command line. #' #' When \code{render = FALSE}: #' silently returns a graph object which is of DiagrammeR's class \code{dgr_graph}. #' This could be useful if one wants to modify some of the graph attributes #' before rendering the graph with \code{\link[DiagrammeR]{render_graph}}. #' #' @examples #' data(agaricus.train, package='xgboost') #' #' bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 3, #' eta = 1, nthread = 2, nrounds = 2,objective = "binary:logistic") #' # plot all the trees #' xgb.plot.tree(model = bst) #' # plot only the first tree and display the node ID: #' xgb.plot.tree(model = bst, trees = 0, show_node_id = TRUE) #' #' \dontrun{ #' # Below is an example of how to save this plot to a file. #' # Note that for `export_graph` to work, the DiagrammeRsvg and rsvg packages must also be installed. #' library(DiagrammeR) #' gr <- xgb.plot.tree(model=bst, trees=0:1, render=FALSE) #' export_graph(gr, 'tree.pdf', width=1500, height=1900) #' export_graph(gr, 'tree.png', width=1500, height=1900) #' } #' #' @export xgb.plot.tree <- function(feature_names = NULL, model = NULL, trees = NULL, plot_width = NULL, plot_height = NULL, render = TRUE, show_node_id = FALSE, ...){ check.deprecation(...) if (!inherits(model, "xgb.Booster")) { stop("model: Has to be an object of class xgb.Booster") } if (!requireNamespace("DiagrammeR", quietly = TRUE)) { stop("DiagrammeR package is required for xgb.plot.tree", call. = FALSE) } dt <- xgb.model.dt.tree(feature_names = feature_names, model = model, trees = trees) dt[, label := paste0(Feature, "\nCover: ", Cover, ifelse(Feature == "Leaf", "\nValue: ", "\nGain: "), Quality)] if (show_node_id) dt[, label := paste0(ID, ": ", label)] dt[Node == 0, label := paste0("Tree ", Tree, "\n", label)] dt[, shape := "rectangle"][Feature == "Leaf", shape := "oval"] dt[, filledcolor := "Beige"][Feature == "Leaf", filledcolor := "Khaki"] # in order to draw the first tree on top: dt <- dt[order(-Tree)] nodes <- DiagrammeR::create_node_df( n = nrow(dt), ID = dt$ID, label = dt$label, fillcolor = dt$filledcolor, shape = dt$shape, data = dt$Feature, fontcolor = "black") edges <- DiagrammeR::create_edge_df( from = match(rep(dt[Feature != "Leaf", c(ID)], 2), dt$ID), to = match(dt[Feature != "Leaf", c(Yes, No)], dt$ID), label = c( dt[Feature != "Leaf", paste("<", Split)], rep("", nrow(dt[Feature != "Leaf"])) ), style = c( dt[Feature != "Leaf", ifelse(Missing == Yes, "bold", "solid")], dt[Feature != "Leaf", ifelse(Missing == No, "bold", "solid")] ), rel = "leading_to") graph <- DiagrammeR::create_graph( nodes_df = nodes, edges_df = edges, attr_theme = NULL ) graph <- DiagrammeR::add_global_graph_attrs( graph = graph, attr_type = "graph", attr = c("layout", "rankdir"), value = c("dot", "LR") ) graph <- DiagrammeR::add_global_graph_attrs( graph = graph, attr_type = "node", attr = c("color", "style", "fontname"), value = c("DimGray", "filled", "Helvetica") ) graph <- DiagrammeR::add_global_graph_attrs( graph = graph, attr_type = "edge", attr = c("color", "arrowsize", "arrowhead", "fontname"), value = c("DimGray", "1.5", "vee", "Helvetica") ) if (!render) return(invisible(graph)) DiagrammeR::render_graph(graph, width = plot_width, height = plot_height) } # Avoid error messages during CRAN check. # The reason is that these variables are never declared # They are mainly column names inferred by Data.table... globalVariables(c("Feature", "ID", "Cover", "Quality", "Split", "Yes", "No", "Missing", ".", "shape", "filledcolor", "label")) xgboost-1.5.2/R-package/R/xgb.save.R000066400000000000000000000041061417122711700170430ustar00rootroot00000000000000#' Save xgboost model to binary file #' #' Save xgboost model to a file in binary format. #' #' @param model model object of \code{xgb.Booster} class. #' @param fname name of the file to write. #' #' @details #' This methods allows to save a model in an xgboost-internal binary format which is universal #' among the various xgboost interfaces. In R, the saved model file could be read-in later #' using either the \code{\link{xgb.load}} function or the \code{xgb_model} parameter #' of \code{\link{xgb.train}}. #' #' Note: a model can also be saved as an R-object (e.g., by using \code{\link[base]{readRDS}} #' or \code{\link[base]{save}}). However, it would then only be compatible with R, and #' corresponding R-methods would need to be used to load it. Moreover, persisting the model with #' \code{\link[base]{readRDS}} or \code{\link[base]{save}}) will cause compatibility problems in #' future versions of XGBoost. Consult \code{\link{a-compatibility-note-for-saveRDS-save}} to learn #' how to persist models in a future-proof way, i.e. to make the model accessible in future #' releases of XGBoost. #' #' @seealso #' \code{\link{xgb.load}}, \code{\link{xgb.Booster.complete}}. #' #' @examples #' data(agaricus.train, package='xgboost') #' data(agaricus.test, package='xgboost') #' train <- agaricus.train #' test <- agaricus.test #' bst <- xgboost(data = train$data, label = train$label, max_depth = 2, #' eta = 1, nthread = 2, nrounds = 2,objective = "binary:logistic") #' xgb.save(bst, 'xgb.model') #' bst <- xgb.load('xgb.model') #' if (file.exists('xgb.model')) file.remove('xgb.model') #' pred <- predict(bst, test$data) #' @export xgb.save <- function(model, fname) { if (typeof(fname) != "character") stop("fname must be character") if (!inherits(model, "xgb.Booster")) { stop("model must be xgb.Booster.", if (inherits(model, "xgb.DMatrix")) " Use xgb.DMatrix.save to save an xgb.DMatrix object." else "") } model <- xgb.Booster.complete(model, saveraw = FALSE) fname <- path.expand(fname) .Call(XGBoosterSaveModel_R, model$handle, fname[1]) return(TRUE) } xgboost-1.5.2/R-package/R/xgb.save.raw.R000066400000000000000000000013211417122711700176270ustar00rootroot00000000000000#' Save xgboost model to R's raw vector, #' user can call xgb.load.raw to load the model back from raw vector #' #' Save xgboost model from xgboost or xgb.train #' #' @param model the model object. #' #' @examples #' data(agaricus.train, package='xgboost') #' data(agaricus.test, package='xgboost') #' train <- agaricus.train #' test <- agaricus.test #' bst <- xgboost(data = train$data, label = train$label, max_depth = 2, #' eta = 1, nthread = 2, nrounds = 2,objective = "binary:logistic") #' raw <- xgb.save.raw(bst) #' bst <- xgb.load.raw(raw) #' pred <- predict(bst, test$data) #' #' @export xgb.save.raw <- function(model) { handle <- xgb.get.handle(model) .Call(XGBoosterModelToRaw_R, handle) } xgboost-1.5.2/R-package/R/xgb.serialize.R000066400000000000000000000014501417122711700200730ustar00rootroot00000000000000#' Serialize the booster instance into R's raw vector. The serialization method differs #' from \code{\link{xgb.save.raw}} as the latter one saves only the model but not #' parameters. This serialization format is not stable across different xgboost versions. #' #' @param booster the booster instance #' #' @examples #' data(agaricus.train, package='xgboost') #' data(agaricus.test, package='xgboost') #' train <- agaricus.train #' test <- agaricus.test #' bst <- xgboost(data = train$data, label = train$label, max_depth = 2, #' eta = 1, nthread = 2, nrounds = 2,objective = "binary:logistic") #' raw <- xgb.serialize(bst) #' bst <- xgb.unserialize(raw) #' #' @export xgb.serialize <- function(booster) { handle <- xgb.get.handle(booster) .Call(XGBoosterSerializeToBuffer_R, handle) } xgboost-1.5.2/R-package/R/xgb.train.R000066400000000000000000000547711417122711700172370ustar00rootroot00000000000000#' eXtreme Gradient Boosting Training #' #' \code{xgb.train} is an advanced interface for training an xgboost model. #' The \code{xgboost} function is a simpler wrapper for \code{xgb.train}. #' #' @param params the list of parameters. The complete list of parameters is #' available in the \href{http://xgboost.readthedocs.io/en/latest/parameter.html}{online documentation}. Below #' is a shorter summary: #' #' 1. General Parameters #' #' \itemize{ #' \item \code{booster} which booster to use, can be \code{gbtree} or \code{gblinear}. Default: \code{gbtree}. #' } #' #' 2. Booster Parameters #' #' 2.1. Parameters for Tree Booster #' #' \itemize{ #' \item \code{eta} control the learning rate: scale the contribution of each tree by a factor of \code{0 < eta < 1} when it is added to the current approximation. Used to prevent overfitting by making the boosting process more conservative. Lower value for \code{eta} implies larger value for \code{nrounds}: low \code{eta} value means model more robust to overfitting but slower to compute. Default: 0.3 #' \item \code{gamma} minimum loss reduction required to make a further partition on a leaf node of the tree. the larger, the more conservative the algorithm will be. #' \item \code{max_depth} maximum depth of a tree. Default: 6 #' \item \code{min_child_weight} minimum sum of instance weight (hessian) needed in a child. If the tree partition step results in a leaf node with the sum of instance weight less than min_child_weight, then the building process will give up further partitioning. In linear regression mode, this simply corresponds to minimum number of instances needed to be in each node. The larger, the more conservative the algorithm will be. Default: 1 #' \item \code{subsample} subsample ratio of the training instance. Setting it to 0.5 means that xgboost randomly collected half of the data instances to grow trees and this will prevent overfitting. It makes computation shorter (because less data to analyse). It is advised to use this parameter with \code{eta} and increase \code{nrounds}. Default: 1 #' \item \code{colsample_bytree} subsample ratio of columns when constructing each tree. Default: 1 #' \item \code{lambda} L2 regularization term on weights. Default: 1 #' \item \code{alpha} L1 regularization term on weights. (there is no L1 reg on bias because it is not important). Default: 0 #' \item \code{num_parallel_tree} Experimental parameter. number of trees to grow per round. Useful to test Random Forest through XGBoost (set \code{colsample_bytree < 1}, \code{subsample < 1} and \code{round = 1}) accordingly. Default: 1 #' \item \code{monotone_constraints} A numerical vector consists of \code{1}, \code{0} and \code{-1} with its length equals to the number of features in the training data. \code{1} is increasing, \code{-1} is decreasing and \code{0} is no constraint. #' \item \code{interaction_constraints} A list of vectors specifying feature indices of permitted interactions. Each item of the list represents one permitted interaction where specified features are allowed to interact with each other. Feature index values should start from \code{0} (\code{0} references the first column). Leave argument unspecified for no interaction constraints. #' } #' #' 2.2. Parameters for Linear Booster #' #' \itemize{ #' \item \code{lambda} L2 regularization term on weights. Default: 0 #' \item \code{lambda_bias} L2 regularization term on bias. Default: 0 #' \item \code{alpha} L1 regularization term on weights. (there is no L1 reg on bias because it is not important). Default: 0 #' } #' #' 3. Task Parameters #' #' \itemize{ #' \item \code{objective} specify the learning task and the corresponding learning objective, users can pass a self-defined function to it. The default objective options are below: #' \itemize{ #' \item \code{reg:squarederror} Regression with squared loss (Default). #' \item \code{reg:squaredlogerror}: regression with squared log loss \eqn{1/2 * (log(pred + 1) - log(label + 1))^2}. All inputs are required to be greater than -1. Also, see metric rmsle for possible issue with this objective. #' \item \code{reg:logistic} logistic regression. #' \item \code{reg:pseudohubererror}: regression with Pseudo Huber loss, a twice differentiable alternative to absolute loss. #' \item \code{binary:logistic} logistic regression for binary classification. Output probability. #' \item \code{binary:logitraw} logistic regression for binary classification, output score before logistic transformation. #' \item \code{binary:hinge}: hinge loss for binary classification. This makes predictions of 0 or 1, rather than producing probabilities. #' \item \code{count:poisson}: Poisson regression for count data, output mean of Poisson distribution. \code{max_delta_step} is set to 0.7 by default in poisson regression (used to safeguard optimization). #' \item \code{survival:cox}: Cox regression for right censored survival time data (negative values are considered right censored). Note that predictions are returned on the hazard ratio scale (i.e., as HR = exp(marginal_prediction) in the proportional hazard function \code{h(t) = h0(t) * HR)}. #' \item \code{survival:aft}: Accelerated failure time model for censored survival time data. See \href{https://xgboost.readthedocs.io/en/latest/tutorials/aft_survival_analysis.html}{Survival Analysis with Accelerated Failure Time} for details. #' \item \code{aft_loss_distribution}: Probability Density Function used by \code{survival:aft} and \code{aft-nloglik} metric. #' \item \code{multi:softmax} set xgboost to do multiclass classification using the softmax objective. Class is represented by a number and should be from 0 to \code{num_class - 1}. #' \item \code{multi:softprob} same as softmax, but prediction outputs a vector of ndata * nclass elements, which can be further reshaped to ndata, nclass matrix. The result contains predicted probabilities of each data point belonging to each class. #' \item \code{rank:pairwise} set xgboost to do ranking task by minimizing the pairwise loss. #' \item \code{rank:ndcg}: Use LambdaMART to perform list-wise ranking where \href{https://en.wikipedia.org/wiki/Discounted_cumulative_gain}{Normalized Discounted Cumulative Gain (NDCG)} is maximized. #' \item \code{rank:map}: Use LambdaMART to perform list-wise ranking where \href{https://en.wikipedia.org/wiki/Evaluation_measures_(information_retrieval)#Mean_average_precision}{Mean Average Precision (MAP)} is maximized. #' \item \code{reg:gamma}: gamma regression with log-link. Output is a mean of gamma distribution. It might be useful, e.g., for modeling insurance claims severity, or for any outcome that might be \href{https://en.wikipedia.org/wiki/Gamma_distribution#Applications}{gamma-distributed}. #' \item \code{reg:tweedie}: Tweedie regression with log-link. It might be useful, e.g., for modeling total loss in insurance, or for any outcome that might be \href{https://en.wikipedia.org/wiki/Tweedie_distribution#Applications}{Tweedie-distributed}. #' } #' \item \code{base_score} the initial prediction score of all instances, global bias. Default: 0.5 #' \item \code{eval_metric} evaluation metrics for validation data. Users can pass a self-defined function to it. Default: metric will be assigned according to objective(rmse for regression, and error for classification, mean average precision for ranking). List is provided in detail section. #' } #' #' @param data training dataset. \code{xgb.train} accepts only an \code{xgb.DMatrix} as the input. #' \code{xgboost}, in addition, also accepts \code{matrix}, \code{dgCMatrix}, or name of a local data file. #' @param nrounds max number of boosting iterations. #' @param watchlist named list of xgb.DMatrix datasets to use for evaluating model performance. #' Metrics specified in either \code{eval_metric} or \code{feval} will be computed for each #' of these datasets during each boosting iteration, and stored in the end as a field named #' \code{evaluation_log} in the resulting object. When either \code{verbose>=1} or #' \code{\link{cb.print.evaluation}} callback is engaged, the performance results are continuously #' printed out during the training. #' E.g., specifying \code{watchlist=list(validation1=mat1, validation2=mat2)} allows to track #' the performance of each round's model on mat1 and mat2. #' @param obj customized objective function. Returns gradient and second order #' gradient with given prediction and dtrain. #' @param feval customized evaluation function. Returns #' \code{list(metric='metric-name', value='metric-value')} with given #' prediction and dtrain. #' @param verbose If 0, xgboost will stay silent. If 1, it will print information about performance. #' If 2, some additional information will be printed out. #' Note that setting \code{verbose > 0} automatically engages the #' \code{cb.print.evaluation(period=1)} callback function. #' @param print_every_n Print each n-th iteration evaluation messages when \code{verbose>0}. #' Default is 1 which means all messages are printed. This parameter is passed to the #' \code{\link{cb.print.evaluation}} callback. #' @param early_stopping_rounds If \code{NULL}, the early stopping function is not triggered. #' If set to an integer \code{k}, training with a validation set will stop if the performance #' doesn't improve for \code{k} rounds. #' Setting this parameter engages the \code{\link{cb.early.stop}} callback. #' @param maximize If \code{feval} and \code{early_stopping_rounds} are set, #' then this parameter must be set as well. #' When it is \code{TRUE}, it means the larger the evaluation score the better. #' This parameter is passed to the \code{\link{cb.early.stop}} callback. #' @param save_period when it is non-NULL, model is saved to disk after every \code{save_period} rounds, #' 0 means save at the end. The saving is handled by the \code{\link{cb.save.model}} callback. #' @param save_name the name or path for periodically saved model file. #' @param xgb_model a previously built model to continue the training from. #' Could be either an object of class \code{xgb.Booster}, or its raw data, or the name of a #' file with a previously saved model. #' @param callbacks a list of callback functions to perform various task during boosting. #' See \code{\link{callbacks}}. Some of the callbacks are automatically created depending on the #' parameters' values. User can provide either existing or their own callback methods in order #' to customize the training process. #' @param ... other parameters to pass to \code{params}. #' @param label vector of response values. Should not be provided when data is #' a local data file name or an \code{xgb.DMatrix}. #' @param missing by default is set to NA, which means that NA values should be considered as 'missing' #' by the algorithm. Sometimes, 0 or other extreme value might be used to represent missing values. #' This parameter is only used when input is a dense matrix. #' @param weight a vector indicating the weight for each row of the input. #' #' @details #' These are the training functions for \code{xgboost}. #' #' The \code{xgb.train} interface supports advanced features such as \code{watchlist}, #' customized objective and evaluation metric functions, therefore it is more flexible #' than the \code{xgboost} interface. #' #' Parallelization is automatically enabled if \code{OpenMP} is present. #' Number of threads can also be manually specified via \code{nthread} parameter. #' #' The evaluation metric is chosen automatically by XGBoost (according to the objective) #' when the \code{eval_metric} parameter is not provided. #' User may set one or several \code{eval_metric} parameters. #' Note that when using a customized metric, only this single metric can be used. #' The following is the list of built-in metrics for which XGBoost provides optimized implementation: #' \itemize{ #' \item \code{rmse} root mean square error. \url{https://en.wikipedia.org/wiki/Root_mean_square_error} #' \item \code{logloss} negative log-likelihood. \url{https://en.wikipedia.org/wiki/Log-likelihood} #' \item \code{mlogloss} multiclass logloss. \url{https://scikit-learn.org/stable/modules/generated/sklearn.metrics.log_loss.html} #' \item \code{error} Binary classification error rate. It is calculated as \code{(# wrong cases) / (# all cases)}. #' By default, it uses the 0.5 threshold for predicted values to define negative and positive instances. #' Different threshold (e.g., 0.) could be specified as "error@0." #' \item \code{merror} Multiclass classification error rate. It is calculated as \code{(# wrong cases) / (# all cases)}. #' \item \code{mae} Mean absolute error #' \item \code{mape} Mean absolute percentage error #' \item \code{auc} Area under the curve. \url{https://en.wikipedia.org/wiki/Receiver_operating_characteristic#'Area_under_curve} for ranking evaluation. #' \item \code{aucpr} Area under the PR curve. \url{https://en.wikipedia.org/wiki/Precision_and_recall} for ranking evaluation. #' \item \code{ndcg} Normalized Discounted Cumulative Gain (for ranking task). \url{https://en.wikipedia.org/wiki/NDCG} #' } #' #' The following callbacks are automatically created when certain parameters are set: #' \itemize{ #' \item \code{cb.print.evaluation} is turned on when \code{verbose > 0}; #' and the \code{print_every_n} parameter is passed to it. #' \item \code{cb.evaluation.log} is on when \code{watchlist} is present. #' \item \code{cb.early.stop}: when \code{early_stopping_rounds} is set. #' \item \code{cb.save.model}: when \code{save_period > 0} is set. #' } #' #' @return #' An object of class \code{xgb.Booster} with the following elements: #' \itemize{ #' \item \code{handle} a handle (pointer) to the xgboost model in memory. #' \item \code{raw} a cached memory dump of the xgboost model saved as R's \code{raw} type. #' \item \code{niter} number of boosting iterations. #' \item \code{evaluation_log} evaluation history stored as a \code{data.table} with the #' first column corresponding to iteration number and the rest corresponding to evaluation #' metrics' values. It is created by the \code{\link{cb.evaluation.log}} callback. #' \item \code{call} a function call. #' \item \code{params} parameters that were passed to the xgboost library. Note that it does not #' capture parameters changed by the \code{\link{cb.reset.parameters}} callback. #' \item \code{callbacks} callback functions that were either automatically assigned or #' explicitly passed. #' \item \code{best_iteration} iteration number with the best evaluation metric value #' (only available with early stopping). #' \item \code{best_score} the best evaluation metric value during early stopping. #' (only available with early stopping). #' \item \code{feature_names} names of the training dataset features #' (only when column names were defined in training data). #' \item \code{nfeatures} number of features in training data. #' } #' #' @seealso #' \code{\link{callbacks}}, #' \code{\link{predict.xgb.Booster}}, #' \code{\link{xgb.cv}} #' #' @references #' #' Tianqi Chen and Carlos Guestrin, "XGBoost: A Scalable Tree Boosting System", #' 22nd SIGKDD Conference on Knowledge Discovery and Data Mining, 2016, \url{https://arxiv.org/abs/1603.02754} #' #' @examples #' data(agaricus.train, package='xgboost') #' data(agaricus.test, package='xgboost') #' #' dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) #' dtest <- with(agaricus.test, xgb.DMatrix(data, label = label)) #' watchlist <- list(train = dtrain, eval = dtest) #' #' ## A simple xgb.train example: #' param <- list(max_depth = 2, eta = 1, verbose = 0, nthread = 2, #' objective = "binary:logistic", eval_metric = "auc") #' bst <- xgb.train(param, dtrain, nrounds = 2, watchlist) #' #' #' ## An xgb.train example where custom objective and evaluation metric are used: #' logregobj <- function(preds, dtrain) { #' labels <- getinfo(dtrain, "label") #' preds <- 1/(1 + exp(-preds)) #' grad <- preds - labels #' hess <- preds * (1 - preds) #' return(list(grad = grad, hess = hess)) #' } #' evalerror <- function(preds, dtrain) { #' labels <- getinfo(dtrain, "label") #' err <- as.numeric(sum(labels != (preds > 0)))/length(labels) #' return(list(metric = "error", value = err)) #' } #' #' # These functions could be used by passing them either: #' # as 'objective' and 'eval_metric' parameters in the params list: #' param <- list(max_depth = 2, eta = 1, verbose = 0, nthread = 2, #' objective = logregobj, eval_metric = evalerror) #' bst <- xgb.train(param, dtrain, nrounds = 2, watchlist) #' #' # or through the ... arguments: #' param <- list(max_depth = 2, eta = 1, verbose = 0, nthread = 2) #' bst <- xgb.train(param, dtrain, nrounds = 2, watchlist, #' objective = logregobj, eval_metric = evalerror) #' #' # or as dedicated 'obj' and 'feval' parameters of xgb.train: #' bst <- xgb.train(param, dtrain, nrounds = 2, watchlist, #' obj = logregobj, feval = evalerror) #' #' #' ## An xgb.train example of using variable learning rates at each iteration: #' param <- list(max_depth = 2, eta = 1, verbose = 0, nthread = 2, #' objective = "binary:logistic", eval_metric = "auc") #' my_etas <- list(eta = c(0.5, 0.1)) #' bst <- xgb.train(param, dtrain, nrounds = 2, watchlist, #' callbacks = list(cb.reset.parameters(my_etas))) #' #' ## Early stopping: #' bst <- xgb.train(param, dtrain, nrounds = 25, watchlist, #' early_stopping_rounds = 3) #' #' ## An 'xgboost' interface example: #' bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, #' max_depth = 2, eta = 1, nthread = 2, nrounds = 2, #' objective = "binary:logistic") #' pred <- predict(bst, agaricus.test$data) #' #' @rdname xgb.train #' @export xgb.train <- function(params = list(), data, nrounds, watchlist = list(), obj = NULL, feval = NULL, verbose = 1, print_every_n = 1L, early_stopping_rounds = NULL, maximize = NULL, save_period = NULL, save_name = "xgboost.model", xgb_model = NULL, callbacks = list(), ...) { check.deprecation(...) params <- check.booster.params(params, ...) check.custom.obj() check.custom.eval() # data & watchlist checks dtrain <- data if (!inherits(dtrain, "xgb.DMatrix")) stop("second argument dtrain must be xgb.DMatrix") if (length(watchlist) > 0) { if (typeof(watchlist) != "list" || !all(vapply(watchlist, inherits, logical(1), what = 'xgb.DMatrix'))) stop("watchlist must be a list of xgb.DMatrix elements") evnames <- names(watchlist) if (is.null(evnames) || any(evnames == "")) stop("each element of the watchlist must have a name tag") } # evaluation printing callback params <- c(params) print_every_n <- max(as.integer(print_every_n), 1L) if (!has.callbacks(callbacks, 'cb.print.evaluation') && verbose) { callbacks <- add.cb(callbacks, cb.print.evaluation(print_every_n)) } # evaluation log callback: it is automatically enabled when watchlist is provided evaluation_log <- list() if (!has.callbacks(callbacks, 'cb.evaluation.log') && length(watchlist) > 0) { callbacks <- add.cb(callbacks, cb.evaluation.log()) } # Model saving callback if (!is.null(save_period) && !has.callbacks(callbacks, 'cb.save.model')) { callbacks <- add.cb(callbacks, cb.save.model(save_period, save_name)) } # Early stopping callback stop_condition <- FALSE if (!is.null(early_stopping_rounds) && !has.callbacks(callbacks, 'cb.early.stop')) { callbacks <- add.cb(callbacks, cb.early.stop(early_stopping_rounds, maximize = maximize, verbose = verbose)) } # Sort the callbacks into categories cb <- categorize.callbacks(callbacks) params['validate_parameters'] <- TRUE if (!is.null(params[['seed']])) { warning("xgb.train: `seed` is ignored in R package. Use `set.seed()` instead.") } # The tree updating process would need slightly different handling is_update <- NVL(params[['process_type']], '.') == 'update' # Construct a booster (either a new one or load from xgb_model) handle <- xgb.Booster.handle(params, append(watchlist, dtrain), xgb_model) bst <- xgb.handleToBooster(handle) # extract parameters that can affect the relationship b/w #trees and #iterations num_class <- max(as.numeric(NVL(params[['num_class']], 1)), 1) num_parallel_tree <- max(as.numeric(NVL(params[['num_parallel_tree']], 1)), 1) # When the 'xgb_model' was set, find out how many boosting iterations it has niter_init <- 0 if (!is.null(xgb_model)) { niter_init <- as.numeric(xgb.attr(bst, 'niter')) + 1 if (length(niter_init) == 0) { niter_init <- xgb.ntree(bst) %/% (num_parallel_tree * num_class) } } if (is_update && nrounds > niter_init) stop("nrounds cannot be larger than ", niter_init, " (nrounds of xgb_model)") niter_skip <- ifelse(is_update, 0, niter_init) begin_iteration <- niter_skip + 1 end_iteration <- niter_skip + nrounds # the main loop for boosting iterations for (iteration in begin_iteration:end_iteration) { for (f in cb$pre_iter) f() xgb.iter.update(bst$handle, dtrain, iteration - 1, obj) if (length(watchlist) > 0) bst_evaluation <- xgb.iter.eval(bst$handle, watchlist, iteration - 1, feval) xgb.attr(bst$handle, 'niter') <- iteration - 1 for (f in cb$post_iter) f() if (stop_condition) break } for (f in cb$finalize) f(finalize = TRUE) bst <- xgb.Booster.complete(bst, saveraw = TRUE) # store the total number of boosting iterations bst$niter <- end_iteration # store the evaluation results if (length(evaluation_log) > 0 && nrow(evaluation_log) > 0) { # include the previous compatible history when available if (inherits(xgb_model, 'xgb.Booster') && !is_update && !is.null(xgb_model$evaluation_log) && isTRUE(all.equal(colnames(evaluation_log), colnames(xgb_model$evaluation_log)))) { evaluation_log <- rbindlist(list(xgb_model$evaluation_log, evaluation_log)) } bst$evaluation_log <- evaluation_log } bst$call <- match.call() bst$params <- params bst$callbacks <- callbacks if (!is.null(colnames(dtrain))) bst$feature_names <- colnames(dtrain) bst$nfeatures <- ncol(dtrain) return(bst) } xgboost-1.5.2/R-package/R/xgb.unserialize.R000066400000000000000000000035611417122711700204430ustar00rootroot00000000000000#' Load the instance back from \code{\link{xgb.serialize}} #' #' @param buffer the buffer containing booster instance saved by \code{\link{xgb.serialize}} #' @param handle An \code{xgb.Booster.handle} object which will be overwritten with #' the new deserialized object. Must be a null handle (e.g. when loading the model through #' `readRDS`). If not provided, a new handle will be created. #' @return An \code{xgb.Booster.handle} object. #' #' @export xgb.unserialize <- function(buffer, handle = NULL) { cachelist <- list() if (is.null(handle)) { handle <- .Call(XGBoosterCreate_R, cachelist) } else { if (!is.null.handle(handle)) stop("'handle' is not null/empty. Cannot overwrite existing handle.") .Call(XGBoosterCreateInEmptyObj_R, cachelist, handle) } tryCatch( .Call(XGBoosterUnserializeFromBuffer_R, handle, buffer), error = function(e) { error_msg <- conditionMessage(e) m <- regexec("(src[\\\\/]learner.cc:[0-9]+): Check failed: (header == serialisation_header_)", error_msg, perl = TRUE) groups <- regmatches(error_msg, m)[[1]] if (length(groups) == 3) { warning(paste("The model had been generated by XGBoost version 1.0.0 or earlier and was ", "loaded from a RDS file. We strongly ADVISE AGAINST using saveRDS() ", "function, to ensure that your model can be read in current and upcoming ", "XGBoost releases. Please use xgb.save() instead to preserve models for the ", "long term. For more details and explanation, see ", "https://xgboost.readthedocs.io/en/latest/tutorials/saving_model.html", sep = "")) .Call(XGBoosterLoadModelFromRaw_R, handle, buffer) } else { stop(e) } }) class(handle) <- "xgb.Booster.handle" return (handle) } xgboost-1.5.2/R-package/R/xgboost.R000066400000000000000000000071051417122711700170150ustar00rootroot00000000000000# Simple interface for training an xgboost model that wraps \code{xgb.train}. # Its documentation is combined with xgb.train. # #' @rdname xgb.train #' @export xgboost <- function(data = NULL, label = NULL, missing = NA, weight = NULL, params = list(), nrounds, verbose = 1, print_every_n = 1L, early_stopping_rounds = NULL, maximize = NULL, save_period = NULL, save_name = "xgboost.model", xgb_model = NULL, callbacks = list(), ...) { merged <- check.booster.params(params, ...) dtrain <- xgb.get.DMatrix(data, label, missing, weight, nthread = merged$nthread) watchlist <- list(train = dtrain) bst <- xgb.train(params, dtrain, nrounds, watchlist, verbose = verbose, print_every_n = print_every_n, early_stopping_rounds = early_stopping_rounds, maximize = maximize, save_period = save_period, save_name = save_name, xgb_model = xgb_model, callbacks = callbacks, ...) return (bst) } #' Training part from Mushroom Data Set #' #' This data set is originally from the Mushroom data set, #' UCI Machine Learning Repository. #' #' This data set includes the following fields: #' #' \itemize{ #' \item \code{label} the label for each record #' \item \code{data} a sparse Matrix of \code{dgCMatrix} class, with 126 columns. #' } #' #' @references #' https://archive.ics.uci.edu/ml/datasets/Mushroom #' #' Bache, K. & Lichman, M. (2013). UCI Machine Learning Repository #' [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, #' School of Information and Computer Science. #' #' @docType data #' @keywords datasets #' @name agaricus.train #' @usage data(agaricus.train) #' @format A list containing a label vector, and a dgCMatrix object with 6513 #' rows and 127 variables NULL #' Test part from Mushroom Data Set #' #' This data set is originally from the Mushroom data set, #' UCI Machine Learning Repository. #' #' This data set includes the following fields: #' #' \itemize{ #' \item \code{label} the label for each record #' \item \code{data} a sparse Matrix of \code{dgCMatrix} class, with 126 columns. #' } #' #' @references #' https://archive.ics.uci.edu/ml/datasets/Mushroom #' #' Bache, K. & Lichman, M. (2013). UCI Machine Learning Repository #' [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, #' School of Information and Computer Science. #' #' @docType data #' @keywords datasets #' @name agaricus.test #' @usage data(agaricus.test) #' @format A list containing a label vector, and a dgCMatrix object with 1611 #' rows and 126 variables NULL # Various imports #' @importClassesFrom Matrix dgCMatrix dgeMatrix #' @importFrom Matrix colSums #' @importFrom Matrix sparse.model.matrix #' @importFrom Matrix sparseVector #' @importFrom Matrix sparseMatrix #' @importFrom Matrix t #' @importFrom data.table data.table #' @importFrom data.table is.data.table #' @importFrom data.table as.data.table #' @importFrom data.table := #' @importFrom data.table rbindlist #' @importFrom data.table setkey #' @importFrom data.table setkeyv #' @importFrom data.table setnames #' @importFrom jsonlite fromJSON #' @importFrom jsonlite toJSON #' @importFrom utils object.size str tail #' @importFrom stats predict #' @importFrom stats median #' @importFrom utils head #' @importFrom graphics barplot #' @importFrom graphics lines #' @importFrom graphics points #' @importFrom graphics grid #' @importFrom graphics par #' @importFrom graphics title #' @importFrom grDevices rgb #' #' @import methods #' @useDynLib xgboost, .registration = TRUE NULL xgboost-1.5.2/R-package/README.md000066400000000000000000000030461417122711700162630ustar00rootroot00000000000000XGBoost R Package for Scalable GBM ================================== [![CRAN Status Badge](http://www.r-pkg.org/badges/version/xgboost)](https://cran.r-project.org/web/packages/xgboost) [![CRAN Downloads](http://cranlogs.r-pkg.org/badges/xgboost)](https://cran.rstudio.com/web/packages/xgboost/index.html) [![Documentation Status](https://readthedocs.org/projects/xgboost/badge/?version=latest)](http://xgboost.readthedocs.org/en/latest/R-package/index.html) Resources --------- * [XGBoost R Package Online Documentation](http://xgboost.readthedocs.org/en/latest/R-package/index.html) - Check this out for detailed documents, examples and tutorials. Installation ------------ We are [on CRAN](https://cran.r-project.org/web/packages/xgboost/index.html) now. For stable/pre-compiled(for Windows and OS X) version, please install from CRAN: ```r install.packages('xgboost') ``` For more detailed installation instructions, please see [here](http://xgboost.readthedocs.org/en/latest/build.html#r-package-installation). Examples -------- * Please visit [walk through example](demo). * See also the [example scripts](../demo/kaggle-higgs) for Kaggle Higgs Challenge, including [speedtest script](../demo/kaggle-higgs/speedtest.R) on this dataset and the one related to [Otto challenge](../demo/kaggle-otto), including a [RMarkdown documentation](../demo/kaggle-otto/understandingXGBoostModel.Rmd). Development ----------- * See the [R Package section](https://xgboost.readthedocs.io/en/latest/contrib/coding_guide.html#r-coding-guideline) of the contributors guide. xgboost-1.5.2/R-package/cleanup000077500000000000000000000000361417122711700163550ustar00rootroot00000000000000#!/bin/sh rm -f src/Makevars xgboost-1.5.2/R-package/configure000077500000000000000000003376351417122711700167310ustar00rootroot00000000000000#! /bin/sh # Guess values for system-dependent variables and create Makefiles. # Generated by GNU Autoconf 2.69 for xgboost 0.6-3. # # # Copyright (C) 1992-1996, 1998-2012 Free Software Foundation, Inc. # # # This configure script is free software; the Free Software Foundation # gives unlimited permission to copy, distribute and modify it. ## -------------------- ## ## M4sh Initialization. ## ## -------------------- ## # Be more Bourne compatible DUALCASE=1; export DUALCASE # for MKS sh if test -n "${ZSH_VERSION+set}" && (emulate sh) >/dev/null 2>&1; then : emulate sh NULLCMD=: # Pre-4.2 versions of Zsh do word splitting on ${1+"$@"}, which # is contrary to our usage. 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train in caret library custom_objective Customize loss function, and evaluation metric boost_from_prediction Boosting from existing prediction predict_first_ntree Predicting using first n trees generalized_linear_model Generalized Linear Model cross_validation Cross validation create_sparse_matrix Create Sparse Matrix predict_leaf_indices Predicting the corresponding leaves early_stopping Early Stop in training poisson_regression Poisson regression on count data tweedie_regression Tweedie regression gpu_accelerated GPU-accelerated tree building algorithms interaction_constraints Interaction constraints among features xgboost-1.5.2/R-package/demo/README.md000066400000000000000000000014721417122711700172100ustar00rootroot00000000000000XGBoost R Feature Walkthrough ==== * [Basic walkthrough of wrappers](basic_walkthrough.R) * [Train a xgboost model from caret library](caret_wrapper.R) * [Customize loss function, and evaluation metric](custom_objective.R) * [Boosting from existing prediction](boost_from_prediction.R) * [Predicting using first n trees](predict_first_ntree.R) * [Generalized Linear Model](generalized_linear_model.R) * [Cross validation](cross_validation.R) * [Create a sparse matrix from a dense one](create_sparse_matrix.R) * [Use GPU-accelerated tree building algorithms](gpu_accelerated.R) Benchmarks ==== * [Starter script for Kaggle Higgs Boson](../../demo/kaggle-higgs) Notes ==== * Contribution of examples, benchmarks is more than welcomed! * If you like to share how you use xgboost to solve your problem, send a pull request :) xgboost-1.5.2/R-package/demo/basic_walkthrough.R000066400000000000000000000125241417122711700215540ustar00rootroot00000000000000require(xgboost) require(methods) # we load in the agaricus dataset # In this example, we are aiming to predict whether a mushroom is edible data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') train <- agaricus.train test <- agaricus.test # the loaded data is stored in sparseMatrix, and label is a numeric vector in {0,1} class(train$label) class(train$data) #-------------Basic Training using XGBoost----------------- # this is the basic usage of xgboost you can put matrix in data field # note: we are putting in sparse matrix here, xgboost naturally handles sparse input # use sparse matrix when your feature is sparse(e.g. when you are using one-hot encoding vector) print("Training xgboost with sparseMatrix") bst <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 1, nrounds = 2, nthread = 2, objective = "binary:logistic") # alternatively, you can put in dense matrix, i.e. basic R-matrix print("Training xgboost with Matrix") bst <- xgboost(data = as.matrix(train$data), label = train$label, max_depth = 2, eta = 1, nrounds = 2, nthread = 2, objective = "binary:logistic") # you can also put in xgb.DMatrix object, which stores label, data and other meta datas needed for advanced features print("Training xgboost with xgb.DMatrix") dtrain <- xgb.DMatrix(data = train$data, label = train$label) bst <- xgboost(data = dtrain, max_depth = 2, eta = 1, nrounds = 2, nthread = 2, objective = "binary:logistic") # Verbose = 0,1,2 print("Train xgboost with verbose 0, no message") bst <- xgboost(data = dtrain, max_depth = 2, eta = 1, nrounds = 2, nthread = 2, objective = "binary:logistic", verbose = 0) print("Train xgboost with verbose 1, print evaluation metric") bst <- xgboost(data = dtrain, max_depth = 2, eta = 1, nrounds = 2, nthread = 2, objective = "binary:logistic", verbose = 1) print("Train xgboost with verbose 2, also print information about tree") bst <- xgboost(data = dtrain, max_depth = 2, eta = 1, nrounds = 2, nthread = 2, objective = "binary:logistic", verbose = 2) # you can also specify data as file path to a LIBSVM format input # since we do not have this file with us, the following line is just for illustration # bst <- xgboost(data = 'agaricus.train.svm', max_depth = 2, eta = 1, nrounds = 2,objective = "binary:logistic") #--------------------basic prediction using xgboost-------------- # you can do prediction using the following line # you can put in Matrix, sparseMatrix, or xgb.DMatrix pred <- predict(bst, test$data) err <- mean(as.numeric(pred > 0.5) != test$label) print(paste("test-error=", err)) #-------------------save and load models------------------------- # save model to binary local file xgb.save(bst, "xgboost.model") # load binary model to R bst2 <- xgb.load("xgboost.model") pred2 <- predict(bst2, test$data) # pred2 should be identical to pred print(paste("sum(abs(pred2-pred))=", sum(abs(pred2 - pred)))) # save model to R's raw vector raw <- xgb.save.raw(bst) # load binary model to R bst3 <- xgb.load(raw) pred3 <- predict(bst3, test$data) # pred3 should be identical to pred print(paste("sum(abs(pred3-pred))=", sum(abs(pred3 - pred)))) #----------------Advanced features -------------- # to use advanced features, we need to put data in xgb.DMatrix dtrain <- xgb.DMatrix(data = train$data, label = train$label) dtest <- xgb.DMatrix(data = test$data, label = test$label) #---------------Using watchlist---------------- # watchlist is a list of xgb.DMatrix, each of them is tagged with name watchlist <- list(train = dtrain, test = dtest) # to train with watchlist, use xgb.train, which contains more advanced features # watchlist allows us to monitor the evaluation result on all data in the list print("Train xgboost using xgb.train with watchlist") bst <- xgb.train(data = dtrain, max_depth = 2, eta = 1, nrounds = 2, watchlist = watchlist, nthread = 2, objective = "binary:logistic") # we can change evaluation metrics, or use multiple evaluation metrics print("train xgboost using xgb.train with watchlist, watch logloss and error") bst <- xgb.train(data = dtrain, max_depth = 2, eta = 1, nrounds = 2, watchlist = watchlist, eval_metric = "error", eval_metric = "logloss", nthread = 2, objective = "binary:logistic") # xgb.DMatrix can also be saved using xgb.DMatrix.save xgb.DMatrix.save(dtrain, "dtrain.buffer") # to load it in, simply call xgb.DMatrix dtrain2 <- xgb.DMatrix("dtrain.buffer") bst <- xgb.train(data = dtrain2, max_depth = 2, eta = 1, nrounds = 2, watchlist = watchlist, nthread = 2, objective = "binary:logistic") # information can be extracted from xgb.DMatrix using getinfo label <- getinfo(dtest, "label") pred <- predict(bst, dtest) err <- as.numeric(sum(as.integer(pred > 0.5) != label)) / length(label) print(paste("test-error=", err)) # You can dump the tree you learned using xgb.dump into a text file dump_path <- file.path(tempdir(), 'dump.raw.txt') xgb.dump(bst, dump_path, with_stats = TRUE) # Finally, you can check which features are the most important. print("Most important features (look at column Gain):") imp_matrix <- xgb.importance(feature_names = colnames(train$data), model = bst) print(imp_matrix) # Feature importance bar plot by gain print("Feature importance Plot : ") print(xgb.plot.importance(importance_matrix = imp_matrix)) xgboost-1.5.2/R-package/demo/boost_from_prediction.R000066400000000000000000000023021417122711700224360ustar00rootroot00000000000000require(xgboost) # load in the agaricus dataset data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') dtrain <- xgb.DMatrix(agaricus.train$data, label = agaricus.train$label) dtest <- xgb.DMatrix(agaricus.test$data, label = agaricus.test$label) watchlist <- list(eval = dtest, train = dtrain) ### # advanced: start from a initial base prediction # print('start running example to start from a initial prediction') # train xgboost for 1 round param <- list(max_depth = 2, eta = 1, nthread = 2, objective = 'binary:logistic') bst <- xgb.train(param, dtrain, 1, watchlist) # Note: we need the margin value instead of transformed prediction in set_base_margin # do predict with output_margin=TRUE, will always give you margin values before logistic transformation ptrain <- predict(bst, dtrain, outputmargin = TRUE) ptest <- predict(bst, dtest, outputmargin = TRUE) # set the base_margin property of dtrain and dtest # base margin is the base prediction we will boost from setinfo(dtrain, "base_margin", ptrain) setinfo(dtest, "base_margin", ptest) print('this is result of boost from initial prediction') bst <- xgb.train(params = param, data = dtrain, nrounds = 1, watchlist = watchlist) xgboost-1.5.2/R-package/demo/caret_wrapper.R000066400000000000000000000042461417122711700207140ustar00rootroot00000000000000# install development version of caret library that contains xgboost models devtools::install_github("topepo/caret/pkg/caret") require(caret) require(xgboost) require(data.table) require(vcd) require(e1071) # Load Arthritis dataset in memory. data(Arthritis) # Create a copy of the dataset with data.table package (data.table is 100% compliant with R dataframe but its syntax is a lot more consistent and its performance are really good). df <- data.table(Arthritis, keep.rownames = FALSE) # Let's add some new categorical features to see if it helps. Of course these feature are highly correlated to the Age feature. Usually it's not a good thing in ML, but Tree algorithms (including boosted trees) are able to select the best features, even in case of highly correlated features. # For the first feature we create groups of age by rounding the real age. Note that we transform it to factor (categorical data) so the algorithm treat them as independant values. df[, AgeDiscret := as.factor(round(Age / 10, 0))] # Here is an even stronger simplification of the real age with an arbitrary split at 30 years old. I choose this value based on nothing. We will see later if simplifying the information based on arbitrary values is a good strategy (I am sure you already have an idea of how well it will work!). df[, AgeCat := as.factor(ifelse(Age > 30, "Old", "Young"))] # We remove ID as there is nothing to learn from this feature (it will just add some noise as the dataset is small). df[, ID := NULL] #-------------Basic Training using XGBoost in caret Library----------------- # Set up control parameters for caret::train # Here we use 10-fold cross-validation, repeating twice, and using random search for tuning hyper-parameters. fitControl <- trainControl(method = "repeatedcv", number = 10, repeats = 2, search = "random") # train a xgbTree model using caret::train model <- train(factor(Improved)~., data = df, method = "xgbTree", trControl = fitControl) # Instead of tree for our boosters, you can also fit a linear regression or logistic regression model using xgbLinear # model <- train(factor(Improved)~., data = df, method = "xgbLinear", trControl = fitControl) # See model results print(model) xgboost-1.5.2/R-package/demo/create_sparse_matrix.R000066400000000000000000000133051417122711700222560ustar00rootroot00000000000000require(xgboost) require(Matrix) require(data.table) if (!require(vcd)) { install.packages('vcd') #Available in CRAN. Used for its dataset with categorical values. require(vcd) } # According to its documentation, XGBoost works only on numbers. # Sometimes the dataset we have to work on have categorical data. # A categorical variable is one which have a fixed number of values. By example, if for each observation a variable called "Colour" can have only "red", "blue" or "green" as value, it is a categorical variable. # # In R, categorical variable is called Factor. # Type ?factor in console for more information. # # In this demo we will see how to transform a dense dataframe with categorical variables to a sparse matrix before analyzing it in XGBoost. # The method we are going to see is usually called "one hot encoding". #load Arthritis dataset in memory. data(Arthritis) # create a copy of the dataset with data.table package (data.table is 100% compliant with R dataframe but its syntax is a lot more consistent and its performance are really good). df <- data.table(Arthritis, keep.rownames = FALSE) # Let's have a look to the data.table cat("Print the dataset\n") print(df) # 2 columns have factor type, one has ordinal type (ordinal variable is a categorical variable with values which can be ordered, here: None > Some > Marked). cat("Structure of the dataset\n") str(df) # Let's add some new categorical features to see if it helps. Of course these feature are highly correlated to the Age feature. Usually it's not a good thing in ML, but Tree algorithms (including boosted trees) are able to select the best features, even in case of highly correlated features. # For the first feature we create groups of age by rounding the real age. Note that we transform it to factor (categorical data) so the algorithm treat them as independent values. df[, AgeDiscret := as.factor(round(Age / 10, 0))] # Here is an even stronger simplification of the real age with an arbitrary split at 30 years old. I choose this value based on nothing. We will see later if simplifying the information based on arbitrary values is a good strategy (I am sure you already have an idea of how well it will work!). df[, AgeCat := as.factor(ifelse(Age > 30, "Old", "Young"))] # We remove ID as there is nothing to learn from this feature (it will just add some noise as the dataset is small). df[, ID := NULL] # List the different values for the column Treatment: Placebo, Treated. cat("Values of the categorical feature Treatment\n") print(levels(df[, Treatment])) # Next step, we will transform the categorical data to dummy variables. # This method is also called one hot encoding. # The purpose is to transform each value of each categorical feature in one binary feature. # # Let's take, the column Treatment will be replaced by two columns, Placebo, and Treated. Each of them will be binary. For example an observation which had the value Placebo in column Treatment before the transformation will have, after the transformation, the value 1 in the new column Placebo and the value 0 in the new column Treated. # # Formulae Improved~.-1 used below means transform all categorical features but column Improved to binary values. # Column Improved is excluded because it will be our output column, the one we want to predict. sparse_matrix <- sparse.model.matrix(Improved ~ . - 1, data = df) cat("Encoding of the sparse Matrix\n") print(sparse_matrix) # Create the output vector (not sparse) # 1. Set, for all rows, field in Y column to 0; # 2. set Y to 1 when Improved == Marked; # 3. Return Y column output_vector <- df[, Y := 0][Improved == "Marked", Y := 1][, Y] # Following is the same process as other demo cat("Learning...\n") bst <- xgboost(data = sparse_matrix, label = output_vector, max_depth = 9, eta = 1, nthread = 2, nrounds = 10, objective = "binary:logistic") importance <- xgb.importance(feature_names = colnames(sparse_matrix), model = bst) print(importance) # According to the matrix below, the most important feature in this dataset to predict if the treatment will work is the Age. The second most important feature is having received a placebo or not. The sex is third. Then we see our generated features (AgeDiscret). We can see that their contribution is very low (Gain column). # Does these result make sense? # Let's check some Chi2 between each of these features and the outcome. print(chisq.test(df$Age, df$Y)) # Pearson correlation between Age and illness disappearing is 35 print(chisq.test(df$AgeDiscret, df$Y)) # Our first simplification of Age gives a Pearson correlation of 8. print(chisq.test(df$AgeCat, df$Y)) # The perfectly random split I did between young and old at 30 years old have a low correlation of 2. It's a result we may expect as may be in my mind > 30 years is being old (I am 32 and starting feeling old, this may explain that), but for the illness we are studying, the age to be vulnerable is not the same. Don't let your "gut" lower the quality of your model. In "data science", there is science :-) # As you can see, in general destroying information by simplifying it won't improve your model. Chi2 just demonstrates that. But in more complex cases, creating a new feature based on existing one which makes link with the outcome more obvious may help the algorithm and improve the model. The case studied here is not enough complex to show that. Check Kaggle forum for some challenging datasets. # However it's almost always worse when you add some arbitrary rules. # Moreover, you can notice that even if we have added some not useful new features highly correlated with other features, the boosting tree algorithm have been able to choose the best one, which in this case is the Age. Linear model may not be that strong in these scenario. xgboost-1.5.2/R-package/demo/cross_validation.R000066400000000000000000000035231417122711700214160ustar00rootroot00000000000000require(xgboost) # load in the agaricus dataset data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') dtrain <- xgb.DMatrix(agaricus.train$data, label = agaricus.train$label) dtest <- xgb.DMatrix(agaricus.test$data, label = agaricus.test$label) nrounds <- 2 param <- list(max_depth = 2, eta = 1, nthread = 2, objective = 'binary:logistic') cat('running cross validation\n') # do cross validation, this will print result out as # [iteration] metric_name:mean_value+std_value # std_value is standard deviation of the metric xgb.cv(param, dtrain, nrounds, nfold = 5, metrics = {'error'}) cat('running cross validation, disable standard deviation display\n') # do cross validation, this will print result out as # [iteration] metric_name:mean_value+std_value # std_value is standard deviation of the metric xgb.cv(param, dtrain, nrounds, nfold = 5, metrics = 'error', showsd = FALSE) ### # you can also do cross validation with customized loss function # See custom_objective.R ## print ('running cross validation, with customized loss function') logregobj <- function(preds, dtrain) { labels <- getinfo(dtrain, "label") preds <- 1 / (1 + exp(-preds)) grad <- preds - labels hess <- preds * (1 - preds) return(list(grad = grad, hess = hess)) } evalerror <- function(preds, dtrain) { labels <- getinfo(dtrain, "label") err <- as.numeric(sum(labels != (preds > 0))) / length(labels) return(list(metric = "error", value = err)) } param <- list(max_depth = 2, eta = 1, objective = logregobj, eval_metric = evalerror) # train with customized objective xgb.cv(params = param, data = dtrain, nrounds = nrounds, nfold = 5) # do cross validation with prediction values for each fold res <- xgb.cv(params = param, data = dtrain, nrounds = nrounds, nfold = 5, prediction = TRUE) res$evaluation_log length(res$pred) xgboost-1.5.2/R-package/demo/custom_objective.R000066400000000000000000000057471417122711700214310ustar00rootroot00000000000000require(xgboost) # load in the agaricus dataset data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') dtrain <- xgb.DMatrix(agaricus.train$data, label = agaricus.train$label) dtest <- xgb.DMatrix(agaricus.test$data, label = agaricus.test$label) # note: for customized objective function, we leave objective as default # note: what we are getting is margin value in prediction # you must know what you are doing watchlist <- list(eval = dtest, train = dtrain) num_round <- 2 # user define objective function, given prediction, return gradient and second order gradient # this is log likelihood loss logregobj <- function(preds, dtrain) { labels <- getinfo(dtrain, "label") preds <- 1 / (1 + exp(-preds)) grad <- preds - labels hess <- preds * (1 - preds) return(list(grad = grad, hess = hess)) } # user defined evaluation function, return a pair metric_name, result # NOTE: when you do customized loss function, the default prediction value is margin # this may make builtin evaluation metric not function properly # for example, we are doing logistic loss, the prediction is score before logistic transformation # the builtin evaluation error assumes input is after logistic transformation # Take this in mind when you use the customization, and maybe you need write customized evaluation function evalerror <- function(preds, dtrain) { labels <- getinfo(dtrain, "label") err <- as.numeric(sum(labels != (preds > 0))) / length(labels) return(list(metric = "error", value = err)) } param <- list(max_depth = 2, eta = 1, nthread = 2, verbosity = 0, objective = logregobj, eval_metric = evalerror) print ('start training with user customized objective') # training with customized objective, we can also do step by step training # simply look at xgboost.py's implementation of train bst <- xgb.train(param, dtrain, num_round, watchlist) # # there can be cases where you want additional information # being considered besides the property of DMatrix you can get by getinfo # you can set additional information as attributes if DMatrix # set label attribute of dtrain to be label, we use label as an example, it can be anything attr(dtrain, 'label') <- getinfo(dtrain, 'label') # this is new customized objective, where you can access things you set # same thing applies to customized evaluation function logregobjattr <- function(preds, dtrain) { # now you can access the attribute in customized function labels <- attr(dtrain, 'label') preds <- 1 / (1 + exp(-preds)) grad <- preds - labels hess <- preds * (1 - preds) return(list(grad = grad, hess = hess)) } param <- list(max_depth = 2, eta = 1, nthread = 2, verbosity = 0, objective = logregobjattr, eval_metric = evalerror) print ('start training with user customized objective, with additional attributes in DMatrix') # training with customized objective, we can also do step by step training # simply look at xgboost.py's implementation of train bst <- xgb.train(param, dtrain, num_round, watchlist) xgboost-1.5.2/R-package/demo/early_stopping.R000066400000000000000000000036771417122711700211240ustar00rootroot00000000000000require(xgboost) # load in the agaricus dataset data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') dtrain <- xgb.DMatrix(agaricus.train$data, label = agaricus.train$label) dtest <- xgb.DMatrix(agaricus.test$data, label = agaricus.test$label) # note: for customized objective function, we leave objective as default # note: what we are getting is margin value in prediction # you must know what you are doing param <- list(max_depth = 2, eta = 1, nthread = 2, verbosity = 0) watchlist <- list(eval = dtest) num_round <- 20 # user define objective function, given prediction, return gradient and second order gradient # this is log likelihood loss logregobj <- function(preds, dtrain) { labels <- getinfo(dtrain, "label") preds <- 1 / (1 + exp(-preds)) grad <- preds - labels hess <- preds * (1 - preds) return(list(grad = grad, hess = hess)) } # user defined evaluation function, return a pair metric_name, result # NOTE: when you do customized loss function, the default prediction value is margin # this may make builtin evaluation metric not function properly # for example, we are doing logistic loss, the prediction is score before logistic transformation # the builtin evaluation error assumes input is after logistic transformation # Take this in mind when you use the customization, and maybe you need write customized evaluation function evalerror <- function(preds, dtrain) { labels <- getinfo(dtrain, "label") err <- as.numeric(sum(labels != (preds > 0))) / length(labels) return(list(metric = "error", value = err)) } print ('start training with early Stopping setting') bst <- xgb.train(param, dtrain, num_round, watchlist, objective = logregobj, eval_metric = evalerror, maximize = FALSE, early_stopping_round = 3) bst <- xgb.cv(param, dtrain, num_round, nfold = 5, objective = logregobj, eval_metric = evalerror, maximize = FALSE, early_stopping_rounds = 3) xgboost-1.5.2/R-package/demo/generalized_linear_model.R000066400000000000000000000025551417122711700230620ustar00rootroot00000000000000require(xgboost) # load in the agaricus dataset data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') dtrain <- xgb.DMatrix(agaricus.train$data, label = agaricus.train$label) dtest <- xgb.DMatrix(agaricus.test$data, label = agaricus.test$label) ## # this script demonstrate how to fit generalized linear model in xgboost # basically, we are using linear model, instead of tree for our boosters # you can fit a linear regression, or logistic regression model ## # change booster to gblinear, so that we are fitting a linear model # alpha is the L1 regularizer # lambda is the L2 regularizer # you can also set lambda_bias which is L2 regularizer on the bias term param <- list(objective = "binary:logistic", booster = "gblinear", nthread = 2, alpha = 0.0001, lambda = 1) # normally, you do not need to set eta (step_size) # XGBoost uses a parallel coordinate descent algorithm (shotgun), # there could be affection on convergence with parallelization on certain cases # setting eta to be smaller value, e.g 0.5 can make the optimization more stable ## # the rest of settings are the same ## watchlist <- list(eval = dtest, train = dtrain) num_round <- 2 bst <- xgb.train(param, dtrain, num_round, watchlist) ypred <- predict(bst, dtest) labels <- getinfo(dtest, 'label') cat('error of preds=', mean(as.numeric(ypred > 0.5) != labels), '\n') xgboost-1.5.2/R-package/demo/gpu_accelerated.R000066400000000000000000000027571417122711700211720ustar00rootroot00000000000000# An example of using GPU-accelerated tree building algorithms # # NOTE: it can only run if you have a CUDA-enable GPU and the package was # specially compiled with GPU support. # # For the current functionality, see # https://xgboost.readthedocs.io/en/latest/gpu/index.html # library('xgboost') # Simulate N x p random matrix with some binomial response dependent on pp columns set.seed(111) N <- 1000000 p <- 50 pp <- 25 X <- matrix(runif(N * p), ncol = p) betas <- 2 * runif(pp) - 1 sel <- sort(sample(p, pp)) m <- X[, sel] %*% betas - 1 + rnorm(N) y <- rbinom(N, 1, plogis(m)) tr <- sample.int(N, N * 0.75) dtrain <- xgb.DMatrix(X[tr, ], label = y[tr]) dtest <- xgb.DMatrix(X[-tr, ], label = y[-tr]) wl <- list(train = dtrain, test = dtest) # An example of running 'gpu_hist' algorithm # which is # - similar to the 'hist' # - the fastest option for moderately large datasets # - current limitations: max_depth < 16, does not implement guided loss # You can use tree_method = 'gpu_hist' for another GPU accelerated algorithm, # which is slower, more memory-hungry, but does not use binning. param <- list(objective = 'reg:logistic', eval_metric = 'auc', subsample = 0.5, nthread = 4, max_bin = 64, tree_method = 'gpu_hist') pt <- proc.time() bst_gpu <- xgb.train(param, dtrain, watchlist = wl, nrounds = 50) proc.time() - pt # Compare to the 'hist' algorithm: param$tree_method <- 'hist' pt <- proc.time() bst_hist <- xgb.train(param, dtrain, watchlist = wl, nrounds = 50) proc.time() - pt xgboost-1.5.2/R-package/demo/interaction_constraints.R000066400000000000000000000110161417122711700230150ustar00rootroot00000000000000library(xgboost) library(data.table) set.seed(1024) # Function to obtain a list of interactions fitted in trees, requires input of maximum depth treeInteractions <- function(input_tree, input_max_depth) { ID_merge <- i.id <- i.feature <- NULL # Suppress warning "no visible binding for global variable" trees <- data.table::copy(input_tree) # copy tree input to prevent overwriting if (input_max_depth < 2) return(list()) # no interactions if max depth < 2 if (nrow(input_tree) == 1) return(list()) # Attach parent nodes for (i in 2:input_max_depth) { if (i == 2) trees[, ID_merge := ID] else trees[, ID_merge := get(paste0('parent_', i - 2))] parents_left <- trees[!is.na(Split), list(i.id = ID, i.feature = Feature, ID_merge = Yes)] parents_right <- trees[!is.na(Split), list(i.id = ID, i.feature = Feature, ID_merge = No)] data.table::setorderv(trees, 'ID_merge') data.table::setorderv(parents_left, 'ID_merge') data.table::setorderv(parents_right, 'ID_merge') trees <- merge(trees, parents_left, by = 'ID_merge', all.x = TRUE) trees[!is.na(i.id), c(paste0('parent_', i - 1), paste0('parent_feat_', i - 1)) := list(i.id, i.feature)] trees[, c('i.id', 'i.feature') := NULL] trees <- merge(trees, parents_right, by = 'ID_merge', all.x = TRUE) trees[!is.na(i.id), c(paste0('parent_', i - 1), paste0('parent_feat_', i - 1)) := list(i.id, i.feature)] trees[, c('i.id', 'i.feature') := NULL] } # Extract nodes with interactions interaction_trees <- trees[!is.na(Split) & !is.na(parent_1), c('Feature', paste0('parent_feat_', 1:(input_max_depth - 1))), with = FALSE] interaction_trees_split <- split(interaction_trees, seq_len(nrow(interaction_trees))) interaction_list <- lapply(interaction_trees_split, as.character) # Remove NAs (no parent interaction) interaction_list <- lapply(interaction_list, function(x) x[!is.na(x)]) # Remove non-interactions (same variable) interaction_list <- lapply(interaction_list, unique) # remove same variables interaction_length <- sapply(interaction_list, length) interaction_list <- interaction_list[interaction_length > 1] interaction_list <- unique(lapply(interaction_list, sort)) return(interaction_list) } # Generate sample data x <- list() for (i in 1:10) { x[[i]] <- i * rnorm(1000, 10) } x <- as.data.table(x) y <- -1 * x[, rowSums(.SD)] + x[['V1']] * x[['V2']] + x[['V3']] * x[['V4']] * x[['V5']] + rnorm(1000, 0.001) + 3 * sin(x[['V7']]) train <- as.matrix(x) # Interaction constraint list (column names form) interaction_list <- list(c('V1', 'V2'), c('V3', 'V4', 'V5')) # Convert interaction constraint list into feature index form cols2ids <- function(object, col_names) { LUT <- seq_along(col_names) - 1 names(LUT) <- col_names rapply(object, function(x) LUT[x], classes = "character", how = "replace") } interaction_list_fid <- cols2ids(interaction_list, colnames(train)) # Fit model with interaction constraints bst <- xgboost(data = train, label = y, max_depth = 4, eta = 0.1, nthread = 2, nrounds = 1000, interaction_constraints = interaction_list_fid) bst_tree <- xgb.model.dt.tree(colnames(train), bst) bst_interactions <- treeInteractions(bst_tree, 4) # interactions constrained to combinations of V1*V2 and V3*V4*V5 # Fit model without interaction constraints bst2 <- xgboost(data = train, label = y, max_depth = 4, eta = 0.1, nthread = 2, nrounds = 1000) bst2_tree <- xgb.model.dt.tree(colnames(train), bst2) bst2_interactions <- treeInteractions(bst2_tree, 4) # much more interactions # Fit model with both interaction and monotonicity constraints bst3 <- xgboost(data = train, label = y, max_depth = 4, eta = 0.1, nthread = 2, nrounds = 1000, interaction_constraints = interaction_list_fid, monotone_constraints = c(-1, 0, 0, 0, 0, 0, 0, 0, 0, 0)) bst3_tree <- xgb.model.dt.tree(colnames(train), bst3) bst3_interactions <- treeInteractions(bst3_tree, 4) # interactions still constrained to combinations of V1*V2 and V3*V4*V5 # Show monotonic constraints still apply by checking scores after incrementing V1 x1 <- sort(unique(x[['V1']])) for (i in seq_along(x1)){ testdata <- copy(x[, - ('V1')]) testdata[['V1']] <- x1[i] testdata <- testdata[, paste0('V', 1:10), with = FALSE] pred <- predict(bst3, as.matrix(testdata)) # Should not print out anything due to monotonic constraints if (i > 1) if (any(pred > prev_pred)) print(i) prev_pred <- pred } xgboost-1.5.2/R-package/demo/poisson_regression.R000066400000000000000000000003561417122711700220060ustar00rootroot00000000000000data(mtcars) head(mtcars) bst <- xgboost(data = as.matrix(mtcars[, -11]), label = mtcars[, 11], objective = 'count:poisson', nrounds = 5) pred <- predict(bst, as.matrix(mtcars[, -11])) sqrt(mean((pred - mtcars[, 11]) ^ 2)) xgboost-1.5.2/R-package/demo/predict_first_ntree.R000066400000000000000000000015741417122711700221150ustar00rootroot00000000000000require(xgboost) # load in the agaricus dataset data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') dtrain <- xgb.DMatrix(agaricus.train$data, label = agaricus.train$label) dtest <- xgb.DMatrix(agaricus.test$data, label = agaricus.test$label) param <- list(max_depth = 2, eta = 1, objective = 'binary:logistic') watchlist <- list(eval = dtest, train = dtrain) nrounds <- 2 # training the model for two rounds bst <- xgb.train(param, dtrain, nrounds, nthread = 2, watchlist) cat('start testing prediction from first n trees\n') labels <- getinfo(dtest, 'label') ### predict using first 1 tree ypred1 <- predict(bst, dtest, ntreelimit = 1) # by default, we predict using all the trees ypred2 <- predict(bst, dtest) cat('error of ypred1=', mean(as.numeric(ypred1 > 0.5) != labels), '\n') cat('error of ypred2=', mean(as.numeric(ypred2 > 0.5) != labels), '\n') xgboost-1.5.2/R-package/demo/predict_leaf_indices.R000066400000000000000000000042661417122711700221770ustar00rootroot00000000000000require(xgboost) require(data.table) require(Matrix) set.seed(1982) # load in the agaricus dataset data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') dtrain <- xgb.DMatrix(data = agaricus.train$data, label = agaricus.train$label) dtest <- xgb.DMatrix(data = agaricus.test$data, label = agaricus.test$label) param <- list(max_depth = 2, eta = 1, objective = 'binary:logistic') nrounds <- 4 # training the model for two rounds bst <- xgb.train(params = param, data = dtrain, nrounds = nrounds, nthread = 2) # Model accuracy without new features accuracy.before <- (sum((predict(bst, agaricus.test$data) >= 0.5) == agaricus.test$label) / length(agaricus.test$label)) # by default, we predict using all the trees pred_with_leaf <- predict(bst, dtest, predleaf = TRUE) head(pred_with_leaf) create.new.tree.features <- function(model, original.features){ pred_with_leaf <- predict(model, original.features, predleaf = TRUE) cols <- list() for (i in 1:model$niter) { # max is not the real max but it s not important for the purpose of adding features leaf.id <- sort(unique(pred_with_leaf[, i])) cols[[i]] <- factor(x = pred_with_leaf[, i], level = leaf.id) } cbind(original.features, sparse.model.matrix(~ . - 1, as.data.frame(cols))) } # Convert previous features to one hot encoding new.features.train <- create.new.tree.features(bst, agaricus.train$data) new.features.test <- create.new.tree.features(bst, agaricus.test$data) colnames(new.features.test) <- colnames(new.features.train) # learning with new features new.dtrain <- xgb.DMatrix(data = new.features.train, label = agaricus.train$label) new.dtest <- xgb.DMatrix(data = new.features.test, label = agaricus.test$label) watchlist <- list(train = new.dtrain) bst <- xgb.train(params = param, data = new.dtrain, nrounds = nrounds, nthread = 2) # Model accuracy with new features accuracy.after <- (sum((predict(bst, new.dtest) >= 0.5) == agaricus.test$label) / length(agaricus.test$label)) # Here the accuracy was already good and is now perfect. cat(paste("The accuracy was", accuracy.before, "before adding leaf features and it is now", accuracy.after, "!\n")) xgboost-1.5.2/R-package/demo/runall.R000066400000000000000000000012451417122711700173470ustar00rootroot00000000000000# running all scripts in demo folder demo(basic_walkthrough, package = 'xgboost') demo(custom_objective, package = 'xgboost') demo(boost_from_prediction, package = 'xgboost') demo(predict_first_ntree, package = 'xgboost') demo(generalized_linear_model, package = 'xgboost') demo(cross_validation, package = 'xgboost') demo(create_sparse_matrix, package = 'xgboost') demo(predict_leaf_indices, package = 'xgboost') demo(early_stopping, package = 'xgboost') demo(poisson_regression, package = 'xgboost') demo(caret_wrapper, package = 'xgboost') demo(tweedie_regression, package = 'xgboost') #demo(gpu_accelerated, package = 'xgboost') # can only run when built with GPU support xgboost-1.5.2/R-package/demo/tweedie_regression.R000066400000000000000000000023561417122711700217440ustar00rootroot00000000000000library(xgboost) library(data.table) library(cplm) data(AutoClaim) # auto insurance dataset analyzed by Yip and Yau (2005) dt <- data.table(AutoClaim) # exclude these columns from the model matrix exclude <- c('POLICYNO', 'PLCYDATE', 'CLM_FREQ5', 'CLM_AMT5', 'CLM_FLAG', 'IN_YY') # retains the missing values # NOTE: this dataset is comes ready out of the box options(na.action = 'na.pass') x <- sparse.model.matrix(~ . - 1, data = dt[, -exclude, with = FALSE]) options(na.action = 'na.omit') # response y <- dt[, CLM_AMT5] d_train <- xgb.DMatrix(data = x, label = y, missing = NA) # the tweedie_variance_power parameter determines the shape of # distribution # - closer to 1 is more poisson like and the mass # is more concentrated near zero # - closer to 2 is more gamma like and the mass spreads to the # the right with less concentration near zero params <- list( objective = 'reg:tweedie', eval_metric = 'rmse', tweedie_variance_power = 1.4, max_depth = 6, eta = 1) bst <- xgb.train( data = d_train, params = params, maximize = FALSE, watchlist = list(train = d_train), nrounds = 20) var_imp <- xgb.importance(attr(x, 'Dimnames')[[2]], model = bst) preds <- predict(bst, d_train) rmse <- sqrt(sum(mean((y - preds) ^ 2))) xgboost-1.5.2/R-package/inst/000077500000000000000000000000001417122711700157565ustar00rootroot00000000000000xgboost-1.5.2/R-package/inst/make-r-def.R000066400000000000000000000054211417122711700200130ustar00rootroot00000000000000# [description] # Create a definition file (.def) from a .dll file, using objdump. This # is used by FindLibR.cmake when building the R package with MSVC. # # [usage] # # Rscript make-r-def.R something.dll something.def # # [references] # * https://www.cs.colorado.edu/~main/cs1300/doc/mingwfaq.html args <- commandArgs(trailingOnly = TRUE) IN_DLL_FILE <- args[[1L]] OUT_DEF_FILE <- args[[2L]] DLL_BASE_NAME <- basename(IN_DLL_FILE) message(sprintf("Creating '%s' from '%s'", OUT_DEF_FILE, IN_DLL_FILE)) # system() will not raise an R exception if the process called # fails. Wrapping it here to get that behavior. # # system() introduces a lot of overhead, at least on Windows, # so trying processx if it is available .pipe_shell_command_to_stdout <- function(command, args, out_file) { has_processx <- suppressMessages({ suppressWarnings({ require("processx") # nolint }) }) if (has_processx) { p <- processx::process$new( command = command , args = args , stdout = out_file , windows_verbatim_args = FALSE ) invisible(p$wait()) } else { message(paste0( "Using system2() to run shell commands. Installing " , "'processx' with install.packages('processx') might " , "make this faster." )) exit_code <- system2( command = command , args = shQuote(args) , stdout = out_file ) if (exit_code != 0L) { stop(paste0("Command failed with exit code: ", exit_code)) } } return(invisible(NULL)) } # use objdump to dump all the symbols OBJDUMP_FILE <- "objdump-out.txt" .pipe_shell_command_to_stdout( command = "objdump" , args = c("-p", IN_DLL_FILE) , out_file = OBJDUMP_FILE ) objdump_results <- readLines(OBJDUMP_FILE) result <- file.remove(OBJDUMP_FILE) # Only one table in the objdump results matters for our purposes, # see https://www.cs.colorado.edu/~main/cs1300/doc/mingwfaq.html start_index <- which( grepl( pattern = "[Ordinal/Name Pointer] Table" , x = objdump_results , fixed = TRUE ) ) empty_lines <- which(objdump_results == "") end_of_table <- empty_lines[empty_lines > start_index][1L] # Read the contents of the table exported_symbols <- objdump_results[(start_index + 1L):end_of_table] exported_symbols <- gsub("\t", "", exported_symbols) exported_symbols <- gsub(".*\\] ", "", exported_symbols) exported_symbols <- gsub(" ", "", exported_symbols) # Write R.def file writeLines( text = c( paste0("LIBRARY \"", DLL_BASE_NAME, "\"") , "EXPORTS" , exported_symbols ) , con = OUT_DEF_FILE , sep = "\n" ) message(sprintf("Successfully created '%s'", OUT_DEF_FILE)) xgboost-1.5.2/R-package/man/000077500000000000000000000000001417122711700155545ustar00rootroot00000000000000xgboost-1.5.2/R-package/man/a-compatibility-note-for-saveRDS-save.Rd000066400000000000000000000063131417122711700251250ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/utils.R \name{a-compatibility-note-for-saveRDS-save} \alias{a-compatibility-note-for-saveRDS-save} \title{Do not use \code{\link[base]{saveRDS}} or \code{\link[base]{save}} for long-term archival of models. Instead, use \code{\link{xgb.save}} or \code{\link{xgb.save.raw}}.} \description{ It is a common practice to use the built-in \code{\link[base]{saveRDS}} function (or \code{\link[base]{save}}) to persist R objects to the disk. While it is possible to persist \code{xgb.Booster} objects using \code{\link[base]{saveRDS}}, it is not advisable to do so if the model is to be accessed in the future. If you train a model with the current version of XGBoost and persist it with \code{\link[base]{saveRDS}}, the model is not guaranteed to be accessible in later releases of XGBoost. To ensure that your model can be accessed in future releases of XGBoost, use \code{\link{xgb.save}} or \code{\link{xgb.save.raw}} instead. } \details{ Use \code{\link{xgb.save}} to save the XGBoost model as a stand-alone file. You may opt into the JSON format by specifying the JSON extension. To read the model back, use \code{\link{xgb.load}}. Use \code{\link{xgb.save.raw}} to save the XGBoost model as a sequence (vector) of raw bytes in a future-proof manner. Future releases of XGBoost will be able to read the raw bytes and re-construct the corresponding model. To read the model back, use \code{\link{xgb.load.raw}}. The \code{\link{xgb.save.raw}} function is useful if you'd like to persist the XGBoost model as part of another R object. Note: Do not use \code{\link{xgb.serialize}} to store models long-term. It persists not only the model but also internal configurations and parameters, and its format is not stable across multiple XGBoost versions. Use \code{\link{xgb.serialize}} only for checkpointing. For more details and explanation about model persistence and archival, consult the page \url{https://xgboost.readthedocs.io/en/latest/tutorials/saving_model.html}. } \examples{ data(agaricus.train, package='xgboost') bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") # Save as a stand-alone file; load it with xgb.load() xgb.save(bst, 'xgb.model') bst2 <- xgb.load('xgb.model') # Save as a stand-alone file (JSON); load it with xgb.load() xgb.save(bst, 'xgb.model.json') bst2 <- xgb.load('xgb.model.json') if (file.exists('xgb.model.json')) file.remove('xgb.model.json') # Save as a raw byte vector; load it with xgb.load.raw() xgb_bytes <- xgb.save.raw(bst) bst2 <- xgb.load.raw(xgb_bytes) # Persist XGBoost model as part of another R object obj <- list(xgb_model_bytes = xgb.save.raw(bst), description = "My first XGBoost model") # Persist the R object. Here, saveRDS() is okay, since it doesn't persist # xgb.Booster directly. What's being persisted is the future-proof byte representation # as given by xgb.save.raw(). saveRDS(obj, 'my_object.rds') # Read back the R object obj2 <- readRDS('my_object.rds') # Re-construct xgb.Booster object from the bytes bst2 <- xgb.load.raw(obj2$xgb_model_bytes) if (file.exists('my_object.rds')) file.remove('my_object.rds') } xgboost-1.5.2/R-package/man/agaricus.test.Rd000066400000000000000000000015621417122711700206230ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgboost.R \docType{data} \name{agaricus.test} \alias{agaricus.test} \title{Test part from Mushroom Data Set} \format{ A list containing a label vector, and a dgCMatrix object with 1611 rows and 126 variables } \usage{ data(agaricus.test) } \description{ This data set is originally from the Mushroom data set, UCI Machine Learning Repository. } \details{ This data set includes the following fields: \itemize{ \item \code{label} the label for each record \item \code{data} a sparse Matrix of \code{dgCMatrix} class, with 126 columns. } } \references{ https://archive.ics.uci.edu/ml/datasets/Mushroom Bache, K. & Lichman, M. (2013). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science. } \keyword{datasets} xgboost-1.5.2/R-package/man/agaricus.train.Rd000066400000000000000000000015711417122711700207610ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgboost.R \docType{data} \name{agaricus.train} \alias{agaricus.train} \title{Training part from Mushroom Data Set} \format{ A list containing a label vector, and a dgCMatrix object with 6513 rows and 127 variables } \usage{ data(agaricus.train) } \description{ This data set is originally from the Mushroom data set, UCI Machine Learning Repository. } \details{ This data set includes the following fields: \itemize{ \item \code{label} the label for each record \item \code{data} a sparse Matrix of \code{dgCMatrix} class, with 126 columns. } } \references{ https://archive.ics.uci.edu/ml/datasets/Mushroom Bache, K. & Lichman, M. (2013). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science. } \keyword{datasets} xgboost-1.5.2/R-package/man/callbacks.Rd000066400000000000000000000032741417122711700177700ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/callbacks.R \name{callbacks} \alias{callbacks} \title{Callback closures for booster training.} \description{ These are used to perform various service tasks either during boosting iterations or at the end. This approach helps to modularize many of such tasks without bloating the main training methods, and it offers . } \details{ By default, a callback function is run after each boosting iteration. An R-attribute \code{is_pre_iteration} could be set for a callback to define a pre-iteration function. When a callback function has \code{finalize} parameter, its finalizer part will also be run after the boosting is completed. WARNING: side-effects!!! Be aware that these callback functions access and modify things in the environment from which they are called from, which is a fairly uncommon thing to do in R. To write a custom callback closure, make sure you first understand the main concepts about R environments. Check either R documentation on \code{\link[base]{environment}} or the \href{http://adv-r.had.co.nz/Environments.html}{Environments chapter} from the "Advanced R" book by Hadley Wickham. Further, the best option is to read the code of some of the existing callbacks - choose ones that do something similar to what you want to achieve. Also, you would need to get familiar with the objects available inside of the \code{xgb.train} and \code{xgb.cv} internal environments. } \seealso{ \code{\link{cb.print.evaluation}}, \code{\link{cb.evaluation.log}}, \code{\link{cb.reset.parameters}}, \code{\link{cb.early.stop}}, \code{\link{cb.save.model}}, \code{\link{cb.cv.predict}}, \code{\link{xgb.train}}, \code{\link{xgb.cv}} } xgboost-1.5.2/R-package/man/cb.cv.predict.Rd000066400000000000000000000032351417122711700204720ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/callbacks.R \name{cb.cv.predict} \alias{cb.cv.predict} \title{Callback closure for returning cross-validation based predictions.} \usage{ cb.cv.predict(save_models = FALSE) } \arguments{ \item{save_models}{a flag for whether to save the folds' models.} } \value{ Predictions are returned inside of the \code{pred} element, which is either a vector or a matrix, depending on the number of prediction outputs per data row. The order of predictions corresponds to the order of rows in the original dataset. Note that when a custom \code{folds} list is provided in \code{xgb.cv}, the predictions would only be returned properly when this list is a non-overlapping list of k sets of indices, as in a standard k-fold CV. The predictions would not be meaningful when user-provided folds have overlapping indices as in, e.g., random sampling splits. When some of the indices in the training dataset are not included into user-provided \code{folds}, their prediction value would be \code{NA}. } \description{ Callback closure for returning cross-validation based predictions. } \details{ This callback function saves predictions for all of the test folds, and also allows to save the folds' models. It is a "finalizer" callback and it uses early stopping information whenever it is available, thus it must be run after the early stopping callback if the early stopping is used. Callback function expects the following values to be set in its calling frame: \code{bst_folds}, \code{basket}, \code{data}, \code{end_iteration}, \code{params}, \code{num_parallel_tree}, \code{num_class}. } \seealso{ \code{\link{callbacks}} } xgboost-1.5.2/R-package/man/cb.early.stop.Rd000066400000000000000000000042201417122711700205240ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/callbacks.R \name{cb.early.stop} \alias{cb.early.stop} \title{Callback closure to activate the early stopping.} \usage{ cb.early.stop( stopping_rounds, maximize = FALSE, metric_name = NULL, verbose = TRUE ) } \arguments{ \item{stopping_rounds}{The number of rounds with no improvement in the evaluation metric in order to stop the training.} \item{maximize}{whether to maximize the evaluation metric} \item{metric_name}{the name of an evaluation column to use as a criteria for early stopping. If not set, the last column would be used. Let's say the test data in \code{watchlist} was labelled as \code{dtest}, and one wants to use the AUC in test data for early stopping regardless of where it is in the \code{watchlist}, then one of the following would need to be set: \code{metric_name='dtest-auc'} or \code{metric_name='dtest_auc'}. All dash '-' characters in metric names are considered equivalent to '_'.} \item{verbose}{whether to print the early stopping information.} } \description{ Callback closure to activate the early stopping. } \details{ This callback function determines the condition for early stopping by setting the \code{stop_condition = TRUE} flag in its calling frame. The following additional fields are assigned to the model's R object: \itemize{ \item \code{best_score} the evaluation score at the best iteration \item \code{best_iteration} at which boosting iteration the best score has occurred (1-based index) } The Same values are also stored as xgb-attributes: \itemize{ \item \code{best_iteration} is stored as a 0-based iteration index (for interoperability of binary models) \item \code{best_msg} message string is also stored. } At least one data element is required in the evaluation watchlist for early stopping to work. Callback function expects the following values to be set in its calling frame: \code{stop_condition}, \code{bst_evaluation}, \code{rank}, \code{bst} (or \code{bst_folds} and \code{basket}), \code{iteration}, \code{begin_iteration}, \code{end_iteration}, \code{num_parallel_tree}. } \seealso{ \code{\link{callbacks}}, \code{\link{xgb.attr}} } xgboost-1.5.2/R-package/man/cb.evaluation.log.Rd000066400000000000000000000020671417122711700213620ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/callbacks.R \name{cb.evaluation.log} \alias{cb.evaluation.log} \title{Callback closure for logging the evaluation history} \usage{ cb.evaluation.log() } \description{ Callback closure for logging the evaluation history } \details{ This callback function appends the current iteration evaluation results \code{bst_evaluation} available in the calling parent frame to the \code{evaluation_log} list in a calling frame. The finalizer callback (called with \code{finalize = TURE} in the end) converts the \code{evaluation_log} list into a final data.table. The iteration evaluation result \code{bst_evaluation} must be a named numeric vector. Note: in the column names of the final data.table, the dash '-' character is replaced with the underscore '_' in order to make the column names more like regular R identifiers. Callback function expects the following values to be set in its calling frame: \code{evaluation_log}, \code{bst_evaluation}, \code{iteration}. } \seealso{ \code{\link{callbacks}} } xgboost-1.5.2/R-package/man/cb.gblinear.history.Rd000066400000000000000000000105231417122711700217120ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/callbacks.R \name{cb.gblinear.history} \alias{cb.gblinear.history} \title{Callback closure for collecting the model coefficients history of a gblinear booster during its training.} \usage{ cb.gblinear.history(sparse = FALSE) } \arguments{ \item{sparse}{when set to FALSE/TRUE, a dense/sparse matrix is used to store the result. Sparse format is useful when one expects only a subset of coefficients to be non-zero, when using the "thrifty" feature selector with fairly small number of top features selected per iteration.} } \value{ Results are stored in the \code{coefs} element of the closure. The \code{\link{xgb.gblinear.history}} convenience function provides an easy way to access it. With \code{xgb.train}, it is either a dense of a sparse matrix. While with \code{xgb.cv}, it is a list (an element per each fold) of such matrices. } \description{ Callback closure for collecting the model coefficients history of a gblinear booster during its training. } \details{ To keep things fast and simple, gblinear booster does not internally store the history of linear model coefficients at each boosting iteration. This callback provides a workaround for storing the coefficients' path, by extracting them after each training iteration. Callback function expects the following values to be set in its calling frame: \code{bst} (or \code{bst_folds}). } \examples{ #### Binary classification: # # In the iris dataset, it is hard to linearly separate Versicolor class from the rest # without considering the 2nd order interactions: x <- model.matrix(Species ~ .^2, iris)[,-1] colnames(x) dtrain <- xgb.DMatrix(scale(x), label = 1*(iris$Species == "versicolor")) param <- list(booster = "gblinear", objective = "reg:logistic", eval_metric = "auc", lambda = 0.0003, alpha = 0.0003, nthread = 2) # For 'shotgun', which is a default linear updater, using high eta values may result in # unstable behaviour in some datasets. With this simple dataset, however, the high learning # rate does not break the convergence, but allows us to illustrate the typical pattern of # "stochastic explosion" behaviour of this lock-free algorithm at early boosting iterations. bst <- xgb.train(param, dtrain, list(tr=dtrain), nrounds = 200, eta = 1., callbacks = list(cb.gblinear.history())) # Extract the coefficients' path and plot them vs boosting iteration number: coef_path <- xgb.gblinear.history(bst) matplot(coef_path, type = 'l') # With the deterministic coordinate descent updater, it is safer to use higher learning rates. # Will try the classical componentwise boosting which selects a single best feature per round: bst <- xgb.train(param, dtrain, list(tr=dtrain), nrounds = 200, eta = 0.8, updater = 'coord_descent', feature_selector = 'thrifty', top_k = 1, callbacks = list(cb.gblinear.history())) matplot(xgb.gblinear.history(bst), type = 'l') # Componentwise boosting is known to have similar effect to Lasso regularization. # Try experimenting with various values of top_k, eta, nrounds, # as well as different feature_selectors. # For xgb.cv: bst <- xgb.cv(param, dtrain, nfold = 5, nrounds = 100, eta = 0.8, callbacks = list(cb.gblinear.history())) # coefficients in the CV fold #3 matplot(xgb.gblinear.history(bst)[[3]], type = 'l') #### Multiclass classification: # dtrain <- xgb.DMatrix(scale(x), label = as.numeric(iris$Species) - 1) param <- list(booster = "gblinear", objective = "multi:softprob", num_class = 3, lambda = 0.0003, alpha = 0.0003, nthread = 2) # For the default linear updater 'shotgun' it sometimes is helpful # to use smaller eta to reduce instability bst <- xgb.train(param, dtrain, list(tr=dtrain), nrounds = 70, eta = 0.5, callbacks = list(cb.gblinear.history())) # Will plot the coefficient paths separately for each class: matplot(xgb.gblinear.history(bst, class_index = 0), type = 'l') matplot(xgb.gblinear.history(bst, class_index = 1), type = 'l') matplot(xgb.gblinear.history(bst, class_index = 2), type = 'l') # CV: bst <- xgb.cv(param, dtrain, nfold = 5, nrounds = 70, eta = 0.5, callbacks = list(cb.gblinear.history(FALSE))) # 1st fold of 1st class matplot(xgb.gblinear.history(bst, class_index = 0)[[1]], type = 'l') } \seealso{ \code{\link{callbacks}}, \code{\link{xgb.gblinear.history}}. } xgboost-1.5.2/R-package/man/cb.print.evaluation.Rd000066400000000000000000000016221417122711700217310ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/callbacks.R \name{cb.print.evaluation} \alias{cb.print.evaluation} \title{Callback closure for printing the result of evaluation} \usage{ cb.print.evaluation(period = 1, showsd = TRUE) } \arguments{ \item{period}{results would be printed every number of periods} \item{showsd}{whether standard deviations should be printed (when available)} } \description{ Callback closure for printing the result of evaluation } \details{ The callback function prints the result of evaluation at every \code{period} iterations. The initial and the last iteration's evaluations are always printed. Callback function expects the following values to be set in its calling frame: \code{bst_evaluation} (also \code{bst_evaluation_err} when available), \code{iteration}, \code{begin_iteration}, \code{end_iteration}. } \seealso{ \code{\link{callbacks}} } xgboost-1.5.2/R-package/man/cb.reset.parameters.Rd000066400000000000000000000024661417122711700217220ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/callbacks.R \name{cb.reset.parameters} \alias{cb.reset.parameters} \title{Callback closure for resetting the booster's parameters at each iteration.} \usage{ cb.reset.parameters(new_params) } \arguments{ \item{new_params}{a list where each element corresponds to a parameter that needs to be reset. Each element's value must be either a vector of values of length \code{nrounds} to be set at each iteration, or a function of two parameters \code{learning_rates(iteration, nrounds)} which returns a new parameter value by using the current iteration number and the total number of boosting rounds.} } \description{ Callback closure for resetting the booster's parameters at each iteration. } \details{ This is a "pre-iteration" callback function used to reset booster's parameters at the beginning of each iteration. Note that when training is resumed from some previous model, and a function is used to reset a parameter value, the \code{nrounds} argument in this function would be the the number of boosting rounds in the current training. Callback function expects the following values to be set in its calling frame: \code{bst} or \code{bst_folds}, \code{iteration}, \code{begin_iteration}, \code{end_iteration}. } \seealso{ \code{\link{callbacks}} } xgboost-1.5.2/R-package/man/cb.save.model.Rd000066400000000000000000000020701417122711700204620ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/callbacks.R \name{cb.save.model} \alias{cb.save.model} \title{Callback closure for saving a model file.} \usage{ cb.save.model(save_period = 0, save_name = "xgboost.model") } \arguments{ \item{save_period}{save the model to disk after every \code{save_period} iterations; 0 means save the model at the end.} \item{save_name}{the name or path for the saved model file. It can contain a \code{\link[base]{sprintf}} formatting specifier to include the integer iteration number in the file name. E.g., with \code{save_name} = 'xgboost_%04d.model', the file saved at iteration 50 would be named "xgboost_0050.model".} } \description{ Callback closure for saving a model file. } \details{ This callback function allows to save an xgb-model file, either periodically after each \code{save_period}'s or at the end. Callback function expects the following values to be set in its calling frame: \code{bst}, \code{iteration}, \code{begin_iteration}, \code{end_iteration}. } \seealso{ \code{\link{callbacks}} } xgboost-1.5.2/R-package/man/dim.xgb.DMatrix.Rd000066400000000000000000000014101417122711700207360ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.DMatrix.R \name{dim.xgb.DMatrix} \alias{dim.xgb.DMatrix} \title{Dimensions of xgb.DMatrix} \usage{ \method{dim}{xgb.DMatrix}(x) } \arguments{ \item{x}{Object of class \code{xgb.DMatrix}} } \description{ Returns a vector of numbers of rows and of columns in an \code{xgb.DMatrix}. } \details{ Note: since \code{nrow} and \code{ncol} internally use \code{dim}, they can also be directly used with an \code{xgb.DMatrix} object. } \examples{ data(agaricus.train, package='xgboost') train <- agaricus.train dtrain <- xgb.DMatrix(train$data, label=train$label) stopifnot(nrow(dtrain) == nrow(train$data)) stopifnot(ncol(dtrain) == ncol(train$data)) stopifnot(all(dim(dtrain) == dim(train$data))) } xgboost-1.5.2/R-package/man/dimnames.xgb.DMatrix.Rd000066400000000000000000000020161417122711700217650ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.DMatrix.R \name{dimnames.xgb.DMatrix} \alias{dimnames.xgb.DMatrix} \alias{dimnames<-.xgb.DMatrix} \title{Handling of column names of \code{xgb.DMatrix}} \usage{ \method{dimnames}{xgb.DMatrix}(x) \method{dimnames}{xgb.DMatrix}(x) <- value } \arguments{ \item{x}{object of class \code{xgb.DMatrix}} \item{value}{a list of two elements: the first one is ignored and the second one is column names} } \description{ Only column names are supported for \code{xgb.DMatrix}, thus setting of row names would have no effect and returned row names would be NULL. } \details{ Generic \code{dimnames} methods are used by \code{colnames}. Since row names are irrelevant, it is recommended to use \code{colnames} directly. } \examples{ data(agaricus.train, package='xgboost') train <- agaricus.train dtrain <- xgb.DMatrix(train$data, label=train$label) dimnames(dtrain) colnames(dtrain) colnames(dtrain) <- make.names(1:ncol(train$data)) print(dtrain, verbose=TRUE) } xgboost-1.5.2/R-package/man/getinfo.Rd000066400000000000000000000022401417122711700174740ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.DMatrix.R \name{getinfo} \alias{getinfo} \alias{getinfo.xgb.DMatrix} \title{Get information of an xgb.DMatrix object} \usage{ getinfo(object, ...) \method{getinfo}{xgb.DMatrix}(object, name, ...) } \arguments{ \item{object}{Object of class \code{xgb.DMatrix}} \item{...}{other parameters} \item{name}{the name of the information field to get (see details)} } \description{ Get information of an xgb.DMatrix object } \details{ The \code{name} field can be one of the following: \itemize{ \item \code{label}: label XGBoost learn from ; \item \code{weight}: to do a weight rescale ; \item \code{base_margin}: base margin is the base prediction XGBoost will boost from ; \item \code{nrow}: number of rows of the \code{xgb.DMatrix}. } \code{group} can be setup by \code{setinfo} but can't be retrieved by \code{getinfo}. } \examples{ data(agaricus.train, package='xgboost') dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) labels <- getinfo(dtrain, 'label') setinfo(dtrain, 'label', 1-labels) labels2 <- getinfo(dtrain, 'label') stopifnot(all(labels2 == 1-labels)) } xgboost-1.5.2/R-package/man/normalize.Rd000066400000000000000000000006221417122711700200430ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.ggplot.R \name{normalize} \alias{normalize} \title{Scale feature value to have mean 0, standard deviation 1} \usage{ normalize(x) } \arguments{ \item{x}{Numeric vector} } \value{ Numeric vector with mean 0 and sd 1. } \description{ This is used to compare multiple features on the same plot. Internal utility function } xgboost-1.5.2/R-package/man/predict.xgb.Booster.Rd000066400000000000000000000217201417122711700216720ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.Booster.R \name{predict.xgb.Booster} \alias{predict.xgb.Booster} \alias{predict.xgb.Booster.handle} \title{Predict method for eXtreme Gradient Boosting model} \usage{ \method{predict}{xgb.Booster}( object, newdata, missing = NA, outputmargin = FALSE, ntreelimit = NULL, predleaf = FALSE, predcontrib = FALSE, approxcontrib = FALSE, predinteraction = FALSE, reshape = FALSE, training = FALSE, iterationrange = NULL, strict_shape = FALSE, ... ) \method{predict}{xgb.Booster.handle}(object, ...) } \arguments{ \item{object}{Object of class \code{xgb.Booster} or \code{xgb.Booster.handle}} \item{newdata}{takes \code{matrix}, \code{dgCMatrix}, local data file or \code{xgb.DMatrix}.} \item{missing}{Missing is only used when input is dense matrix. Pick a float value that represents missing values in data (e.g., sometimes 0 or some other extreme value is used).} \item{outputmargin}{whether the prediction should be returned in the for of original untransformed sum of predictions from boosting iterations' results. E.g., setting \code{outputmargin=TRUE} for logistic regression would result in predictions for log-odds instead of probabilities.} \item{ntreelimit}{Deprecated, use \code{iterationrange} instead.} \item{predleaf}{whether predict leaf index.} \item{predcontrib}{whether to return feature contributions to individual predictions (see Details).} \item{approxcontrib}{whether to use a fast approximation for feature contributions (see Details).} \item{predinteraction}{whether to return contributions of feature interactions to individual predictions (see Details).} \item{reshape}{whether to reshape the vector of predictions to a matrix form when there are several prediction outputs per case. This option has no effect when either of predleaf, predcontrib, or predinteraction flags is TRUE.} \item{training}{whether is the prediction result used for training. For dart booster, training predicting will perform dropout.} \item{iterationrange}{Specifies which layer of trees are used in prediction. For example, if a random forest is trained with 100 rounds. Specifying `iteration_range=(1, 21)`, then only the forests built during [1, 21) (half open set) rounds are used in this prediction. It's 1-based index just like R vector. When set to \code{c(1, 1)} XGBoost will use all trees.} \item{strict_shape}{Default is \code{FALSE}. When it's set to \code{TRUE}, output type and shape of prediction are invariant to model type.} \item{...}{Parameters passed to \code{predict.xgb.Booster}} } \value{ The return type is different depending whether \code{strict_shape} is set to \code{TRUE}. By default, for regression or binary classification, it returns a vector of length \code{nrows(newdata)}. For multiclass classification, either a \code{num_class * nrows(newdata)} vector or a \code{(nrows(newdata), num_class)} dimension matrix is returned, depending on the \code{reshape} value. When \code{predleaf = TRUE}, the output is a matrix object with the number of columns corresponding to the number of trees. When \code{predcontrib = TRUE} and it is not a multiclass setting, the output is a matrix object with \code{num_features + 1} columns. The last "+ 1" column in a matrix corresponds to bias. For a multiclass case, a list of \code{num_class} elements is returned, where each element is such a matrix. The contribution values are on the scale of untransformed margin (e.g., for binary classification would mean that the contributions are log-odds deviations from bias). When \code{predinteraction = TRUE} and it is not a multiclass setting, the output is a 3d array with dimensions \code{c(nrow, num_features + 1, num_features + 1)}. The off-diagonal (in the last two dimensions) elements represent different features interaction contributions. The array is symmetric WRT the last two dimensions. The "+ 1" columns corresponds to bias. Summing this array along the last dimension should produce practically the same result as predict with \code{predcontrib = TRUE}. For a multiclass case, a list of \code{num_class} elements is returned, where each element is such an array. When \code{strict_shape} is set to \code{TRUE}, the output is always an array. For normal prediction, the output is a 2-dimension array \code{(num_class, nrow(newdata))}. For \code{predcontrib = TRUE}, output is \code{(ncol(newdata) + 1, num_class, nrow(newdata))} For \code{predinteraction = TRUE}, output is \code{(ncol(newdata) + 1, ncol(newdata) + 1, num_class, nrow(newdata))} For \code{predleaf = TRUE}, output is \code{(n_trees_in_forest, num_class, n_iterations, nrow(newdata))} } \description{ Predicted values based on either xgboost model or model handle object. } \details{ Note that \code{iterationrange} would currently do nothing for predictions from gblinear, since gblinear doesn't keep its boosting history. One possible practical applications of the \code{predleaf} option is to use the model as a generator of new features which capture non-linearity and interactions, e.g., as implemented in \code{\link{xgb.create.features}}. Setting \code{predcontrib = TRUE} allows to calculate contributions of each feature to individual predictions. For "gblinear" booster, feature contributions are simply linear terms (feature_beta * feature_value). For "gbtree" booster, feature contributions are SHAP values (Lundberg 2017) that sum to the difference between the expected output of the model and the current prediction (where the hessian weights are used to compute the expectations). Setting \code{approxcontrib = TRUE} approximates these values following the idea explained in \url{http://blog.datadive.net/interpreting-random-forests/}. With \code{predinteraction = TRUE}, SHAP values of contributions of interaction of each pair of features are computed. Note that this operation might be rather expensive in terms of compute and memory. Since it quadratically depends on the number of features, it is recommended to perform selection of the most important features first. See below about the format of the returned results. } \examples{ ## binary classification: data(agaricus.train, package='xgboost') data(agaricus.test, package='xgboost') train <- agaricus.train test <- agaricus.test bst <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 0.5, nthread = 2, nrounds = 5, objective = "binary:logistic") # use all trees by default pred <- predict(bst, test$data) # use only the 1st tree pred1 <- predict(bst, test$data, iterationrange = c(1, 2)) # Predicting tree leafs: # the result is an nsamples X ntrees matrix pred_leaf <- predict(bst, test$data, predleaf = TRUE) str(pred_leaf) # Predicting feature contributions to predictions: # the result is an nsamples X (nfeatures + 1) matrix pred_contr <- predict(bst, test$data, predcontrib = TRUE) str(pred_contr) # verify that contributions' sums are equal to log-odds of predictions (up to float precision): summary(rowSums(pred_contr) - qlogis(pred)) # for the 1st record, let's inspect its features that had non-zero contribution to prediction: contr1 <- pred_contr[1,] contr1 <- contr1[-length(contr1)] # drop BIAS contr1 <- contr1[contr1 != 0] # drop non-contributing features contr1 <- contr1[order(abs(contr1))] # order by contribution magnitude old_mar <- par("mar") par(mar = old_mar + c(0,7,0,0)) barplot(contr1, horiz = TRUE, las = 2, xlab = "contribution to prediction in log-odds") par(mar = old_mar) ## multiclass classification in iris dataset: lb <- as.numeric(iris$Species) - 1 num_class <- 3 set.seed(11) bst <- xgboost(data = as.matrix(iris[, -5]), label = lb, max_depth = 4, eta = 0.5, nthread = 2, nrounds = 10, subsample = 0.5, objective = "multi:softprob", num_class = num_class) # predict for softmax returns num_class probability numbers per case: pred <- predict(bst, as.matrix(iris[, -5])) str(pred) # reshape it to a num_class-columns matrix pred <- matrix(pred, ncol=num_class, byrow=TRUE) # convert the probabilities to softmax labels pred_labels <- max.col(pred) - 1 # the following should result in the same error as seen in the last iteration sum(pred_labels != lb)/length(lb) # compare that to the predictions from softmax: set.seed(11) bst <- xgboost(data = as.matrix(iris[, -5]), label = lb, max_depth = 4, eta = 0.5, nthread = 2, nrounds = 10, subsample = 0.5, objective = "multi:softmax", num_class = num_class) pred <- predict(bst, as.matrix(iris[, -5])) str(pred) all.equal(pred, pred_labels) # prediction from using only 5 iterations should result # in the same error as seen in iteration 5: pred5 <- predict(bst, as.matrix(iris[, -5]), iterationrange=c(1, 6)) sum(pred5 != lb)/length(lb) } \references{ Scott M. Lundberg, Su-In Lee, "A Unified Approach to Interpreting Model Predictions", NIPS Proceedings 2017, \url{https://arxiv.org/abs/1705.07874} Scott M. Lundberg, Su-In Lee, "Consistent feature attribution for tree ensembles", \url{https://arxiv.org/abs/1706.06060} } \seealso{ \code{\link{xgb.train}}. } xgboost-1.5.2/R-package/man/prepare.ggplot.shap.data.Rd000066400000000000000000000015331417122711700226400ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.ggplot.R \name{prepare.ggplot.shap.data} \alias{prepare.ggplot.shap.data} \title{Combine and melt feature values and SHAP contributions for sample observations.} \usage{ prepare.ggplot.shap.data(data_list, normalize = FALSE) } \arguments{ \item{data_list}{List containing 'data' and 'shap_contrib' returned by \code{xgb.shap.data()}.} \item{normalize}{Whether to standardize feature values to have mean 0 and standard deviation 1 (useful for comparing multiple features on the same plot). Default \code{FALSE}.} } \value{ A data.table containing the observation ID, the feature name, the feature value (normalized if specified), and the SHAP contribution value. } \description{ Conforms to data format required for ggplot functions. } \details{ Internal utility function. } xgboost-1.5.2/R-package/man/print.xgb.Booster.Rd000066400000000000000000000013341417122711700213730ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.Booster.R \name{print.xgb.Booster} \alias{print.xgb.Booster} \title{Print xgb.Booster} \usage{ \method{print}{xgb.Booster}(x, verbose = FALSE, ...) } \arguments{ \item{x}{an xgb.Booster object} \item{verbose}{whether to print detailed data (e.g., attribute values)} \item{...}{not currently used} } \description{ Print information about xgb.Booster. } \examples{ data(agaricus.train, package='xgboost') train <- agaricus.train bst <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") attr(bst, 'myattr') <- 'memo' print(bst) print(bst, verbose=TRUE) } xgboost-1.5.2/R-package/man/print.xgb.DMatrix.Rd000066400000000000000000000012131417122711700213220ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.DMatrix.R \name{print.xgb.DMatrix} \alias{print.xgb.DMatrix} \title{Print xgb.DMatrix} \usage{ \method{print}{xgb.DMatrix}(x, verbose = FALSE, ...) } \arguments{ \item{x}{an xgb.DMatrix object} \item{verbose}{whether to print colnames (when present)} \item{...}{not currently used} } \description{ Print information about xgb.DMatrix. Currently it displays dimensions and presence of info-fields and colnames. } \examples{ data(agaricus.train, package='xgboost') dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) dtrain print(dtrain, verbose=TRUE) } xgboost-1.5.2/R-package/man/print.xgb.cv.Rd000066400000000000000000000015311417122711700203650ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.cv.R \name{print.xgb.cv.synchronous} \alias{print.xgb.cv.synchronous} \title{Print xgb.cv result} \usage{ \method{print}{xgb.cv.synchronous}(x, verbose = FALSE, ...) } \arguments{ \item{x}{an \code{xgb.cv.synchronous} object} \item{verbose}{whether to print detailed data} \item{...}{passed to \code{data.table.print}} } \description{ Prints formatted results of \code{xgb.cv}. } \details{ When not verbose, it would only print the evaluation results, including the best iteration (when available). } \examples{ data(agaricus.train, package='xgboost') train <- agaricus.train cv <- xgb.cv(data = train$data, label = train$label, nfold = 5, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") print(cv) print(cv, verbose=TRUE) } xgboost-1.5.2/R-package/man/setinfo.Rd000066400000000000000000000022131417122711700175100ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.DMatrix.R \name{setinfo} \alias{setinfo} \alias{setinfo.xgb.DMatrix} \title{Set information of an xgb.DMatrix object} \usage{ setinfo(object, ...) \method{setinfo}{xgb.DMatrix}(object, name, info, ...) } \arguments{ \item{object}{Object of class "xgb.DMatrix"} \item{...}{other parameters} \item{name}{the name of the field to get} \item{info}{the specific field of information to set} } \description{ Set information of an xgb.DMatrix object } \details{ The \code{name} field can be one of the following: \itemize{ \item \code{label}: label XGBoost learn from ; \item \code{weight}: to do a weight rescale ; \item \code{base_margin}: base margin is the base prediction XGBoost will boost from ; \item \code{group}: number of rows in each group (to use with \code{rank:pairwise} objective). } } \examples{ data(agaricus.train, package='xgboost') dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) labels <- getinfo(dtrain, 'label') setinfo(dtrain, 'label', 1-labels) labels2 <- getinfo(dtrain, 'label') stopifnot(all.equal(labels2, 1-labels)) } xgboost-1.5.2/R-package/man/slice.xgb.DMatrix.Rd000066400000000000000000000017411417122711700212730ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.DMatrix.R \name{slice} \alias{slice} \alias{slice.xgb.DMatrix} \alias{[.xgb.DMatrix} \title{Get a new DMatrix containing the specified rows of original xgb.DMatrix object} \usage{ slice(object, ...) \method{slice}{xgb.DMatrix}(object, idxset, ...) \method{[}{xgb.DMatrix}(object, idxset, colset = NULL) } \arguments{ \item{object}{Object of class "xgb.DMatrix"} \item{...}{other parameters (currently not used)} \item{idxset}{a integer vector of indices of rows needed} \item{colset}{currently not used (columns subsetting is not available)} } \description{ Get a new DMatrix containing the specified rows of original xgb.DMatrix object } \examples{ data(agaricus.train, package='xgboost') dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) dsub <- slice(dtrain, 1:42) labels1 <- getinfo(dsub, 'label') dsub <- dtrain[1:42, ] labels2 <- getinfo(dsub, 'label') all.equal(labels1, labels2) } xgboost-1.5.2/R-package/man/xgb.Booster.complete.Rd000066400000000000000000000041541417122711700220520ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.Booster.R \name{xgb.Booster.complete} \alias{xgb.Booster.complete} \title{Restore missing parts of an incomplete xgb.Booster object.} \usage{ xgb.Booster.complete(object, saveraw = TRUE) } \arguments{ \item{object}{object of class \code{xgb.Booster}} \item{saveraw}{a flag indicating whether to append \code{raw} Booster memory dump data when it doesn't already exist.} } \value{ An object of \code{xgb.Booster} class. } \description{ It attempts to complete an \code{xgb.Booster} object by restoring either its missing raw model memory dump (when it has no \code{raw} data but its \code{xgb.Booster.handle} is valid) or its missing internal handle (when its \code{xgb.Booster.handle} is not valid but it has a raw Booster memory dump). } \details{ While this method is primarily for internal use, it might be useful in some practical situations. E.g., when an \code{xgb.Booster} model is saved as an R object and then is loaded as an R object, its handle (pointer) to an internal xgboost model would be invalid. The majority of xgboost methods should still work for such a model object since those methods would be using \code{xgb.Booster.complete} internally. However, one might find it to be more efficient to call the \code{xgb.Booster.complete} function explicitly once after loading a model as an R-object. That would prevent further repeated implicit reconstruction of an internal booster model. } \examples{ data(agaricus.train, package='xgboost') bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") saveRDS(bst, "xgb.model.rds") # Warning: The resulting RDS file is only compatible with the current XGBoost version. # Refer to the section titled "a-compatibility-note-for-saveRDS-save". bst1 <- readRDS("xgb.model.rds") if (file.exists("xgb.model.rds")) file.remove("xgb.model.rds") # the handle is invalid: print(bst1$handle) bst1 <- xgb.Booster.complete(bst1) # now the handle points to a valid internal booster model: print(bst1$handle) } xgboost-1.5.2/R-package/man/xgb.DMatrix.Rd000066400000000000000000000030441417122711700201730ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.DMatrix.R \name{xgb.DMatrix} \alias{xgb.DMatrix} \title{Construct xgb.DMatrix object} \usage{ xgb.DMatrix( data, info = list(), missing = NA, silent = FALSE, nthread = NULL, ... ) } \arguments{ \item{data}{a \code{matrix} object (either numeric or integer), a \code{dgCMatrix} object, or a character string representing a filename.} \item{info}{a named list of additional information to store in the \code{xgb.DMatrix} object. See \code{\link{setinfo}} for the specific allowed kinds of} \item{missing}{a float value to represents missing values in data (used only when input is a dense matrix). It is useful when a 0 or some other extreme value represents missing values in data.} \item{silent}{whether to suppress printing an informational message after loading from a file.} \item{nthread}{Number of threads used for creating DMatrix.} \item{...}{the \code{info} data could be passed directly as parameters, without creating an \code{info} list.} } \description{ Construct xgb.DMatrix object from either a dense matrix, a sparse matrix, or a local file. Supported input file formats are either a LIBSVM text file or a binary file that was created previously by \code{\link{xgb.DMatrix.save}}). } \examples{ data(agaricus.train, package='xgboost') dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) xgb.DMatrix.save(dtrain, 'xgb.DMatrix.data') dtrain <- xgb.DMatrix('xgb.DMatrix.data') if (file.exists('xgb.DMatrix.data')) file.remove('xgb.DMatrix.data') } xgboost-1.5.2/R-package/man/xgb.DMatrix.save.Rd000066400000000000000000000012371417122711700211320ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.DMatrix.save.R \name{xgb.DMatrix.save} \alias{xgb.DMatrix.save} \title{Save xgb.DMatrix object to binary file} \usage{ xgb.DMatrix.save(dmatrix, fname) } \arguments{ \item{dmatrix}{the \code{xgb.DMatrix} object} \item{fname}{the name of the file to write.} } \description{ Save xgb.DMatrix object to binary file } \examples{ data(agaricus.train, package='xgboost') dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) xgb.DMatrix.save(dtrain, 'xgb.DMatrix.data') dtrain <- xgb.DMatrix('xgb.DMatrix.data') if (file.exists('xgb.DMatrix.data')) file.remove('xgb.DMatrix.data') } xgboost-1.5.2/R-package/man/xgb.attr.Rd000066400000000000000000000066051417122711700176030ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.Booster.R \name{xgb.attr} \alias{xgb.attr} \alias{xgb.attr<-} \alias{xgb.attributes} \alias{xgb.attributes<-} \title{Accessors for serializable attributes of a model.} \usage{ xgb.attr(object, name) xgb.attr(object, name) <- value xgb.attributes(object) xgb.attributes(object) <- value } \arguments{ \item{object}{Object of class \code{xgb.Booster} or \code{xgb.Booster.handle}.} \item{name}{a non-empty character string specifying which attribute is to be accessed.} \item{value}{a value of an attribute for \code{xgb.attr<-}; for \code{xgb.attributes<-} it's a list (or an object coercible to a list) with the names of attributes to set and the elements corresponding to attribute values. Non-character values are converted to character. When attribute value is not a scalar, only the first index is used. Use \code{NULL} to remove an attribute.} } \value{ \code{xgb.attr} returns either a string value of an attribute or \code{NULL} if an attribute wasn't stored in a model. \code{xgb.attributes} returns a list of all attribute stored in a model or \code{NULL} if a model has no stored attributes. } \description{ These methods allow to manipulate the key-value attribute strings of an xgboost model. } \details{ The primary purpose of xgboost model attributes is to store some meta-data about the model. Note that they are a separate concept from the object attributes in R. Specifically, they refer to key-value strings that can be attached to an xgboost model, stored together with the model's binary representation, and accessed later (from R or any other interface). In contrast, any R-attribute assigned to an R-object of \code{xgb.Booster} class would not be saved by \code{xgb.save} because an xgboost model is an external memory object and its serialization is handled externally. Also, setting an attribute that has the same name as one of xgboost's parameters wouldn't change the value of that parameter for a model. Use \code{\link{xgb.parameters<-}} to set or change model parameters. The attribute setters would usually work more efficiently for \code{xgb.Booster.handle} than for \code{xgb.Booster}, since only just a handle (pointer) would need to be copied. That would only matter if attributes need to be set many times. Note, however, that when feeding a handle of an \code{xgb.Booster} object to the attribute setters, the raw model cache of an \code{xgb.Booster} object would not be automatically updated, and it would be user's responsibility to call \code{xgb.serialize} to update it. The \code{xgb.attributes<-} setter either updates the existing or adds one or several attributes, but it doesn't delete the other existing attributes. } \examples{ data(agaricus.train, package='xgboost') train <- agaricus.train bst <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") xgb.attr(bst, "my_attribute") <- "my attribute value" print(xgb.attr(bst, "my_attribute")) xgb.attributes(bst) <- list(a = 123, b = "abc") xgb.save(bst, 'xgb.model') bst1 <- xgb.load('xgb.model') if (file.exists('xgb.model')) file.remove('xgb.model') print(xgb.attr(bst1, "my_attribute")) print(xgb.attributes(bst1)) # deletion: xgb.attr(bst1, "my_attribute") <- NULL print(xgb.attributes(bst1)) xgb.attributes(bst1) <- list(a = NULL, b = NULL) print(xgb.attributes(bst1)) } xgboost-1.5.2/R-package/man/xgb.config.Rd000066400000000000000000000012441417122711700200700ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.Booster.R \name{xgb.config} \alias{xgb.config} \alias{xgb.config<-} \title{Accessors for model parameters as JSON string.} \usage{ xgb.config(object) xgb.config(object) <- value } \arguments{ \item{object}{Object of class \code{xgb.Booster}} \item{value}{A JSON string.} } \description{ Accessors for model parameters as JSON string. } \examples{ data(agaricus.train, package='xgboost') train <- agaricus.train bst <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") config <- xgb.config(bst) } xgboost-1.5.2/R-package/man/xgb.create.features.Rd000066400000000000000000000071241417122711700217060ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.create.features.R \name{xgb.create.features} \alias{xgb.create.features} \title{Create new features from a previously learned model} \usage{ xgb.create.features(model, data, ...) } \arguments{ \item{model}{decision tree boosting model learned on the original data} \item{data}{original data (usually provided as a \code{dgCMatrix} matrix)} \item{...}{currently not used} } \value{ \code{dgCMatrix} matrix including both the original data and the new features. } \description{ May improve the learning by adding new features to the training data based on the decision trees from a previously learned model. } \details{ This is the function inspired from the paragraph 3.1 of the paper: \strong{Practical Lessons from Predicting Clicks on Ads at Facebook} \emph{(Xinran He, Junfeng Pan, Ou Jin, Tianbing Xu, Bo Liu, Tao Xu, Yan, xin Shi, Antoine Atallah, Ralf Herbrich, Stuart Bowers, Joaquin Quinonero Candela)} International Workshop on Data Mining for Online Advertising (ADKDD) - August 24, 2014 \url{https://research.fb.com/publications/practical-lessons-from-predicting-clicks-on-ads-at-facebook/}. Extract explaining the method: "We found that boosted decision trees are a powerful and very convenient way to implement non-linear and tuple transformations of the kind we just described. We treat each individual tree as a categorical feature that takes as value the index of the leaf an instance ends up falling in. We use 1-of-K coding of this type of features. For example, consider the boosted tree model in Figure 1 with 2 subtrees, where the first subtree has 3 leafs and the second 2 leafs. If an instance ends up in leaf 2 in the first subtree and leaf 1 in second subtree, the overall input to the linear classifier will be the binary vector \code{[0, 1, 0, 1, 0]}, where the first 3 entries correspond to the leaves of the first subtree and last 2 to those of the second subtree. [...] We can understand boosted decision tree based transformation as a supervised feature encoding that converts a real-valued vector into a compact binary-valued vector. A traversal from root node to a leaf node represents a rule on certain features." } \examples{ data(agaricus.train, package='xgboost') data(agaricus.test, package='xgboost') dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) dtest <- with(agaricus.test, xgb.DMatrix(data, label = label)) param <- list(max_depth=2, eta=1, silent=1, objective='binary:logistic') nrounds = 4 bst = xgb.train(params = param, data = dtrain, nrounds = nrounds, nthread = 2) # Model accuracy without new features accuracy.before <- sum((predict(bst, agaricus.test$data) >= 0.5) == agaricus.test$label) / length(agaricus.test$label) # Convert previous features to one hot encoding new.features.train <- xgb.create.features(model = bst, agaricus.train$data) new.features.test <- xgb.create.features(model = bst, agaricus.test$data) # learning with new features new.dtrain <- xgb.DMatrix(data = new.features.train, label = agaricus.train$label) new.dtest <- xgb.DMatrix(data = new.features.test, label = agaricus.test$label) watchlist <- list(train = new.dtrain) bst <- xgb.train(params = param, data = new.dtrain, nrounds = nrounds, nthread = 2) # Model accuracy with new features accuracy.after <- sum((predict(bst, new.dtest) >= 0.5) == agaricus.test$label) / length(agaricus.test$label) # Here the accuracy was already good and is now perfect. cat(paste("The accuracy was", accuracy.before, "before adding leaf features and it is now", accuracy.after, "!\n")) } xgboost-1.5.2/R-package/man/xgb.cv.Rd000066400000000000000000000162771417122711700172470ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.cv.R \name{xgb.cv} \alias{xgb.cv} \title{Cross Validation} \usage{ xgb.cv( params = list(), data, nrounds, nfold, label = NULL, missing = NA, prediction = FALSE, showsd = TRUE, metrics = list(), obj = NULL, feval = NULL, stratified = TRUE, folds = NULL, train_folds = NULL, verbose = TRUE, print_every_n = 1L, early_stopping_rounds = NULL, maximize = NULL, callbacks = list(), ... ) } \arguments{ \item{params}{the list of parameters. The complete list of parameters is available in the \href{http://xgboost.readthedocs.io/en/latest/parameter.html}{online documentation}. Below is a shorter summary: \itemize{ \item \code{objective} objective function, common ones are \itemize{ \item \code{reg:squarederror} Regression with squared loss. \item \code{binary:logistic} logistic regression for classification. \item See \code{\link[=xgb.train]{xgb.train}()} for complete list of objectives. } \item \code{eta} step size of each boosting step \item \code{max_depth} maximum depth of the tree \item \code{nthread} number of thread used in training, if not set, all threads are used } See \code{\link{xgb.train}} for further details. See also demo/ for walkthrough example in R.} \item{data}{takes an \code{xgb.DMatrix}, \code{matrix}, or \code{dgCMatrix} as the input.} \item{nrounds}{the max number of iterations} \item{nfold}{the original dataset is randomly partitioned into \code{nfold} equal size subsamples.} \item{label}{vector of response values. Should be provided only when data is an R-matrix.} \item{missing}{is only used when input is a dense matrix. By default is set to NA, which means that NA values should be considered as 'missing' by the algorithm. Sometimes, 0 or other extreme value might be used to represent missing values.} \item{prediction}{A logical value indicating whether to return the test fold predictions from each CV model. This parameter engages the \code{\link{cb.cv.predict}} callback.} \item{showsd}{\code{boolean}, whether to show standard deviation of cross validation} \item{metrics, }{list of evaluation metrics to be used in cross validation, when it is not specified, the evaluation metric is chosen according to objective function. Possible options are: \itemize{ \item \code{error} binary classification error rate \item \code{rmse} Rooted mean square error \item \code{logloss} negative log-likelihood function \item \code{mae} Mean absolute error \item \code{mape} Mean absolute percentage error \item \code{auc} Area under curve \item \code{aucpr} Area under PR curve \item \code{merror} Exact matching error, used to evaluate multi-class classification }} \item{obj}{customized objective function. Returns gradient and second order gradient with given prediction and dtrain.} \item{feval}{customized evaluation function. Returns \code{list(metric='metric-name', value='metric-value')} with given prediction and dtrain.} \item{stratified}{a \code{boolean} indicating whether sampling of folds should be stratified by the values of outcome labels.} \item{folds}{\code{list} provides a possibility to use a list of pre-defined CV folds (each element must be a vector of test fold's indices). When folds are supplied, the \code{nfold} and \code{stratified} parameters are ignored.} \item{train_folds}{\code{list} list specifying which indicies to use for training. If \code{NULL} (the default) all indices not specified in \code{folds} will be used for training.} \item{verbose}{\code{boolean}, print the statistics during the process} \item{print_every_n}{Print each n-th iteration evaluation messages when \code{verbose>0}. Default is 1 which means all messages are printed. This parameter is passed to the \code{\link{cb.print.evaluation}} callback.} \item{early_stopping_rounds}{If \code{NULL}, the early stopping function is not triggered. If set to an integer \code{k}, training with a validation set will stop if the performance doesn't improve for \code{k} rounds. Setting this parameter engages the \code{\link{cb.early.stop}} callback.} \item{maximize}{If \code{feval} and \code{early_stopping_rounds} are set, then this parameter must be set as well. When it is \code{TRUE}, it means the larger the evaluation score the better. This parameter is passed to the \code{\link{cb.early.stop}} callback.} \item{callbacks}{a list of callback functions to perform various task during boosting. See \code{\link{callbacks}}. Some of the callbacks are automatically created depending on the parameters' values. User can provide either existing or their own callback methods in order to customize the training process.} \item{...}{other parameters to pass to \code{params}.} } \value{ An object of class \code{xgb.cv.synchronous} with the following elements: \itemize{ \item \code{call} a function call. \item \code{params} parameters that were passed to the xgboost library. Note that it does not capture parameters changed by the \code{\link{cb.reset.parameters}} callback. \item \code{callbacks} callback functions that were either automatically assigned or explicitly passed. \item \code{evaluation_log} evaluation history stored as a \code{data.table} with the first column corresponding to iteration number and the rest corresponding to the CV-based evaluation means and standard deviations for the training and test CV-sets. It is created by the \code{\link{cb.evaluation.log}} callback. \item \code{niter} number of boosting iterations. \item \code{nfeatures} number of features in training data. \item \code{folds} the list of CV folds' indices - either those passed through the \code{folds} parameter or randomly generated. \item \code{best_iteration} iteration number with the best evaluation metric value (only available with early stopping). \item \code{best_ntreelimit} and the \code{ntreelimit} Deprecated attributes, use \code{best_iteration} instead. \item \code{pred} CV prediction values available when \code{prediction} is set. It is either vector or matrix (see \code{\link{cb.cv.predict}}). \item \code{models} a list of the CV folds' models. It is only available with the explicit setting of the \code{cb.cv.predict(save_models = TRUE)} callback. } } \description{ The cross validation function of xgboost } \details{ The original sample is randomly partitioned into \code{nfold} equal size subsamples. Of the \code{nfold} subsamples, a single subsample is retained as the validation data for testing the model, and the remaining \code{nfold - 1} subsamples are used as training data. The cross-validation process is then repeated \code{nrounds} times, with each of the \code{nfold} subsamples used exactly once as the validation data. All observations are used for both training and validation. Adapted from \url{https://en.wikipedia.org/wiki/Cross-validation_\%28statistics\%29} } \examples{ data(agaricus.train, package='xgboost') dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) cv <- xgb.cv(data = dtrain, nrounds = 3, nthread = 2, nfold = 5, metrics = list("rmse","auc"), max_depth = 3, eta = 1, objective = "binary:logistic") print(cv) print(cv, verbose=TRUE) } xgboost-1.5.2/R-package/man/xgb.dump.Rd000066400000000000000000000037171417122711700175770ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.dump.R \name{xgb.dump} \alias{xgb.dump} \title{Dump an xgboost model in text format.} \usage{ xgb.dump( model, fname = NULL, fmap = "", with_stats = FALSE, dump_format = c("text", "json"), ... ) } \arguments{ \item{model}{the model object.} \item{fname}{the name of the text file where to save the model text dump. If not provided or set to \code{NULL}, the model is returned as a \code{character} vector.} \item{fmap}{feature map file representing feature types. Detailed description could be found at \url{https://github.com/dmlc/xgboost/wiki/Binary-Classification#dump-model}. See demo/ for walkthrough example in R, and \url{https://github.com/dmlc/xgboost/blob/master/demo/data/featmap.txt} for example Format.} \item{with_stats}{whether to dump some additional statistics about the splits. When this option is on, the model dump contains two additional values: gain is the approximate loss function gain we get in each split; cover is the sum of second order gradient in each node.} \item{dump_format}{either 'text' or 'json' format could be specified.} \item{...}{currently not used} } \value{ If fname is not provided or set to \code{NULL} the function will return the model as a \code{character} vector. Otherwise it will return \code{TRUE}. } \description{ Dump an xgboost model in text format. } \examples{ data(agaricus.train, package='xgboost') data(agaricus.test, package='xgboost') train <- agaricus.train test <- agaricus.test bst <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") # save the model in file 'xgb.model.dump' dump_path = file.path(tempdir(), 'model.dump') xgb.dump(bst, dump_path, with_stats = TRUE) # print the model without saving it to a file print(xgb.dump(bst, with_stats = TRUE)) # print in JSON format: cat(xgb.dump(bst, with_stats = TRUE, dump_format='json')) } xgboost-1.5.2/R-package/man/xgb.gblinear.history.Rd000066400000000000000000000021711417122711700221060ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/callbacks.R \name{xgb.gblinear.history} \alias{xgb.gblinear.history} \title{Extract gblinear coefficients history.} \usage{ xgb.gblinear.history(model, class_index = NULL) } \arguments{ \item{model}{either an \code{xgb.Booster} or a result of \code{xgb.cv()}, trained using the \code{cb.gblinear.history()} callback.} \item{class_index}{zero-based class index to extract the coefficients for only that specific class in a multinomial multiclass model. When it is NULL, all the coefficients are returned. Has no effect in non-multiclass models.} } \value{ For an \code{xgb.train} result, a matrix (either dense or sparse) with the columns corresponding to iteration's coefficients (in the order as \code{xgb.dump()} would return) and the rows corresponding to boosting iterations. For an \code{xgb.cv} result, a list of such matrices is returned with the elements corresponding to CV folds. } \description{ A helper function to extract the matrix of linear coefficients' history from a gblinear model created while using the \code{cb.gblinear.history()} callback. } xgboost-1.5.2/R-package/man/xgb.importance.Rd000066400000000000000000000101061417122711700207610ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.importance.R \name{xgb.importance} \alias{xgb.importance} \title{Importance of features in a model.} \usage{ xgb.importance( feature_names = NULL, model = NULL, trees = NULL, data = NULL, label = NULL, target = NULL ) } \arguments{ \item{feature_names}{character vector of feature names. If the model already contains feature names, those would be used when \code{feature_names=NULL} (default value). Non-null \code{feature_names} could be provided to override those in the model.} \item{model}{object of class \code{xgb.Booster}.} \item{trees}{(only for the gbtree booster) an integer vector of tree indices that should be included into the importance calculation. If set to \code{NULL}, all trees of the model are parsed. It could be useful, e.g., in multiclass classification to get feature importances for each class separately. IMPORTANT: the tree index in xgboost models is zero-based (e.g., use \code{trees = 0:4} for first 5 trees).} \item{data}{deprecated.} \item{label}{deprecated.} \item{target}{deprecated.} } \value{ For a tree model, a \code{data.table} with the following columns: \itemize{ \item \code{Features} names of the features used in the model; \item \code{Gain} represents fractional contribution of each feature to the model based on the total gain of this feature's splits. Higher percentage means a more important predictive feature. \item \code{Cover} metric of the number of observation related to this feature; \item \code{Frequency} percentage representing the relative number of times a feature have been used in trees. } A linear model's importance \code{data.table} has the following columns: \itemize{ \item \code{Features} names of the features used in the model; \item \code{Weight} the linear coefficient of this feature; \item \code{Class} (only for multiclass models) class label. } If \code{feature_names} is not provided and \code{model} doesn't have \code{feature_names}, index of the features will be used instead. Because the index is extracted from the model dump (based on C++ code), it starts at 0 (as in C/C++ or Python) instead of 1 (usual in R). } \description{ Creates a \code{data.table} of feature importances in a model. } \details{ This function works for both linear and tree models. For linear models, the importance is the absolute magnitude of linear coefficients. For that reason, in order to obtain a meaningful ranking by importance for a linear model, the features need to be on the same scale (which you also would want to do when using either L1 or L2 regularization). } \examples{ # binomial classification using gbtree: data(agaricus.train, package='xgboost') bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") xgb.importance(model = bst) # binomial classification using gblinear: bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, booster = "gblinear", eta = 0.3, nthread = 1, nrounds = 20, objective = "binary:logistic") xgb.importance(model = bst) # multiclass classification using gbtree: nclass <- 3 nrounds <- 10 mbst <- xgboost(data = as.matrix(iris[, -5]), label = as.numeric(iris$Species) - 1, max_depth = 3, eta = 0.2, nthread = 2, nrounds = nrounds, objective = "multi:softprob", num_class = nclass) # all classes clumped together: xgb.importance(model = mbst) # inspect importances separately for each class: xgb.importance(model = mbst, trees = seq(from=0, by=nclass, length.out=nrounds)) xgb.importance(model = mbst, trees = seq(from=1, by=nclass, length.out=nrounds)) xgb.importance(model = mbst, trees = seq(from=2, by=nclass, length.out=nrounds)) # multiclass classification using gblinear: mbst <- xgboost(data = scale(as.matrix(iris[, -5])), label = as.numeric(iris$Species) - 1, booster = "gblinear", eta = 0.2, nthread = 1, nrounds = 15, objective = "multi:softprob", num_class = nclass) xgb.importance(model = mbst) } xgboost-1.5.2/R-package/man/xgb.load.Rd000066400000000000000000000024471417122711700175500ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.load.R \name{xgb.load} \alias{xgb.load} \title{Load xgboost model from binary file} \usage{ xgb.load(modelfile) } \arguments{ \item{modelfile}{the name of the binary input file.} } \value{ An object of \code{xgb.Booster} class. } \description{ Load xgboost model from the binary model file. } \details{ The input file is expected to contain a model saved in an xgboost-internal binary format using either \code{\link{xgb.save}} or \code{\link{cb.save.model}} in R, or using some appropriate methods from other xgboost interfaces. E.g., a model trained in Python and saved from there in xgboost format, could be loaded from R. Note: a model saved as an R-object, has to be loaded using corresponding R-methods, not \code{xgb.load}. } \examples{ data(agaricus.train, package='xgboost') data(agaricus.test, package='xgboost') train <- agaricus.train test <- agaricus.test bst <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2,objective = "binary:logistic") xgb.save(bst, 'xgb.model') bst <- xgb.load('xgb.model') if (file.exists('xgb.model')) file.remove('xgb.model') pred <- predict(bst, test$data) } \seealso{ \code{\link{xgb.save}}, \code{\link{xgb.Booster.complete}}. } xgboost-1.5.2/R-package/man/xgb.load.raw.Rd000066400000000000000000000005541417122711700203350ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.load.raw.R \name{xgb.load.raw} \alias{xgb.load.raw} \title{Load serialised xgboost model from R's raw vector} \usage{ xgb.load.raw(buffer) } \arguments{ \item{buffer}{the buffer returned by xgb.save.raw} } \description{ User can generate raw memory buffer by calling xgb.save.raw } xgboost-1.5.2/R-package/man/xgb.model.dt.tree.Rd000066400000000000000000000065651417122711700213020ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.model.dt.tree.R \name{xgb.model.dt.tree} \alias{xgb.model.dt.tree} \title{Parse a boosted tree model text dump} \usage{ xgb.model.dt.tree( feature_names = NULL, model = NULL, text = NULL, trees = NULL, use_int_id = FALSE, ... ) } \arguments{ \item{feature_names}{character vector of feature names. If the model already contains feature names, those would be used when \code{feature_names=NULL} (default value). Non-null \code{feature_names} could be provided to override those in the model.} \item{model}{object of class \code{xgb.Booster}} \item{text}{\code{character} vector previously generated by the \code{xgb.dump} function (where parameter \code{with_stats = TRUE} should have been set). \code{text} takes precedence over \code{model}.} \item{trees}{an integer vector of tree indices that should be parsed. If set to \code{NULL}, all trees of the model are parsed. It could be useful, e.g., in multiclass classification to get only the trees of one certain class. IMPORTANT: the tree index in xgboost models is zero-based (e.g., use \code{trees = 0:4} for first 5 trees).} \item{use_int_id}{a logical flag indicating whether nodes in columns "Yes", "No", "Missing" should be represented as integers (when FALSE) or as "Tree-Node" character strings (when FALSE).} \item{...}{currently not used.} } \value{ A \code{data.table} with detailed information about model trees' nodes. The columns of the \code{data.table} are: \itemize{ \item \code{Tree}: integer ID of a tree in a model (zero-based index) \item \code{Node}: integer ID of a node in a tree (zero-based index) \item \code{ID}: character identifier of a node in a model (only when \code{use_int_id=FALSE}) \item \code{Feature}: for a branch node, it's a feature id or name (when available); for a leaf note, it simply labels it as \code{'Leaf'} \item \code{Split}: location of the split for a branch node (split condition is always "less than") \item \code{Yes}: ID of the next node when the split condition is met \item \code{No}: ID of the next node when the split condition is not met \item \code{Missing}: ID of the next node when branch value is missing \item \code{Quality}: either the split gain (change in loss) or the leaf value \item \code{Cover}: metric related to the number of observation either seen by a split or collected by a leaf during training. } When \code{use_int_id=FALSE}, columns "Yes", "No", and "Missing" point to model-wide node identifiers in the "ID" column. When \code{use_int_id=TRUE}, those columns point to node identifiers from the corresponding trees in the "Node" column. } \description{ Parse a boosted tree model text dump into a \code{data.table} structure. } \examples{ # Basic use: data(agaricus.train, package='xgboost') bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2,objective = "binary:logistic") (dt <- xgb.model.dt.tree(colnames(agaricus.train$data), bst)) # This bst model already has feature_names stored with it, so those would be used when # feature_names is not set: (dt <- xgb.model.dt.tree(model = bst)) # How to match feature names of splits that are following a current 'Yes' branch: merge(dt, dt[, .(ID, Y.Feature=Feature)], by.x='Yes', by.y='ID', all.x=TRUE)[order(Tree,Node)] } xgboost-1.5.2/R-package/man/xgb.parameters.Rd000066400000000000000000000017371417122711700207750ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.Booster.R \name{xgb.parameters<-} \alias{xgb.parameters<-} \title{Accessors for model parameters.} \usage{ xgb.parameters(object) <- value } \arguments{ \item{object}{Object of class \code{xgb.Booster} or \code{xgb.Booster.handle}.} \item{value}{a list (or an object coercible to a list) with the names of parameters to set and the elements corresponding to parameter values.} } \description{ Only the setter for xgboost parameters is currently implemented. } \details{ Note that the setter would usually work more efficiently for \code{xgb.Booster.handle} than for \code{xgb.Booster}, since only just a handle would need to be copied. } \examples{ data(agaricus.train, package='xgboost') train <- agaricus.train bst <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") xgb.parameters(bst) <- list(eta = 0.1) } xgboost-1.5.2/R-package/man/xgb.plot.deepness.Rd000066400000000000000000000056471417122711700214210ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.ggplot.R, R/xgb.plot.deepness.R \name{xgb.ggplot.deepness} \alias{xgb.ggplot.deepness} \alias{xgb.plot.deepness} \title{Plot model trees deepness} \usage{ xgb.ggplot.deepness( model = NULL, which = c("2x1", "max.depth", "med.depth", "med.weight") ) xgb.plot.deepness( model = NULL, which = c("2x1", "max.depth", "med.depth", "med.weight"), plot = TRUE, ... ) } \arguments{ \item{model}{either an \code{xgb.Booster} model generated by the \code{xgb.train} function or a data.table result of the \code{xgb.model.dt.tree} function.} \item{which}{which distribution to plot (see details).} \item{plot}{(base R barplot) whether a barplot should be produced. If FALSE, only a data.table is returned.} \item{...}{other parameters passed to \code{barplot} or \code{plot}.} } \value{ Other than producing plots (when \code{plot=TRUE}), the \code{xgb.plot.deepness} function silently returns a processed data.table where each row corresponds to a terminal leaf in a tree model, and contains information about leaf's depth, cover, and weight (which is used in calculating predictions). The \code{xgb.ggplot.deepness} silently returns either a list of two ggplot graphs when \code{which="2x1"} or a single ggplot graph for the other \code{which} options. } \description{ Visualizes distributions related to depth of tree leafs. \code{xgb.plot.deepness} uses base R graphics, while \code{xgb.ggplot.deepness} uses the ggplot backend. } \details{ When \code{which="2x1"}, two distributions with respect to the leaf depth are plotted on top of each other: \itemize{ \item the distribution of the number of leafs in a tree model at a certain depth; \item the distribution of average weighted number of observations ("cover") ending up in leafs at certain depth. } Those could be helpful in determining sensible ranges of the \code{max_depth} and \code{min_child_weight} parameters. When \code{which="max.depth"} or \code{which="med.depth"}, plots of either maximum or median depth per tree with respect to tree number are created. And \code{which="med.weight"} allows to see how a tree's median absolute leaf weight changes through the iterations. This function was inspired by the blog post \url{https://github.com/aysent/random-forest-leaf-visualization}. } \examples{ data(agaricus.train, package='xgboost') # Change max_depth to a higher number to get a more significant result bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 6, eta = 0.1, nthread = 2, nrounds = 50, objective = "binary:logistic", subsample = 0.5, min_child_weight = 2) xgb.plot.deepness(bst) xgb.ggplot.deepness(bst) xgb.plot.deepness(bst, which='max.depth', pch=16, col=rgb(0,0,1,0.3), cex=2) xgb.plot.deepness(bst, which='med.weight', pch=16, col=rgb(0,0,1,0.3), cex=2) } \seealso{ \code{\link{xgb.train}}, \code{\link{xgb.model.dt.tree}}. } xgboost-1.5.2/R-package/man/xgb.plot.importance.Rd000066400000000000000000000071541417122711700217470ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.ggplot.R, R/xgb.plot.importance.R \name{xgb.ggplot.importance} \alias{xgb.ggplot.importance} \alias{xgb.plot.importance} \title{Plot feature importance as a bar graph} \usage{ xgb.ggplot.importance( importance_matrix = NULL, top_n = NULL, measure = NULL, rel_to_first = FALSE, n_clusters = c(1:10), ... ) xgb.plot.importance( importance_matrix = NULL, top_n = NULL, measure = NULL, rel_to_first = FALSE, left_margin = 10, cex = NULL, plot = TRUE, ... ) } \arguments{ \item{importance_matrix}{a \code{data.table} returned by \code{\link{xgb.importance}}.} \item{top_n}{maximal number of top features to include into the plot.} \item{measure}{the name of importance measure to plot. When \code{NULL}, 'Gain' would be used for trees and 'Weight' would be used for gblinear.} \item{rel_to_first}{whether importance values should be represented as relative to the highest ranked feature. See Details.} \item{n_clusters}{(ggplot only) a \code{numeric} vector containing the min and the max range of the possible number of clusters of bars.} \item{...}{other parameters passed to \code{barplot} (except horiz, border, cex.names, names.arg, and las).} \item{left_margin}{(base R barplot) allows to adjust the left margin size to fit feature names. When it is NULL, the existing \code{par('mar')} is used.} \item{cex}{(base R barplot) passed as \code{cex.names} parameter to \code{barplot}.} \item{plot}{(base R barplot) whether a barplot should be produced. If FALSE, only a data.table is returned.} } \value{ The \code{xgb.plot.importance} function creates a \code{barplot} (when \code{plot=TRUE}) and silently returns a processed data.table with \code{n_top} features sorted by importance. The \code{xgb.ggplot.importance} function returns a ggplot graph which could be customized afterwards. E.g., to change the title of the graph, add \code{+ ggtitle("A GRAPH NAME")} to the result. } \description{ Represents previously calculated feature importance as a bar graph. \code{xgb.plot.importance} uses base R graphics, while \code{xgb.ggplot.importance} uses the ggplot backend. } \details{ The graph represents each feature as a horizontal bar of length proportional to the importance of a feature. Features are shown ranked in a decreasing importance order. It works for importances from both \code{gblinear} and \code{gbtree} models. When \code{rel_to_first = FALSE}, the values would be plotted as they were in \code{importance_matrix}. For gbtree model, that would mean being normalized to the total of 1 ("what is feature's importance contribution relative to the whole model?"). For linear models, \code{rel_to_first = FALSE} would show actual values of the coefficients. Setting \code{rel_to_first = TRUE} allows to see the picture from the perspective of "what is feature's importance contribution relative to the most important feature?" The ggplot-backend method also performs 1-D clustering of the importance values, with bar colors corresponding to different clusters that have somewhat similar importance values. } \examples{ data(agaricus.train) bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 3, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") importance_matrix <- xgb.importance(colnames(agaricus.train$data), model = bst) xgb.plot.importance(importance_matrix, rel_to_first = TRUE, xlab = "Relative importance") (gg <- xgb.ggplot.importance(importance_matrix, measure = "Frequency", rel_to_first = TRUE)) gg + ggplot2::ylab("Frequency") } \seealso{ \code{\link[graphics]{barplot}}. } xgboost-1.5.2/R-package/man/xgb.plot.multi.trees.Rd000066400000000000000000000055241417122711700220600ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.plot.multi.trees.R \name{xgb.plot.multi.trees} \alias{xgb.plot.multi.trees} \title{Project all trees on one tree and plot it} \usage{ xgb.plot.multi.trees( model, feature_names = NULL, features_keep = 5, plot_width = NULL, plot_height = NULL, render = TRUE, ... ) } \arguments{ \item{model}{produced by the \code{xgb.train} function.} \item{feature_names}{names of each feature as a \code{character} vector.} \item{features_keep}{number of features to keep in each position of the multi trees.} \item{plot_width}{width in pixels of the graph to produce} \item{plot_height}{height in pixels of the graph to produce} \item{render}{a logical flag for whether the graph should be rendered (see Value).} \item{...}{currently not used} } \value{ When \code{render = TRUE}: returns a rendered graph object which is an \code{htmlwidget} of class \code{grViz}. Similar to ggplot objects, it needs to be printed to see it when not running from command line. When \code{render = FALSE}: silently returns a graph object which is of DiagrammeR's class \code{dgr_graph}. This could be useful if one wants to modify some of the graph attributes before rendering the graph with \code{\link[DiagrammeR]{render_graph}}. } \description{ Visualization of the ensemble of trees as a single collective unit. } \details{ This function tries to capture the complexity of a gradient boosted tree model in a cohesive way by compressing an ensemble of trees into a single tree-graph representation. The goal is to improve the interpretability of a model generally seen as black box. Note: this function is applicable to tree booster-based models only. It takes advantage of the fact that the shape of a binary tree is only defined by its depth (therefore, in a boosting model, all trees have similar shape). Moreover, the trees tend to reuse the same features. The function projects each tree onto one, and keeps for each position the \code{features_keep} first features (based on the Gain per feature measure). This function is inspired by this blog post: \url{https://wellecks.wordpress.com/2015/02/21/peering-into-the-black-box-visualizing-lambdamart/} } \examples{ data(agaricus.train, package='xgboost') bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 15, eta = 1, nthread = 2, nrounds = 30, objective = "binary:logistic", min_child_weight = 50, verbose = 0) p <- xgb.plot.multi.trees(model = bst, features_keep = 3) print(p) \dontrun{ # Below is an example of how to save this plot to a file. # Note that for `export_graph` to work, the DiagrammeRsvg and rsvg packages must also be installed. library(DiagrammeR) gr <- xgb.plot.multi.trees(model=bst, features_keep = 3, render=FALSE) export_graph(gr, 'tree.pdf', width=1500, height=600) } } xgboost-1.5.2/R-package/man/xgb.plot.shap.Rd000066400000000000000000000146121417122711700205360ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.plot.shap.R \name{xgb.plot.shap} \alias{xgb.plot.shap} \title{SHAP contribution dependency plots} \usage{ xgb.plot.shap( data, shap_contrib = NULL, features = NULL, top_n = 1, model = NULL, trees = NULL, target_class = NULL, approxcontrib = FALSE, subsample = NULL, n_col = 1, col = rgb(0, 0, 1, 0.2), pch = ".", discrete_n_uniq = 5, discrete_jitter = 0.01, ylab = "SHAP", plot_NA = TRUE, col_NA = rgb(0.7, 0, 1, 0.6), pch_NA = ".", pos_NA = 1.07, plot_loess = TRUE, col_loess = 2, span_loess = 0.5, which = c("1d", "2d"), plot = TRUE, ... ) } \arguments{ \item{data}{data as a \code{matrix} or \code{dgCMatrix}.} \item{shap_contrib}{a matrix of SHAP contributions that was computed earlier for the above \code{data}. When it is NULL, it is computed internally using \code{model} and \code{data}.} \item{features}{a vector of either column indices or of feature names to plot. When it is NULL, feature importance is calculated, and \code{top_n} high ranked features are taken.} \item{top_n}{when \code{features} is NULL, top_n [1, 100] most important features in a model are taken.} \item{model}{an \code{xgb.Booster} model. It has to be provided when either \code{shap_contrib} or \code{features} is missing.} \item{trees}{passed to \code{\link{xgb.importance}} when \code{features = NULL}.} \item{target_class}{is only relevant for multiclass models. When it is set to a 0-based class index, only SHAP contributions for that specific class are used. If it is not set, SHAP importances are averaged over all classes.} \item{approxcontrib}{passed to \code{\link{predict.xgb.Booster}} when \code{shap_contrib = NULL}.} \item{subsample}{a random fraction of data points to use for plotting. When it is NULL, it is set so that up to 100K data points are used.} \item{n_col}{a number of columns in a grid of plots.} \item{col}{color of the scatterplot markers.} \item{pch}{scatterplot marker.} \item{discrete_n_uniq}{a maximal number of unique values in a feature to consider it as discrete.} \item{discrete_jitter}{an \code{amount} parameter of jitter added to discrete features' positions.} \item{ylab}{a y-axis label in 1D plots.} \item{plot_NA}{whether the contributions of cases with missing values should also be plotted.} \item{col_NA}{a color of marker for missing value contributions.} \item{pch_NA}{a marker type for NA values.} \item{pos_NA}{a relative position of the x-location where NA values are shown: \code{min(x) + (max(x) - min(x)) * pos_NA}.} \item{plot_loess}{whether to plot loess-smoothed curves. The smoothing is only done for features with more than 5 distinct values.} \item{col_loess}{a color to use for the loess curves.} \item{span_loess}{the \code{span} parameter in \code{\link[stats]{loess}}'s call.} \item{which}{whether to do univariate or bivariate plotting. NOTE: only 1D is implemented so far.} \item{plot}{whether a plot should be drawn. If FALSE, only a list of matrices is returned.} \item{...}{other parameters passed to \code{plot}.} } \value{ In addition to producing plots (when \code{plot=TRUE}), it silently returns a list of two matrices: \itemize{ \item \code{data} the values of selected features; \item \code{shap_contrib} the contributions of selected features. } } \description{ Visualizing the SHAP feature contribution to prediction dependencies on feature value. } \details{ These scatterplots represent how SHAP feature contributions depend of feature values. The similarity to partial dependency plots is that they also give an idea for how feature values affect predictions. However, in partial dependency plots, we usually see marginal dependencies of model prediction on feature value, while SHAP contribution dependency plots display the estimated contributions of a feature to model prediction for each individual case. When \code{plot_loess = TRUE} is set, feature values are rounded to 3 significant digits and weighted LOESS is computed and plotted, where weights are the numbers of data points at each rounded value. Note: SHAP contributions are shown on the scale of model margin. E.g., for a logistic binomial objective, the margin is prediction before a sigmoidal transform into probability-like values. Also, since SHAP stands for "SHapley Additive exPlanation" (model prediction = sum of SHAP contributions for all features + bias), depending on the objective used, transforming SHAP contributions for a feature from the marginal to the prediction space is not necessarily a meaningful thing to do. } \examples{ data(agaricus.train, package='xgboost') data(agaricus.test, package='xgboost') bst <- xgboost(agaricus.train$data, agaricus.train$label, nrounds = 50, eta = 0.1, max_depth = 3, subsample = .5, method = "hist", objective = "binary:logistic", nthread = 2, verbose = 0) xgb.plot.shap(agaricus.test$data, model = bst, features = "odor=none") contr <- predict(bst, agaricus.test$data, predcontrib = TRUE) xgb.plot.shap(agaricus.test$data, contr, model = bst, top_n = 12, n_col = 3) xgb.ggplot.shap.summary(agaricus.test$data, contr, model = bst, top_n = 12) # Summary plot # multiclass example - plots for each class separately: nclass <- 3 nrounds <- 20 x <- as.matrix(iris[, -5]) set.seed(123) is.na(x[sample(nrow(x) * 4, 30)]) <- TRUE # introduce some missing values mbst <- xgboost(data = x, label = as.numeric(iris$Species) - 1, nrounds = nrounds, max_depth = 2, eta = 0.3, subsample = .5, nthread = 2, objective = "multi:softprob", num_class = nclass, verbose = 0) trees0 <- seq(from=0, by=nclass, length.out=nrounds) col <- rgb(0, 0, 1, 0.5) xgb.plot.shap(x, model = mbst, trees = trees0, target_class = 0, top_n = 4, n_col = 2, col = col, pch = 16, pch_NA = 17) xgb.plot.shap(x, model = mbst, trees = trees0 + 1, target_class = 1, top_n = 4, n_col = 2, col = col, pch = 16, pch_NA = 17) xgb.plot.shap(x, model = mbst, trees = trees0 + 2, target_class = 2, top_n = 4, n_col = 2, col = col, pch = 16, pch_NA = 17) xgb.ggplot.shap.summary(x, model = mbst, target_class = 0, top_n = 4) # Summary plot } \references{ Scott M. Lundberg, Su-In Lee, "A Unified Approach to Interpreting Model Predictions", NIPS Proceedings 2017, \url{https://arxiv.org/abs/1705.07874} Scott M. Lundberg, Su-In Lee, "Consistent feature attribution for tree ensembles", \url{https://arxiv.org/abs/1706.06060} } xgboost-1.5.2/R-package/man/xgb.plot.shap.summary.Rd000066400000000000000000000051471417122711700222350ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.ggplot.R, R/xgb.plot.shap.R \name{xgb.ggplot.shap.summary} \alias{xgb.ggplot.shap.summary} \alias{xgb.plot.shap.summary} \title{SHAP contribution dependency summary plot} \usage{ xgb.ggplot.shap.summary( data, shap_contrib = NULL, features = NULL, top_n = 10, model = NULL, trees = NULL, target_class = NULL, approxcontrib = FALSE, subsample = NULL ) xgb.plot.shap.summary( data, shap_contrib = NULL, features = NULL, top_n = 10, model = NULL, trees = NULL, target_class = NULL, approxcontrib = FALSE, subsample = NULL ) } \arguments{ \item{data}{data as a \code{matrix} or \code{dgCMatrix}.} \item{shap_contrib}{a matrix of SHAP contributions that was computed earlier for the above \code{data}. When it is NULL, it is computed internally using \code{model} and \code{data}.} \item{features}{a vector of either column indices or of feature names to plot. When it is NULL, feature importance is calculated, and \code{top_n} high ranked features are taken.} \item{top_n}{when \code{features} is NULL, top_n [1, 100] most important features in a model are taken.} \item{model}{an \code{xgb.Booster} model. It has to be provided when either \code{shap_contrib} or \code{features} is missing.} \item{trees}{passed to \code{\link{xgb.importance}} when \code{features = NULL}.} \item{target_class}{is only relevant for multiclass models. When it is set to a 0-based class index, only SHAP contributions for that specific class are used. If it is not set, SHAP importances are averaged over all classes.} \item{approxcontrib}{passed to \code{\link{predict.xgb.Booster}} when \code{shap_contrib = NULL}.} \item{subsample}{a random fraction of data points to use for plotting. When it is NULL, it is set so that up to 100K data points are used.} } \value{ A \code{ggplot2} object. } \description{ Compare SHAP contributions of different features. } \details{ A point plot (each point representing one sample from \code{data}) is produced for each feature, with the points plotted on the SHAP value axis. Each point (observation) is coloured based on its feature value. The plot hence allows us to see which features have a negative / positive contribution on the model prediction, and whether the contribution is different for larger or smaller values of the feature. We effectively try to replicate the \code{summary_plot} function from https://github.com/slundberg/shap. } \examples{ # See \code{\link{xgb.plot.shap}}. } \seealso{ \code{\link{xgb.plot.shap}}, \code{\link{xgb.ggplot.shap.summary}}, \url{https://github.com/slundberg/shap} } xgboost-1.5.2/R-package/man/xgb.plot.tree.Rd000066400000000000000000000063271417122711700205460ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.plot.tree.R \name{xgb.plot.tree} \alias{xgb.plot.tree} \title{Plot a boosted tree model} \usage{ xgb.plot.tree( feature_names = NULL, model = NULL, trees = NULL, plot_width = NULL, plot_height = NULL, render = TRUE, show_node_id = FALSE, ... ) } \arguments{ \item{feature_names}{names of each feature as a \code{character} vector.} \item{model}{produced by the \code{xgb.train} function.} \item{trees}{an integer vector of tree indices that should be visualized. If set to \code{NULL}, all trees of the model are included. IMPORTANT: the tree index in xgboost model is zero-based (e.g., use \code{trees = 0:2} for the first 3 trees in a model).} \item{plot_width}{the width of the diagram in pixels.} \item{plot_height}{the height of the diagram in pixels.} \item{render}{a logical flag for whether the graph should be rendered (see Value).} \item{show_node_id}{a logical flag for whether to show node id's in the graph.} \item{...}{currently not used.} } \value{ When \code{render = TRUE}: returns a rendered graph object which is an \code{htmlwidget} of class \code{grViz}. Similar to ggplot objects, it needs to be printed to see it when not running from command line. When \code{render = FALSE}: silently returns a graph object which is of DiagrammeR's class \code{dgr_graph}. This could be useful if one wants to modify some of the graph attributes before rendering the graph with \code{\link[DiagrammeR]{render_graph}}. } \description{ Read a tree model text dump and plot the model. } \details{ The content of each node is organised that way: \itemize{ \item Feature name. \item \code{Cover}: The sum of second order gradient of training data classified to the leaf. If it is square loss, this simply corresponds to the number of instances seen by a split or collected by a leaf during training. The deeper in the tree a node is, the lower this metric will be. \item \code{Gain} (for split nodes): the information gain metric of a split (corresponds to the importance of the node in the model). \item \code{Value} (for leafs): the margin value that the leaf may contribute to prediction. } The tree root nodes also indicate the Tree index (0-based). The "Yes" branches are marked by the "< split_value" label. The branches that also used for missing values are marked as bold (as in "carrying extra capacity"). This function uses \href{http://www.graphviz.org/}{GraphViz} as a backend of DiagrammeR. } \examples{ data(agaricus.train, package='xgboost') bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 3, eta = 1, nthread = 2, nrounds = 2,objective = "binary:logistic") # plot all the trees xgb.plot.tree(model = bst) # plot only the first tree and display the node ID: xgb.plot.tree(model = bst, trees = 0, show_node_id = TRUE) \dontrun{ # Below is an example of how to save this plot to a file. # Note that for `export_graph` to work, the DiagrammeRsvg and rsvg packages must also be installed. library(DiagrammeR) gr <- xgb.plot.tree(model=bst, trees=0:1, render=FALSE) export_graph(gr, 'tree.pdf', width=1500, height=1900) export_graph(gr, 'tree.png', width=1500, height=1900) } } xgboost-1.5.2/R-package/man/xgb.save.Rd000066400000000000000000000033251417122711700175630ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.save.R \name{xgb.save} \alias{xgb.save} \title{Save xgboost model to binary file} \usage{ xgb.save(model, fname) } \arguments{ \item{model}{model object of \code{xgb.Booster} class.} \item{fname}{name of the file to write.} } \description{ Save xgboost model to a file in binary format. } \details{ This methods allows to save a model in an xgboost-internal binary format which is universal among the various xgboost interfaces. In R, the saved model file could be read-in later using either the \code{\link{xgb.load}} function or the \code{xgb_model} parameter of \code{\link{xgb.train}}. Note: a model can also be saved as an R-object (e.g., by using \code{\link[base]{readRDS}} or \code{\link[base]{save}}). However, it would then only be compatible with R, and corresponding R-methods would need to be used to load it. Moreover, persisting the model with \code{\link[base]{readRDS}} or \code{\link[base]{save}}) will cause compatibility problems in future versions of XGBoost. Consult \code{\link{a-compatibility-note-for-saveRDS-save}} to learn how to persist models in a future-proof way, i.e. to make the model accessible in future releases of XGBoost. } \examples{ data(agaricus.train, package='xgboost') data(agaricus.test, package='xgboost') train <- agaricus.train test <- agaricus.test bst <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2,objective = "binary:logistic") xgb.save(bst, 'xgb.model') bst <- xgb.load('xgb.model') if (file.exists('xgb.model')) file.remove('xgb.model') pred <- predict(bst, test$data) } \seealso{ \code{\link{xgb.load}}, \code{\link{xgb.Booster.complete}}. } xgboost-1.5.2/R-package/man/xgb.save.raw.Rd000066400000000000000000000013621417122711700203520ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.save.raw.R \name{xgb.save.raw} \alias{xgb.save.raw} \title{Save xgboost model to R's raw vector, user can call xgb.load.raw to load the model back from raw vector} \usage{ xgb.save.raw(model) } \arguments{ \item{model}{the model object.} } \description{ Save xgboost model from xgboost or xgb.train } \examples{ data(agaricus.train, package='xgboost') data(agaricus.test, package='xgboost') train <- agaricus.train test <- agaricus.test bst <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2,objective = "binary:logistic") raw <- xgb.save.raw(bst) bst <- xgb.load.raw(raw) pred <- predict(bst, test$data) } xgboost-1.5.2/R-package/man/xgb.serialize.Rd000066400000000000000000000021061417122711700206100ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.serialize.R \name{xgb.serialize} \alias{xgb.serialize} \title{Serialize the booster instance into R's raw vector. The serialization method differs from \code{\link{xgb.save.raw}} as the latter one saves only the model but not parameters. This serialization format is not stable across different xgboost versions.} \usage{ xgb.serialize(booster) } \arguments{ \item{booster}{the booster instance} } \description{ Serialize the booster instance into R's raw vector. The serialization method differs from \code{\link{xgb.save.raw}} as the latter one saves only the model but not parameters. This serialization format is not stable across different xgboost versions. } \examples{ data(agaricus.train, package='xgboost') data(agaricus.test, package='xgboost') train <- agaricus.train test <- agaricus.test bst <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2,objective = "binary:logistic") raw <- xgb.serialize(bst) bst <- xgb.unserialize(raw) } xgboost-1.5.2/R-package/man/xgb.shap.data.Rd000066400000000000000000000037731417122711700204770ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.plot.shap.R \name{xgb.shap.data} \alias{xgb.shap.data} \title{Prepare data for SHAP plots. To be used in xgb.plot.shap, xgb.plot.shap.summary, etc. Internal utility function.} \usage{ xgb.shap.data( data, shap_contrib = NULL, features = NULL, top_n = 1, model = NULL, trees = NULL, target_class = NULL, approxcontrib = FALSE, subsample = NULL, max_observations = 1e+05 ) } \arguments{ \item{data}{data as a \code{matrix} or \code{dgCMatrix}.} \item{shap_contrib}{a matrix of SHAP contributions that was computed earlier for the above \code{data}. When it is NULL, it is computed internally using \code{model} and \code{data}.} \item{features}{a vector of either column indices or of feature names to plot. When it is NULL, feature importance is calculated, and \code{top_n} high ranked features are taken.} \item{top_n}{when \code{features} is NULL, top_n [1, 100] most important features in a model are taken.} \item{model}{an \code{xgb.Booster} model. It has to be provided when either \code{shap_contrib} or \code{features} is missing.} \item{trees}{passed to \code{\link{xgb.importance}} when \code{features = NULL}.} \item{target_class}{is only relevant for multiclass models. When it is set to a 0-based class index, only SHAP contributions for that specific class are used. If it is not set, SHAP importances are averaged over all classes.} \item{approxcontrib}{passed to \code{\link{predict.xgb.Booster}} when \code{shap_contrib = NULL}.} \item{subsample}{a random fraction of data points to use for plotting. When it is NULL, it is set so that up to 100K data points are used.} } \value{ A list containing: 'data', a matrix containing sample observations and their feature values; 'shap_contrib', a matrix containing the SHAP contribution values for these observations. } \description{ Prepare data for SHAP plots. To be used in xgb.plot.shap, xgb.plot.shap.summary, etc. Internal utility function. } \keyword{internal} xgboost-1.5.2/R-package/man/xgb.train.Rd000066400000000000000000000434621417122711700177500ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.train.R, R/xgboost.R \name{xgb.train} \alias{xgb.train} \alias{xgboost} \title{eXtreme Gradient Boosting Training} \usage{ xgb.train( params = list(), data, nrounds, watchlist = list(), obj = NULL, feval = NULL, verbose = 1, print_every_n = 1L, early_stopping_rounds = NULL, maximize = NULL, save_period = NULL, save_name = "xgboost.model", xgb_model = NULL, callbacks = list(), ... ) xgboost( data = NULL, label = NULL, missing = NA, weight = NULL, params = list(), nrounds, verbose = 1, print_every_n = 1L, early_stopping_rounds = NULL, maximize = NULL, save_period = NULL, save_name = "xgboost.model", xgb_model = NULL, callbacks = list(), ... ) } \arguments{ \item{params}{the list of parameters. The complete list of parameters is available in the \href{http://xgboost.readthedocs.io/en/latest/parameter.html}{online documentation}. Below is a shorter summary: 1. General Parameters \itemize{ \item \code{booster} which booster to use, can be \code{gbtree} or \code{gblinear}. Default: \code{gbtree}. } 2. Booster Parameters 2.1. Parameters for Tree Booster \itemize{ \item \code{eta} control the learning rate: scale the contribution of each tree by a factor of \code{0 < eta < 1} when it is added to the current approximation. Used to prevent overfitting by making the boosting process more conservative. Lower value for \code{eta} implies larger value for \code{nrounds}: low \code{eta} value means model more robust to overfitting but slower to compute. Default: 0.3 \item \code{gamma} minimum loss reduction required to make a further partition on a leaf node of the tree. the larger, the more conservative the algorithm will be. \item \code{max_depth} maximum depth of a tree. Default: 6 \item \code{min_child_weight} minimum sum of instance weight (hessian) needed in a child. If the tree partition step results in a leaf node with the sum of instance weight less than min_child_weight, then the building process will give up further partitioning. In linear regression mode, this simply corresponds to minimum number of instances needed to be in each node. The larger, the more conservative the algorithm will be. Default: 1 \item \code{subsample} subsample ratio of the training instance. Setting it to 0.5 means that xgboost randomly collected half of the data instances to grow trees and this will prevent overfitting. It makes computation shorter (because less data to analyse). It is advised to use this parameter with \code{eta} and increase \code{nrounds}. Default: 1 \item \code{colsample_bytree} subsample ratio of columns when constructing each tree. Default: 1 \item \code{lambda} L2 regularization term on weights. Default: 1 \item \code{alpha} L1 regularization term on weights. (there is no L1 reg on bias because it is not important). Default: 0 \item \code{num_parallel_tree} Experimental parameter. number of trees to grow per round. Useful to test Random Forest through XGBoost (set \code{colsample_bytree < 1}, \code{subsample < 1} and \code{round = 1}) accordingly. Default: 1 \item \code{monotone_constraints} A numerical vector consists of \code{1}, \code{0} and \code{-1} with its length equals to the number of features in the training data. \code{1} is increasing, \code{-1} is decreasing and \code{0} is no constraint. \item \code{interaction_constraints} A list of vectors specifying feature indices of permitted interactions. Each item of the list represents one permitted interaction where specified features are allowed to interact with each other. Feature index values should start from \code{0} (\code{0} references the first column). Leave argument unspecified for no interaction constraints. } 2.2. Parameters for Linear Booster \itemize{ \item \code{lambda} L2 regularization term on weights. Default: 0 \item \code{lambda_bias} L2 regularization term on bias. Default: 0 \item \code{alpha} L1 regularization term on weights. (there is no L1 reg on bias because it is not important). Default: 0 } 3. Task Parameters \itemize{ \item \code{objective} specify the learning task and the corresponding learning objective, users can pass a self-defined function to it. The default objective options are below: \itemize{ \item \code{reg:squarederror} Regression with squared loss (Default). \item \code{reg:squaredlogerror}: regression with squared log loss \eqn{1/2 * (log(pred + 1) - log(label + 1))^2}. All inputs are required to be greater than -1. Also, see metric rmsle for possible issue with this objective. \item \code{reg:logistic} logistic regression. \item \code{reg:pseudohubererror}: regression with Pseudo Huber loss, a twice differentiable alternative to absolute loss. \item \code{binary:logistic} logistic regression for binary classification. Output probability. \item \code{binary:logitraw} logistic regression for binary classification, output score before logistic transformation. \item \code{binary:hinge}: hinge loss for binary classification. This makes predictions of 0 or 1, rather than producing probabilities. \item \code{count:poisson}: Poisson regression for count data, output mean of Poisson distribution. \code{max_delta_step} is set to 0.7 by default in poisson regression (used to safeguard optimization). \item \code{survival:cox}: Cox regression for right censored survival time data (negative values are considered right censored). Note that predictions are returned on the hazard ratio scale (i.e., as HR = exp(marginal_prediction) in the proportional hazard function \code{h(t) = h0(t) * HR)}. \item \code{survival:aft}: Accelerated failure time model for censored survival time data. See \href{https://xgboost.readthedocs.io/en/latest/tutorials/aft_survival_analysis.html}{Survival Analysis with Accelerated Failure Time} for details. \item \code{aft_loss_distribution}: Probability Density Function used by \code{survival:aft} and \code{aft-nloglik} metric. \item \code{multi:softmax} set xgboost to do multiclass classification using the softmax objective. Class is represented by a number and should be from 0 to \code{num_class - 1}. \item \code{multi:softprob} same as softmax, but prediction outputs a vector of ndata * nclass elements, which can be further reshaped to ndata, nclass matrix. The result contains predicted probabilities of each data point belonging to each class. \item \code{rank:pairwise} set xgboost to do ranking task by minimizing the pairwise loss. \item \code{rank:ndcg}: Use LambdaMART to perform list-wise ranking where \href{https://en.wikipedia.org/wiki/Discounted_cumulative_gain}{Normalized Discounted Cumulative Gain (NDCG)} is maximized. \item \code{rank:map}: Use LambdaMART to perform list-wise ranking where \href{https://en.wikipedia.org/wiki/Evaluation_measures_(information_retrieval)#Mean_average_precision}{Mean Average Precision (MAP)} is maximized. \item \code{reg:gamma}: gamma regression with log-link. Output is a mean of gamma distribution. It might be useful, e.g., for modeling insurance claims severity, or for any outcome that might be \href{https://en.wikipedia.org/wiki/Gamma_distribution#Applications}{gamma-distributed}. \item \code{reg:tweedie}: Tweedie regression with log-link. It might be useful, e.g., for modeling total loss in insurance, or for any outcome that might be \href{https://en.wikipedia.org/wiki/Tweedie_distribution#Applications}{Tweedie-distributed}. } \item \code{base_score} the initial prediction score of all instances, global bias. Default: 0.5 \item \code{eval_metric} evaluation metrics for validation data. Users can pass a self-defined function to it. Default: metric will be assigned according to objective(rmse for regression, and error for classification, mean average precision for ranking). List is provided in detail section. }} \item{data}{training dataset. \code{xgb.train} accepts only an \code{xgb.DMatrix} as the input. \code{xgboost}, in addition, also accepts \code{matrix}, \code{dgCMatrix}, or name of a local data file.} \item{nrounds}{max number of boosting iterations.} \item{watchlist}{named list of xgb.DMatrix datasets to use for evaluating model performance. Metrics specified in either \code{eval_metric} or \code{feval} will be computed for each of these datasets during each boosting iteration, and stored in the end as a field named \code{evaluation_log} in the resulting object. When either \code{verbose>=1} or \code{\link{cb.print.evaluation}} callback is engaged, the performance results are continuously printed out during the training. E.g., specifying \code{watchlist=list(validation1=mat1, validation2=mat2)} allows to track the performance of each round's model on mat1 and mat2.} \item{obj}{customized objective function. Returns gradient and second order gradient with given prediction and dtrain.} \item{feval}{customized evaluation function. Returns \code{list(metric='metric-name', value='metric-value')} with given prediction and dtrain.} \item{verbose}{If 0, xgboost will stay silent. If 1, it will print information about performance. If 2, some additional information will be printed out. Note that setting \code{verbose > 0} automatically engages the \code{cb.print.evaluation(period=1)} callback function.} \item{print_every_n}{Print each n-th iteration evaluation messages when \code{verbose>0}. Default is 1 which means all messages are printed. This parameter is passed to the \code{\link{cb.print.evaluation}} callback.} \item{early_stopping_rounds}{If \code{NULL}, the early stopping function is not triggered. If set to an integer \code{k}, training with a validation set will stop if the performance doesn't improve for \code{k} rounds. Setting this parameter engages the \code{\link{cb.early.stop}} callback.} \item{maximize}{If \code{feval} and \code{early_stopping_rounds} are set, then this parameter must be set as well. When it is \code{TRUE}, it means the larger the evaluation score the better. This parameter is passed to the \code{\link{cb.early.stop}} callback.} \item{save_period}{when it is non-NULL, model is saved to disk after every \code{save_period} rounds, 0 means save at the end. The saving is handled by the \code{\link{cb.save.model}} callback.} \item{save_name}{the name or path for periodically saved model file.} \item{xgb_model}{a previously built model to continue the training from. Could be either an object of class \code{xgb.Booster}, or its raw data, or the name of a file with a previously saved model.} \item{callbacks}{a list of callback functions to perform various task during boosting. See \code{\link{callbacks}}. Some of the callbacks are automatically created depending on the parameters' values. User can provide either existing or their own callback methods in order to customize the training process.} \item{...}{other parameters to pass to \code{params}.} \item{label}{vector of response values. Should not be provided when data is a local data file name or an \code{xgb.DMatrix}.} \item{missing}{by default is set to NA, which means that NA values should be considered as 'missing' by the algorithm. Sometimes, 0 or other extreme value might be used to represent missing values. This parameter is only used when input is a dense matrix.} \item{weight}{a vector indicating the weight for each row of the input.} } \value{ An object of class \code{xgb.Booster} with the following elements: \itemize{ \item \code{handle} a handle (pointer) to the xgboost model in memory. \item \code{raw} a cached memory dump of the xgboost model saved as R's \code{raw} type. \item \code{niter} number of boosting iterations. \item \code{evaluation_log} evaluation history stored as a \code{data.table} with the first column corresponding to iteration number and the rest corresponding to evaluation metrics' values. It is created by the \code{\link{cb.evaluation.log}} callback. \item \code{call} a function call. \item \code{params} parameters that were passed to the xgboost library. Note that it does not capture parameters changed by the \code{\link{cb.reset.parameters}} callback. \item \code{callbacks} callback functions that were either automatically assigned or explicitly passed. \item \code{best_iteration} iteration number with the best evaluation metric value (only available with early stopping). \item \code{best_score} the best evaluation metric value during early stopping. (only available with early stopping). \item \code{feature_names} names of the training dataset features (only when column names were defined in training data). \item \code{nfeatures} number of features in training data. } } \description{ \code{xgb.train} is an advanced interface for training an xgboost model. The \code{xgboost} function is a simpler wrapper for \code{xgb.train}. } \details{ These are the training functions for \code{xgboost}. The \code{xgb.train} interface supports advanced features such as \code{watchlist}, customized objective and evaluation metric functions, therefore it is more flexible than the \code{xgboost} interface. Parallelization is automatically enabled if \code{OpenMP} is present. Number of threads can also be manually specified via \code{nthread} parameter. The evaluation metric is chosen automatically by XGBoost (according to the objective) when the \code{eval_metric} parameter is not provided. User may set one or several \code{eval_metric} parameters. Note that when using a customized metric, only this single metric can be used. The following is the list of built-in metrics for which XGBoost provides optimized implementation: \itemize{ \item \code{rmse} root mean square error. \url{https://en.wikipedia.org/wiki/Root_mean_square_error} \item \code{logloss} negative log-likelihood. \url{https://en.wikipedia.org/wiki/Log-likelihood} \item \code{mlogloss} multiclass logloss. \url{https://scikit-learn.org/stable/modules/generated/sklearn.metrics.log_loss.html} \item \code{error} Binary classification error rate. It is calculated as \code{(# wrong cases) / (# all cases)}. By default, it uses the 0.5 threshold for predicted values to define negative and positive instances. Different threshold (e.g., 0.) could be specified as "error@0." \item \code{merror} Multiclass classification error rate. It is calculated as \code{(# wrong cases) / (# all cases)}. \item \code{mae} Mean absolute error \item \code{mape} Mean absolute percentage error \item \code{auc} Area under the curve. \url{https://en.wikipedia.org/wiki/Receiver_operating_characteristic#'Area_under_curve} for ranking evaluation. \item \code{aucpr} Area under the PR curve. \url{https://en.wikipedia.org/wiki/Precision_and_recall} for ranking evaluation. \item \code{ndcg} Normalized Discounted Cumulative Gain (for ranking task). \url{https://en.wikipedia.org/wiki/NDCG} } The following callbacks are automatically created when certain parameters are set: \itemize{ \item \code{cb.print.evaluation} is turned on when \code{verbose > 0}; and the \code{print_every_n} parameter is passed to it. \item \code{cb.evaluation.log} is on when \code{watchlist} is present. \item \code{cb.early.stop}: when \code{early_stopping_rounds} is set. \item \code{cb.save.model}: when \code{save_period > 0} is set. } } \examples{ data(agaricus.train, package='xgboost') data(agaricus.test, package='xgboost') dtrain <- with(agaricus.train, xgb.DMatrix(data, label = label)) dtest <- with(agaricus.test, xgb.DMatrix(data, label = label)) watchlist <- list(train = dtrain, eval = dtest) ## A simple xgb.train example: param <- list(max_depth = 2, eta = 1, verbose = 0, nthread = 2, objective = "binary:logistic", eval_metric = "auc") bst <- xgb.train(param, dtrain, nrounds = 2, watchlist) ## An xgb.train example where custom objective and evaluation metric are used: logregobj <- function(preds, dtrain) { labels <- getinfo(dtrain, "label") preds <- 1/(1 + exp(-preds)) grad <- preds - labels hess <- preds * (1 - preds) return(list(grad = grad, hess = hess)) } evalerror <- function(preds, dtrain) { labels <- getinfo(dtrain, "label") err <- as.numeric(sum(labels != (preds > 0)))/length(labels) return(list(metric = "error", value = err)) } # These functions could be used by passing them either: # as 'objective' and 'eval_metric' parameters in the params list: param <- list(max_depth = 2, eta = 1, verbose = 0, nthread = 2, objective = logregobj, eval_metric = evalerror) bst <- xgb.train(param, dtrain, nrounds = 2, watchlist) # or through the ... arguments: param <- list(max_depth = 2, eta = 1, verbose = 0, nthread = 2) bst <- xgb.train(param, dtrain, nrounds = 2, watchlist, objective = logregobj, eval_metric = evalerror) # or as dedicated 'obj' and 'feval' parameters of xgb.train: bst <- xgb.train(param, dtrain, nrounds = 2, watchlist, obj = logregobj, feval = evalerror) ## An xgb.train example of using variable learning rates at each iteration: param <- list(max_depth = 2, eta = 1, verbose = 0, nthread = 2, objective = "binary:logistic", eval_metric = "auc") my_etas <- list(eta = c(0.5, 0.1)) bst <- xgb.train(param, dtrain, nrounds = 2, watchlist, callbacks = list(cb.reset.parameters(my_etas))) ## Early stopping: bst <- xgb.train(param, dtrain, nrounds = 25, watchlist, early_stopping_rounds = 3) ## An 'xgboost' interface example: bst <- xgboost(data = agaricus.train$data, label = agaricus.train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") pred <- predict(bst, agaricus.test$data) } \references{ Tianqi Chen and Carlos Guestrin, "XGBoost: A Scalable Tree Boosting System", 22nd SIGKDD Conference on Knowledge Discovery and Data Mining, 2016, \url{https://arxiv.org/abs/1603.02754} } \seealso{ \code{\link{callbacks}}, \code{\link{predict.xgb.Booster}}, \code{\link{xgb.cv}} } xgboost-1.5.2/R-package/man/xgb.unserialize.Rd000066400000000000000000000013061417122711700211540ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.unserialize.R \name{xgb.unserialize} \alias{xgb.unserialize} \title{Load the instance back from \code{\link{xgb.serialize}}} \usage{ xgb.unserialize(buffer, handle = NULL) } \arguments{ \item{buffer}{the buffer containing booster instance saved by \code{\link{xgb.serialize}}} \item{handle}{An \code{xgb.Booster.handle} object which will be overwritten with the new deserialized object. Must be a null handle (e.g. when loading the model through `readRDS`). If not provided, a new handle will be created.} } \value{ An \code{xgb.Booster.handle} object. } \description{ Load the instance back from \code{\link{xgb.serialize}} } xgboost-1.5.2/R-package/man/xgbConfig.Rd000066400000000000000000000025221417122711700177520ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/xgb.config.R \name{xgb.set.config, xgb.get.config} \alias{xgb.set.config, xgb.get.config} \alias{xgb.set.config} \alias{xgb.get.config} \title{Set and get global configuration} \usage{ xgb.set.config(...) xgb.get.config() } \arguments{ \item{...}{List of parameters to be set, as keyword arguments} } \value{ \code{xgb.set.config} returns \code{TRUE} to signal success. \code{xgb.get.config} returns a list containing all global-scope parameters and their values. } \description{ Global configuration consists of a collection of parameters that can be applied in the global scope. See \url{https://xgboost.readthedocs.io/en/stable/parameter.html} for the full list of parameters supported in the global configuration. Use \code{xgb.set.config} to update the values of one or more global-scope parameters. Use \code{xgb.get.config} to fetch the current values of all global-scope parameters (listed in \url{https://xgboost.readthedocs.io/en/stable/parameter.html}). } \examples{ # Set verbosity level to silent (0) xgb.set.config(verbosity = 0) # Now global verbosity level is 0 config <- xgb.get.config() print(config$verbosity) # Set verbosity level to warning (1) xgb.set.config(verbosity = 1) # Now global verbosity level is 1 config <- xgb.get.config() print(config$verbosity) } xgboost-1.5.2/R-package/man/xgboost-deprecated.Rd000066400000000000000000000012621417122711700216270ustar00rootroot00000000000000% Generated by roxygen2: do not edit by hand % Please edit documentation in R/utils.R \name{xgboost-deprecated} \alias{xgboost-deprecated} \title{Deprecation notices.} \description{ At this time, some of the parameter names were changed in order to make the code style more uniform. The deprecated parameters would be removed in the next release. } \details{ To see all the current deprecated and new parameters, check the \code{xgboost:::depr_par_lut} table. A deprecation warning is shown when any of the deprecated parameters is used in a call. An additional warning is shown when there was a partial match to a deprecated parameter (as R is able to partially match parameter names). } xgboost-1.5.2/R-package/remove_warning_suppression_pragma.sh000077500000000000000000000005541417122711700243670ustar00rootroot00000000000000#!/bin/bash # remove all #pragma's that suppress compiler warnings set -e set -x for file in xgboost/src/dmlc-core/include/dmlc/*.h do sed -i.bak -e 's/^.*#pragma GCC diagnostic.*$//' -e 's/^.*#pragma clang diagnostic.*$//' -e 's/^.*#pragma warning.*$//' "${file}" done for file in xgboost/src/dmlc-core/include/dmlc/*.h.bak do rm "${file}" done set +x set +e xgboost-1.5.2/R-package/src/000077500000000000000000000000001417122711700155705ustar00rootroot00000000000000xgboost-1.5.2/R-package/src/Makevars.in000066400000000000000000000020751417122711700176750ustar00rootroot00000000000000# package root PKGROOT=../../ ENABLE_STD_THREAD=1 # _*_ mode: Makefile; _*_ CXX_STD = CXX14 XGB_RFLAGS = -DXGBOOST_STRICT_R_MODE=1 -DDMLC_LOG_BEFORE_THROW=0\ -DDMLC_ENABLE_STD_THREAD=$(ENABLE_STD_THREAD) -DDMLC_DISABLE_STDIN=1\ -DDMLC_LOG_CUSTOMIZE=1 -DXGBOOST_CUSTOMIZE_LOGGER=1\ -DRABIT_CUSTOMIZE_MSG_ # disable the use of thread_local for 32 bit windows: ifeq ($(R_OSTYPE)$(WIN),windows) XGB_RFLAGS += -DDMLC_CXX11_THREAD_LOCAL=0 endif $(foreach v, $(XGB_RFLAGS), $(warning $(v))) PKG_CPPFLAGS= -I$(PKGROOT)/include -I$(PKGROOT)/dmlc-core/include -I$(PKGROOT)/rabit/include -I$(PKGROOT) $(XGB_RFLAGS) PKG_CXXFLAGS= @OPENMP_CXXFLAGS@ @ENDIAN_FLAG@ -pthread $(CXX_VISIBILITY) PKG_LIBS = @OPENMP_CXXFLAGS@ @OPENMP_LIB@ @ENDIAN_FLAG@ @BACKTRACE_LIB@ -pthread OBJECTS= ./xgboost_R.o ./xgboost_custom.o ./xgboost_assert.o ./init.o \ $(PKGROOT)/amalgamation/xgboost-all0.o $(PKGROOT)/amalgamation/dmlc-minimum0.o \ $(PKGROOT)/rabit/src/engine.o $(PKGROOT)/rabit/src/rabit_c_api.o \ $(PKGROOT)/rabit/src/allreduce_base.o xgboost-1.5.2/R-package/src/Makevars.win000066400000000000000000000025251417122711700200640ustar00rootroot00000000000000# package root PKGROOT=./ ENABLE_STD_THREAD=0 # _*_ mode: Makefile; _*_ # This file is only used for Windows compilation from GitHub # It will be replaced with Makevars.in for the CRAN version .PHONY: all xgblib all: $(SHLIB) $(SHLIB): xgblib xgblib: cp -r ../../src . cp -r ../../rabit . cp -r ../../dmlc-core . cp -r ../../include . cp -r ../../amalgamation . CXX_STD = CXX14 XGB_RFLAGS = -DXGBOOST_STRICT_R_MODE=1 -DDMLC_LOG_BEFORE_THROW=0\ -DDMLC_ENABLE_STD_THREAD=$(ENABLE_STD_THREAD) -DDMLC_DISABLE_STDIN=1\ -DDMLC_LOG_CUSTOMIZE=1 -DXGBOOST_CUSTOMIZE_LOGGER=1\ -DRABIT_CUSTOMIZE_MSG_ # disable the use of thread_local for 32 bit windows: ifeq ($(R_OSTYPE)$(WIN),windows) XGB_RFLAGS += -DDMLC_CXX11_THREAD_LOCAL=0 endif $(foreach v, $(XGB_RFLAGS), $(warning $(v))) PKG_CPPFLAGS= -I$(PKGROOT)/include -I$(PKGROOT)/dmlc-core/include -I$(PKGROOT)/rabit/include -I$(PKGROOT) $(XGB_RFLAGS) PKG_CXXFLAGS= $(SHLIB_OPENMP_CXXFLAGS) $(SHLIB_PTHREAD_FLAGS) PKG_LIBS = $(SHLIB_OPENMP_CXXFLAGS) $(SHLIB_PTHREAD_FLAGS) OBJECTS= ./xgboost_R.o ./xgboost_custom.o ./xgboost_assert.o ./init.o \ $(PKGROOT)/amalgamation/xgboost-all0.o $(PKGROOT)/amalgamation/dmlc-minimum0.o \ $(PKGROOT)/rabit/src/engine.o $(PKGROOT)/rabit/src/rabit_c_api.o \ $(PKGROOT)/rabit/src/allreduce_base.o $(OBJECTS) : xgblib xgboost-1.5.2/R-package/src/init.c000066400000000000000000000120231417122711700166750ustar00rootroot00000000000000/* Copyright (c) 2015 by Contributors * * This file was initially generated using the following R command: * tools::package_native_routine_registration_skeleton('.', con = 'src/init.c', character_only = F) * and edited to conform to xgboost C linter requirements. For details, see * https://cran.r-project.org/doc/manuals/r-release/R-exts.html#Registering-native-routines */ #include #include #include #include #include /* FIXME: Check these declarations against the C/Fortran source code. */ /* .Call calls */ extern SEXP XGBoosterBoostOneIter_R(SEXP, SEXP, SEXP, SEXP); extern SEXP XGBoosterCreate_R(SEXP); extern SEXP XGBoosterCreateInEmptyObj_R(SEXP, SEXP); extern SEXP XGBoosterDumpModel_R(SEXP, SEXP, SEXP, SEXP); extern SEXP XGBoosterEvalOneIter_R(SEXP, SEXP, SEXP, SEXP); extern SEXP XGBoosterGetAttrNames_R(SEXP); extern SEXP XGBoosterGetAttr_R(SEXP, SEXP); extern SEXP XGBoosterLoadModelFromRaw_R(SEXP, SEXP); extern SEXP XGBoosterLoadModel_R(SEXP, SEXP); extern SEXP XGBoosterSaveJsonConfig_R(SEXP handle); extern SEXP XGBoosterLoadJsonConfig_R(SEXP handle, SEXP value); extern SEXP XGBoosterSerializeToBuffer_R(SEXP handle); extern SEXP XGBoosterUnserializeFromBuffer_R(SEXP handle, SEXP raw); extern SEXP XGBoosterModelToRaw_R(SEXP); extern SEXP XGBoosterPredict_R(SEXP, SEXP, SEXP, SEXP, SEXP); extern SEXP XGBoosterPredictFromDMatrix_R(SEXP, SEXP, SEXP); extern SEXP XGBoosterSaveModel_R(SEXP, SEXP); extern SEXP XGBoosterSetAttr_R(SEXP, SEXP, SEXP); extern SEXP XGBoosterSetParam_R(SEXP, SEXP, SEXP); extern SEXP XGBoosterUpdateOneIter_R(SEXP, SEXP, SEXP); extern SEXP XGCheckNullPtr_R(SEXP); extern SEXP XGDMatrixCreateFromCSC_R(SEXP, SEXP, SEXP, SEXP); extern SEXP XGDMatrixCreateFromFile_R(SEXP, SEXP); extern SEXP XGDMatrixCreateFromMat_R(SEXP, SEXP, SEXP); extern SEXP XGDMatrixGetInfo_R(SEXP, SEXP); extern SEXP XGDMatrixNumCol_R(SEXP); extern SEXP XGDMatrixNumRow_R(SEXP); extern SEXP XGDMatrixSaveBinary_R(SEXP, SEXP, SEXP); extern SEXP XGDMatrixSetInfo_R(SEXP, SEXP, SEXP); extern SEXP XGDMatrixSliceDMatrix_R(SEXP, SEXP); extern SEXP XGBSetGlobalConfig_R(SEXP); extern SEXP XGBGetGlobalConfig_R(); extern SEXP XGBoosterFeatureScore_R(SEXP, SEXP); static const R_CallMethodDef CallEntries[] = { {"XGBoosterBoostOneIter_R", (DL_FUNC) &XGBoosterBoostOneIter_R, 4}, {"XGBoosterCreate_R", (DL_FUNC) &XGBoosterCreate_R, 1}, {"XGBoosterCreateInEmptyObj_R", (DL_FUNC) &XGBoosterCreateInEmptyObj_R, 2}, {"XGBoosterDumpModel_R", (DL_FUNC) &XGBoosterDumpModel_R, 4}, {"XGBoosterEvalOneIter_R", (DL_FUNC) &XGBoosterEvalOneIter_R, 4}, {"XGBoosterGetAttrNames_R", (DL_FUNC) &XGBoosterGetAttrNames_R, 1}, {"XGBoosterGetAttr_R", (DL_FUNC) &XGBoosterGetAttr_R, 2}, {"XGBoosterLoadModelFromRaw_R", (DL_FUNC) &XGBoosterLoadModelFromRaw_R, 2}, {"XGBoosterLoadModel_R", (DL_FUNC) &XGBoosterLoadModel_R, 2}, {"XGBoosterSaveJsonConfig_R", (DL_FUNC) &XGBoosterSaveJsonConfig_R, 1}, {"XGBoosterLoadJsonConfig_R", (DL_FUNC) &XGBoosterLoadJsonConfig_R, 2}, {"XGBoosterSerializeToBuffer_R", (DL_FUNC) &XGBoosterSerializeToBuffer_R, 1}, {"XGBoosterUnserializeFromBuffer_R", (DL_FUNC) &XGBoosterUnserializeFromBuffer_R, 2}, {"XGBoosterModelToRaw_R", (DL_FUNC) &XGBoosterModelToRaw_R, 1}, {"XGBoosterPredict_R", (DL_FUNC) &XGBoosterPredict_R, 5}, {"XGBoosterPredictFromDMatrix_R", (DL_FUNC) &XGBoosterPredictFromDMatrix_R, 3}, {"XGBoosterSaveModel_R", (DL_FUNC) &XGBoosterSaveModel_R, 2}, {"XGBoosterSetAttr_R", (DL_FUNC) &XGBoosterSetAttr_R, 3}, {"XGBoosterSetParam_R", (DL_FUNC) &XGBoosterSetParam_R, 3}, {"XGBoosterUpdateOneIter_R", (DL_FUNC) &XGBoosterUpdateOneIter_R, 3}, {"XGCheckNullPtr_R", (DL_FUNC) &XGCheckNullPtr_R, 1}, {"XGDMatrixCreateFromCSC_R", (DL_FUNC) &XGDMatrixCreateFromCSC_R, 4}, {"XGDMatrixCreateFromFile_R", (DL_FUNC) &XGDMatrixCreateFromFile_R, 2}, {"XGDMatrixCreateFromMat_R", (DL_FUNC) &XGDMatrixCreateFromMat_R, 3}, {"XGDMatrixGetInfo_R", (DL_FUNC) &XGDMatrixGetInfo_R, 2}, {"XGDMatrixNumCol_R", (DL_FUNC) &XGDMatrixNumCol_R, 1}, {"XGDMatrixNumRow_R", (DL_FUNC) &XGDMatrixNumRow_R, 1}, {"XGDMatrixSaveBinary_R", (DL_FUNC) &XGDMatrixSaveBinary_R, 3}, {"XGDMatrixSetInfo_R", (DL_FUNC) &XGDMatrixSetInfo_R, 3}, {"XGDMatrixSliceDMatrix_R", (DL_FUNC) &XGDMatrixSliceDMatrix_R, 2}, {"XGBSetGlobalConfig_R", (DL_FUNC) &XGBSetGlobalConfig_R, 1}, {"XGBGetGlobalConfig_R", (DL_FUNC) &XGBGetGlobalConfig_R, 0}, {"XGBoosterFeatureScore_R", (DL_FUNC) &XGBoosterFeatureScore_R, 2}, {NULL, NULL, 0} }; #if defined(_WIN32) __declspec(dllexport) #endif // defined(_WIN32) void attribute_visible R_init_xgboost(DllInfo *dll) { R_registerRoutines(dll, NULL, CallEntries, NULL, NULL); R_useDynamicSymbols(dll, FALSE); } xgboost-1.5.2/R-package/src/xgboost-win.def000066400000000000000000000000541417122711700205270ustar00rootroot00000000000000LIBRARY xgboost.dll EXPORTS R_init_xgboost xgboost-1.5.2/R-package/src/xgboost_R.cc000066400000000000000000000442571417122711700200610ustar00rootroot00000000000000// Copyright (c) 2014 by Contributors #include #include #include #include #include #include #include #include #include #include #include "../../src/common/threading_utils.h" #include "./xgboost_R.h" /*! * \brief macro to annotate begin of api */ #define R_API_BEGIN() \ GetRNGstate(); \ try { /*! * \brief macro to annotate end of api */ #define R_API_END() \ } catch(dmlc::Error& e) { \ PutRNGstate(); \ error(e.what()); \ } \ PutRNGstate(); /*! * \brief macro to check the call. */ #define CHECK_CALL(x) \ if ((x) != 0) { \ error(XGBGetLastError()); \ } using namespace dmlc; XGB_DLL SEXP XGCheckNullPtr_R(SEXP handle) { return ScalarLogical(R_ExternalPtrAddr(handle) == NULL); } XGB_DLL void _DMatrixFinalizer(SEXP ext) { R_API_BEGIN(); if (R_ExternalPtrAddr(ext) == NULL) return; CHECK_CALL(XGDMatrixFree(R_ExternalPtrAddr(ext))); R_ClearExternalPtr(ext); R_API_END(); } XGB_DLL SEXP XGBSetGlobalConfig_R(SEXP json_str) { R_API_BEGIN(); CHECK_CALL(XGBSetGlobalConfig(CHAR(asChar(json_str)))); R_API_END(); return R_NilValue; } XGB_DLL SEXP XGBGetGlobalConfig_R() { const char* json_str; R_API_BEGIN(); CHECK_CALL(XGBGetGlobalConfig(&json_str)); R_API_END(); return mkString(json_str); } XGB_DLL SEXP XGDMatrixCreateFromFile_R(SEXP fname, SEXP silent) { SEXP ret; R_API_BEGIN(); DMatrixHandle handle; CHECK_CALL(XGDMatrixCreateFromFile(CHAR(asChar(fname)), asInteger(silent), &handle)); ret = PROTECT(R_MakeExternalPtr(handle, R_NilValue, R_NilValue)); R_RegisterCFinalizerEx(ret, _DMatrixFinalizer, TRUE); R_API_END(); UNPROTECT(1); return ret; } XGB_DLL SEXP XGDMatrixCreateFromMat_R(SEXP mat, SEXP missing, SEXP n_threads) { SEXP ret; R_API_BEGIN(); SEXP dim = getAttrib(mat, R_DimSymbol); size_t nrow = static_cast(INTEGER(dim)[0]); size_t ncol = static_cast(INTEGER(dim)[1]); const bool is_int = TYPEOF(mat) == INTSXP; double *din; int *iin; if (is_int) { iin = INTEGER(mat); } else { din = REAL(mat); } std::vector data(nrow * ncol); dmlc::OMPException exc; int32_t threads = xgboost::common::OmpGetNumThreads(asInteger(n_threads)); #pragma omp parallel for schedule(static) num_threads(threads) for (omp_ulong i = 0; i < nrow; ++i) { exc.Run([&]() { for (size_t j = 0; j < ncol; ++j) { data[i * ncol +j] = is_int ? static_cast(iin[i + nrow * j]) : din[i + nrow * j]; } }); } exc.Rethrow(); DMatrixHandle handle; CHECK_CALL(XGDMatrixCreateFromMat_omp(BeginPtr(data), nrow, ncol, asReal(missing), &handle, threads)); ret = PROTECT(R_MakeExternalPtr(handle, R_NilValue, R_NilValue)); R_RegisterCFinalizerEx(ret, _DMatrixFinalizer, TRUE); R_API_END(); UNPROTECT(1); return ret; } XGB_DLL SEXP XGDMatrixCreateFromCSC_R(SEXP indptr, SEXP indices, SEXP data, SEXP num_row) { SEXP ret; R_API_BEGIN(); const int *p_indptr = INTEGER(indptr); const int *p_indices = INTEGER(indices); const double *p_data = REAL(data); size_t nindptr = static_cast(length(indptr)); size_t ndata = static_cast(length(data)); size_t nrow = static_cast(INTEGER(num_row)[0]); std::vector col_ptr_(nindptr); std::vector indices_(ndata); std::vector data_(ndata); for (size_t i = 0; i < nindptr; ++i) { col_ptr_[i] = static_cast(p_indptr[i]); } dmlc::OMPException exc; #pragma omp parallel for schedule(static) for (int64_t i = 0; i < static_cast(ndata); ++i) { exc.Run([&]() { indices_[i] = static_cast(p_indices[i]); data_[i] = static_cast(p_data[i]); }); } exc.Rethrow(); DMatrixHandle handle; CHECK_CALL(XGDMatrixCreateFromCSCEx(BeginPtr(col_ptr_), BeginPtr(indices_), BeginPtr(data_), nindptr, ndata, nrow, &handle)); ret = PROTECT(R_MakeExternalPtr(handle, R_NilValue, R_NilValue)); R_RegisterCFinalizerEx(ret, _DMatrixFinalizer, TRUE); R_API_END(); UNPROTECT(1); return ret; } XGB_DLL SEXP XGDMatrixSliceDMatrix_R(SEXP handle, SEXP idxset) { SEXP ret; R_API_BEGIN(); int len = length(idxset); std::vector idxvec(len); for (int i = 0; i < len; ++i) { idxvec[i] = INTEGER(idxset)[i] - 1; } DMatrixHandle res; CHECK_CALL(XGDMatrixSliceDMatrixEx(R_ExternalPtrAddr(handle), BeginPtr(idxvec), len, &res, 0)); ret = PROTECT(R_MakeExternalPtr(res, R_NilValue, R_NilValue)); R_RegisterCFinalizerEx(ret, _DMatrixFinalizer, TRUE); R_API_END(); UNPROTECT(1); return ret; } XGB_DLL SEXP XGDMatrixSaveBinary_R(SEXP handle, SEXP fname, SEXP silent) { R_API_BEGIN(); CHECK_CALL(XGDMatrixSaveBinary(R_ExternalPtrAddr(handle), CHAR(asChar(fname)), asInteger(silent))); R_API_END(); return R_NilValue; } XGB_DLL SEXP XGDMatrixSetInfo_R(SEXP handle, SEXP field, SEXP array) { R_API_BEGIN(); int len = length(array); const char *name = CHAR(asChar(field)); dmlc::OMPException exc; if (!strcmp("group", name)) { std::vector vec(len); #pragma omp parallel for schedule(static) for (int i = 0; i < len; ++i) { exc.Run([&]() { vec[i] = static_cast(INTEGER(array)[i]); }); } exc.Rethrow(); CHECK_CALL(XGDMatrixSetUIntInfo(R_ExternalPtrAddr(handle), CHAR(asChar(field)), BeginPtr(vec), len)); } else { std::vector vec(len); #pragma omp parallel for schedule(static) for (int i = 0; i < len; ++i) { exc.Run([&]() { vec[i] = REAL(array)[i]; }); } exc.Rethrow(); CHECK_CALL(XGDMatrixSetFloatInfo(R_ExternalPtrAddr(handle), CHAR(asChar(field)), BeginPtr(vec), len)); } R_API_END(); return R_NilValue; } XGB_DLL SEXP XGDMatrixGetInfo_R(SEXP handle, SEXP field) { SEXP ret; R_API_BEGIN(); bst_ulong olen; const float *res; CHECK_CALL(XGDMatrixGetFloatInfo(R_ExternalPtrAddr(handle), CHAR(asChar(field)), &olen, &res)); ret = PROTECT(allocVector(REALSXP, olen)); for (size_t i = 0; i < olen; ++i) { REAL(ret)[i] = res[i]; } R_API_END(); UNPROTECT(1); return ret; } XGB_DLL SEXP XGDMatrixNumRow_R(SEXP handle) { bst_ulong nrow; R_API_BEGIN(); CHECK_CALL(XGDMatrixNumRow(R_ExternalPtrAddr(handle), &nrow)); R_API_END(); return ScalarInteger(static_cast(nrow)); } XGB_DLL SEXP XGDMatrixNumCol_R(SEXP handle) { bst_ulong ncol; R_API_BEGIN(); CHECK_CALL(XGDMatrixNumCol(R_ExternalPtrAddr(handle), &ncol)); R_API_END(); return ScalarInteger(static_cast(ncol)); } // functions related to booster void _BoosterFinalizer(SEXP ext) { if (R_ExternalPtrAddr(ext) == NULL) return; CHECK_CALL(XGBoosterFree(R_ExternalPtrAddr(ext))); R_ClearExternalPtr(ext); } XGB_DLL SEXP XGBoosterCreate_R(SEXP dmats) { SEXP ret; R_API_BEGIN(); int len = length(dmats); std::vector dvec; for (int i = 0; i < len; ++i) { dvec.push_back(R_ExternalPtrAddr(VECTOR_ELT(dmats, i))); } BoosterHandle handle; CHECK_CALL(XGBoosterCreate(BeginPtr(dvec), dvec.size(), &handle)); ret = PROTECT(R_MakeExternalPtr(handle, R_NilValue, R_NilValue)); R_RegisterCFinalizerEx(ret, _BoosterFinalizer, TRUE); R_API_END(); UNPROTECT(1); return ret; } XGB_DLL SEXP XGBoosterCreateInEmptyObj_R(SEXP dmats, SEXP R_handle) { R_API_BEGIN(); int len = length(dmats); std::vector dvec; for (int i = 0; i < len; ++i) { dvec.push_back(R_ExternalPtrAddr(VECTOR_ELT(dmats, i))); } BoosterHandle handle; CHECK_CALL(XGBoosterCreate(BeginPtr(dvec), dvec.size(), &handle)); R_SetExternalPtrAddr(R_handle, handle); R_RegisterCFinalizerEx(R_handle, _BoosterFinalizer, TRUE); R_API_END(); return R_NilValue; } XGB_DLL SEXP XGBoosterSetParam_R(SEXP handle, SEXP name, SEXP val) { R_API_BEGIN(); CHECK_CALL(XGBoosterSetParam(R_ExternalPtrAddr(handle), CHAR(asChar(name)), CHAR(asChar(val)))); R_API_END(); return R_NilValue; } XGB_DLL SEXP XGBoosterUpdateOneIter_R(SEXP handle, SEXP iter, SEXP dtrain) { R_API_BEGIN(); CHECK_CALL(XGBoosterUpdateOneIter(R_ExternalPtrAddr(handle), asInteger(iter), R_ExternalPtrAddr(dtrain))); R_API_END(); return R_NilValue; } XGB_DLL SEXP XGBoosterBoostOneIter_R(SEXP handle, SEXP dtrain, SEXP grad, SEXP hess) { R_API_BEGIN(); CHECK_EQ(length(grad), length(hess)) << "gradient and hess must have same length"; int len = length(grad); std::vector tgrad(len), thess(len); dmlc::OMPException exc; #pragma omp parallel for schedule(static) for (int j = 0; j < len; ++j) { exc.Run([&]() { tgrad[j] = REAL(grad)[j]; thess[j] = REAL(hess)[j]; }); } exc.Rethrow(); CHECK_CALL(XGBoosterBoostOneIter(R_ExternalPtrAddr(handle), R_ExternalPtrAddr(dtrain), BeginPtr(tgrad), BeginPtr(thess), len)); R_API_END(); return R_NilValue; } XGB_DLL SEXP XGBoosterEvalOneIter_R(SEXP handle, SEXP iter, SEXP dmats, SEXP evnames) { const char *ret; R_API_BEGIN(); CHECK_EQ(length(dmats), length(evnames)) << "dmats and evnams must have same length"; int len = length(dmats); std::vector vec_dmats; std::vector vec_names; std::vector vec_sptr; for (int i = 0; i < len; ++i) { vec_dmats.push_back(R_ExternalPtrAddr(VECTOR_ELT(dmats, i))); vec_names.push_back(std::string(CHAR(asChar(VECTOR_ELT(evnames, i))))); } for (int i = 0; i < len; ++i) { vec_sptr.push_back(vec_names[i].c_str()); } CHECK_CALL(XGBoosterEvalOneIter(R_ExternalPtrAddr(handle), asInteger(iter), BeginPtr(vec_dmats), BeginPtr(vec_sptr), len, &ret)); R_API_END(); return mkString(ret); } XGB_DLL SEXP XGBoosterPredict_R(SEXP handle, SEXP dmat, SEXP option_mask, SEXP ntree_limit, SEXP training) { SEXP ret; R_API_BEGIN(); bst_ulong olen; const float *res; CHECK_CALL(XGBoosterPredict(R_ExternalPtrAddr(handle), R_ExternalPtrAddr(dmat), asInteger(option_mask), asInteger(ntree_limit), asInteger(training), &olen, &res)); ret = PROTECT(allocVector(REALSXP, olen)); for (size_t i = 0; i < olen; ++i) { REAL(ret)[i] = res[i]; } R_API_END(); UNPROTECT(1); return ret; } XGB_DLL SEXP XGBoosterPredictFromDMatrix_R(SEXP handle, SEXP dmat, SEXP json_config) { SEXP r_out_shape; SEXP r_out_result; SEXP r_out; R_API_BEGIN(); char const *c_json_config = CHAR(asChar(json_config)); bst_ulong out_dim; bst_ulong const *out_shape; float const *out_result; CHECK_CALL(XGBoosterPredictFromDMatrix(R_ExternalPtrAddr(handle), R_ExternalPtrAddr(dmat), c_json_config, &out_shape, &out_dim, &out_result)); r_out_shape = PROTECT(allocVector(INTSXP, out_dim)); size_t len = 1; for (size_t i = 0; i < out_dim; ++i) { INTEGER(r_out_shape)[i] = out_shape[i]; len *= out_shape[i]; } r_out_result = PROTECT(allocVector(REALSXP, len)); #pragma omp parallel for for (omp_ulong i = 0; i < len; ++i) { REAL(r_out_result)[i] = out_result[i]; } r_out = PROTECT(allocVector(VECSXP, 2)); SET_VECTOR_ELT(r_out, 0, r_out_shape); SET_VECTOR_ELT(r_out, 1, r_out_result); R_API_END(); UNPROTECT(3); return r_out; } XGB_DLL SEXP XGBoosterLoadModel_R(SEXP handle, SEXP fname) { R_API_BEGIN(); CHECK_CALL(XGBoosterLoadModel(R_ExternalPtrAddr(handle), CHAR(asChar(fname)))); R_API_END(); return R_NilValue; } XGB_DLL SEXP XGBoosterSaveModel_R(SEXP handle, SEXP fname) { R_API_BEGIN(); CHECK_CALL(XGBoosterSaveModel(R_ExternalPtrAddr(handle), CHAR(asChar(fname)))); R_API_END(); return R_NilValue; } XGB_DLL SEXP XGBoosterModelToRaw_R(SEXP handle) { SEXP ret; R_API_BEGIN(); bst_ulong olen; const char *raw; CHECK_CALL(XGBoosterGetModelRaw(R_ExternalPtrAddr(handle), &olen, &raw)); ret = PROTECT(allocVector(RAWSXP, olen)); if (olen != 0) { memcpy(RAW(ret), raw, olen); } R_API_END(); UNPROTECT(1); return ret; } XGB_DLL SEXP XGBoosterLoadModelFromRaw_R(SEXP handle, SEXP raw) { R_API_BEGIN(); CHECK_CALL(XGBoosterLoadModelFromBuffer(R_ExternalPtrAddr(handle), RAW(raw), length(raw))); R_API_END(); return R_NilValue; } XGB_DLL SEXP XGBoosterSaveJsonConfig_R(SEXP handle) { const char* ret; R_API_BEGIN(); bst_ulong len {0}; CHECK_CALL(XGBoosterSaveJsonConfig(R_ExternalPtrAddr(handle), &len, &ret)); R_API_END(); return mkString(ret); } XGB_DLL SEXP XGBoosterLoadJsonConfig_R(SEXP handle, SEXP value) { R_API_BEGIN(); CHECK_CALL(XGBoosterLoadJsonConfig(R_ExternalPtrAddr(handle), CHAR(asChar(value)))); R_API_END(); return R_NilValue; } XGB_DLL SEXP XGBoosterSerializeToBuffer_R(SEXP handle) { SEXP ret; R_API_BEGIN(); bst_ulong out_len; const char *raw; CHECK_CALL(XGBoosterSerializeToBuffer(R_ExternalPtrAddr(handle), &out_len, &raw)); ret = PROTECT(allocVector(RAWSXP, out_len)); if (out_len != 0) { memcpy(RAW(ret), raw, out_len); } R_API_END(); UNPROTECT(1); return ret; } XGB_DLL SEXP XGBoosterUnserializeFromBuffer_R(SEXP handle, SEXP raw) { R_API_BEGIN(); CHECK_CALL(XGBoosterUnserializeFromBuffer(R_ExternalPtrAddr(handle), RAW(raw), length(raw))); R_API_END(); return R_NilValue; } XGB_DLL SEXP XGBoosterDumpModel_R(SEXP handle, SEXP fmap, SEXP with_stats, SEXP dump_format) { SEXP out; R_API_BEGIN(); bst_ulong olen; const char **res; const char *fmt = CHAR(asChar(dump_format)); CHECK_CALL(XGBoosterDumpModelEx(R_ExternalPtrAddr(handle), CHAR(asChar(fmap)), asInteger(with_stats), fmt, &olen, &res)); out = PROTECT(allocVector(STRSXP, olen)); if (!strcmp("json", fmt)) { std::stringstream stream; stream << "[\n"; for (size_t i = 0; i < olen; ++i) { stream << res[i]; if (i < olen - 1) { stream << ",\n"; } else { stream << "\n"; } } stream << "]"; SET_STRING_ELT(out, 0, mkChar(stream.str().c_str())); } else { for (size_t i = 0; i < olen; ++i) { std::stringstream stream; stream << "booster[" << i <<"]\n" << res[i]; SET_STRING_ELT(out, i, mkChar(stream.str().c_str())); } } R_API_END(); UNPROTECT(1); return out; } XGB_DLL SEXP XGBoosterGetAttr_R(SEXP handle, SEXP name) { SEXP out; R_API_BEGIN(); int success; const char *val; CHECK_CALL(XGBoosterGetAttr(R_ExternalPtrAddr(handle), CHAR(asChar(name)), &val, &success)); if (success) { out = PROTECT(allocVector(STRSXP, 1)); SET_STRING_ELT(out, 0, mkChar(val)); } else { out = PROTECT(R_NilValue); } R_API_END(); UNPROTECT(1); return out; } XGB_DLL SEXP XGBoosterSetAttr_R(SEXP handle, SEXP name, SEXP val) { R_API_BEGIN(); const char *v = isNull(val) ? nullptr : CHAR(asChar(val)); CHECK_CALL(XGBoosterSetAttr(R_ExternalPtrAddr(handle), CHAR(asChar(name)), v)); R_API_END(); return R_NilValue; } XGB_DLL SEXP XGBoosterGetAttrNames_R(SEXP handle) { SEXP out; R_API_BEGIN(); bst_ulong len; const char **res; CHECK_CALL(XGBoosterGetAttrNames(R_ExternalPtrAddr(handle), &len, &res)); if (len > 0) { out = PROTECT(allocVector(STRSXP, len)); for (size_t i = 0; i < len; ++i) { SET_STRING_ELT(out, i, mkChar(res[i])); } } else { out = PROTECT(R_NilValue); } R_API_END(); UNPROTECT(1); return out; } XGB_DLL SEXP XGBoosterFeatureScore_R(SEXP handle, SEXP json_config) { SEXP out_features_sexp; SEXP out_scores_sexp; SEXP out_shape_sexp; SEXP r_out; R_API_BEGIN(); char const *c_json_config = CHAR(asChar(json_config)); bst_ulong out_n_features; char const **out_features; bst_ulong out_dim; bst_ulong const *out_shape; float const *out_scores; CHECK_CALL(XGBoosterFeatureScore(R_ExternalPtrAddr(handle), c_json_config, &out_n_features, &out_features, &out_dim, &out_shape, &out_scores)); out_shape_sexp = PROTECT(allocVector(INTSXP, out_dim)); size_t len = 1; for (size_t i = 0; i < out_dim; ++i) { INTEGER(out_shape_sexp)[i] = out_shape[i]; len *= out_shape[i]; } out_scores_sexp = PROTECT(allocVector(REALSXP, len)); #pragma omp parallel for for (omp_ulong i = 0; i < len; ++i) { REAL(out_scores_sexp)[i] = out_scores[i]; } out_features_sexp = PROTECT(allocVector(STRSXP, out_n_features)); for (size_t i = 0; i < out_n_features; ++i) { SET_STRING_ELT(out_features_sexp, i, mkChar(out_features[i])); } r_out = PROTECT(allocVector(VECSXP, 3)); SET_VECTOR_ELT(r_out, 0, out_features_sexp); SET_VECTOR_ELT(r_out, 1, out_shape_sexp); SET_VECTOR_ELT(r_out, 2, out_scores_sexp); R_API_END(); UNPROTECT(4); return r_out; } xgboost-1.5.2/R-package/src/xgboost_R.h000066400000000000000000000204361417122711700177140ustar00rootroot00000000000000/*! * Copyright 2014 (c) by Contributors * \file xgboost_R.h * \author Tianqi Chen * \brief R wrapper of xgboost */ #ifndef XGBOOST_R_H_ // NOLINT(*) #define XGBOOST_R_H_ // NOLINT(*) #include #include #include #include /*! * \brief check whether a handle is NULL * \param handle * \return whether it is null ptr */ XGB_DLL SEXP XGCheckNullPtr_R(SEXP handle); /*! * \brief Set global configuration * \param json_str a JSON string representing the list of key-value pairs * \return R_NilValue */ XGB_DLL SEXP XGBSetGlobalConfig_R(SEXP json_str); /*! * \brief Get global configuration * \return JSON string */ XGB_DLL SEXP XGBGetGlobalConfig_R(); /*! * \brief load a data matrix * \param fname name of the content * \param silent whether print messages * \return a loaded data matrix */ XGB_DLL SEXP XGDMatrixCreateFromFile_R(SEXP fname, SEXP silent); /*! * \brief create matrix content from dense matrix * This assumes the matrix is stored in column major format * \param data R Matrix object * \param missing which value to represent missing value * \param n_threads Number of threads used to construct DMatrix from dense matrix. * \return created dmatrix */ XGB_DLL SEXP XGDMatrixCreateFromMat_R(SEXP mat, SEXP missing, SEXP n_threads); /*! * \brief create a matrix content from CSC format * \param indptr pointer to column headers * \param indices row indices * \param data content of the data * \param num_row numer of rows (when it's set to 0, then guess from data) * \return created dmatrix */ XGB_DLL SEXP XGDMatrixCreateFromCSC_R(SEXP indptr, SEXP indices, SEXP data, SEXP num_row); /*! * \brief create a new dmatrix from sliced content of existing matrix * \param handle instance of data matrix to be sliced * \param idxset index set * \return a sliced new matrix */ XGB_DLL SEXP XGDMatrixSliceDMatrix_R(SEXP handle, SEXP idxset); /*! * \brief load a data matrix into binary file * \param handle a instance of data matrix * \param fname file name * \param silent print statistics when saving * \return R_NilValue */ XGB_DLL SEXP XGDMatrixSaveBinary_R(SEXP handle, SEXP fname, SEXP silent); /*! * \brief set information to dmatrix * \param handle a instance of data matrix * \param field field name, can be label, weight * \param array pointer to float vector * \return R_NilValue */ XGB_DLL SEXP XGDMatrixSetInfo_R(SEXP handle, SEXP field, SEXP array); /*! * \brief get info vector from matrix * \param handle a instance of data matrix * \param field field name * \return info vector */ XGB_DLL SEXP XGDMatrixGetInfo_R(SEXP handle, SEXP field); /*! * \brief return number of rows * \param handle an instance of data matrix */ XGB_DLL SEXP XGDMatrixNumRow_R(SEXP handle); /*! * \brief return number of columns * \param handle an instance of data matrix */ XGB_DLL SEXP XGDMatrixNumCol_R(SEXP handle); /*! * \brief create xgboost learner * \param dmats a list of dmatrix handles that will be cached */ XGB_DLL SEXP XGBoosterCreate_R(SEXP dmats); /*! * \brief create xgboost learner, saving the pointer into an existing R object * \param dmats a list of dmatrix handles that will be cached * \param R_handle a clean R external pointer (not holding any object) */ XGB_DLL SEXP XGBoosterCreateInEmptyObj_R(SEXP dmats, SEXP R_handle); /*! * \brief set parameters * \param handle handle * \param name parameter name * \param val value of parameter * \return R_NilValue */ XGB_DLL SEXP XGBoosterSetParam_R(SEXP handle, SEXP name, SEXP val); /*! * \brief update the model in one round using dtrain * \param handle handle * \param iter current iteration rounds * \param dtrain training data * \return R_NilValue */ XGB_DLL SEXP XGBoosterUpdateOneIter_R(SEXP ext, SEXP iter, SEXP dtrain); /*! * \brief update the model, by directly specify gradient and second order gradient, * this can be used to replace UpdateOneIter, to support customized loss function * \param handle handle * \param dtrain training data * \param grad gradient statistics * \param hess second order gradient statistics * \return R_NilValue */ XGB_DLL SEXP XGBoosterBoostOneIter_R(SEXP handle, SEXP dtrain, SEXP grad, SEXP hess); /*! * \brief get evaluation statistics for xgboost * \param handle handle * \param iter current iteration rounds * \param dmats list of handles to dmatrices * \param evname name of evaluation * \return the string containing evaluation stats */ XGB_DLL SEXP XGBoosterEvalOneIter_R(SEXP handle, SEXP iter, SEXP dmats, SEXP evnames); /*! * \brief (Deprecated) make prediction based on dmat * \param handle handle * \param dmat data matrix * \param option_mask output_margin:1 predict_leaf:2 * \param ntree_limit limit number of trees used in prediction * \param training Whether the prediction value is used for training. */ XGB_DLL SEXP XGBoosterPredict_R(SEXP handle, SEXP dmat, SEXP option_mask, SEXP ntree_limit, SEXP training); /*! * \brief Run prediction on DMatrix, replacing `XGBoosterPredict_R` * \param handle handle * \param dmat data matrix * \param json_config See `XGBoosterPredictFromDMatrix` in xgboost c_api.h * * \return A list containing 2 vectors, first one for shape while second one for prediction result. */ XGB_DLL SEXP XGBoosterPredictFromDMatrix_R(SEXP handle, SEXP dmat, SEXP json_config); /*! * \brief load model from existing file * \param handle handle * \param fname file name * \return R_NilValue */ XGB_DLL SEXP XGBoosterLoadModel_R(SEXP handle, SEXP fname); /*! * \brief save model into existing file * \param handle handle * \param fname file name * \return R_NilValue */ XGB_DLL SEXP XGBoosterSaveModel_R(SEXP handle, SEXP fname); /*! * \brief load model from raw array * \param handle handle * \return R_NilValue */ XGB_DLL SEXP XGBoosterLoadModelFromRaw_R(SEXP handle, SEXP raw); /*! * \brief save model into R's raw array * \param handle handle * \return raw array */ XGB_DLL SEXP XGBoosterModelToRaw_R(SEXP handle); /*! * \brief Save internal parameters as a JSON string * \param handle handle * \return JSON string */ XGB_DLL SEXP XGBoosterSaveJsonConfig_R(SEXP handle); /*! * \brief Load the JSON string returnd by XGBoosterSaveJsonConfig_R * \param handle handle * \param value JSON string * \return R_NilValue */ XGB_DLL SEXP XGBoosterLoadJsonConfig_R(SEXP handle, SEXP value); /*! * \brief Memory snapshot based serialization method. Saves everything states * into buffer. * \param handle handle to booster */ XGB_DLL SEXP XGBoosterSerializeToBuffer_R(SEXP handle); /*! * \brief Memory snapshot based serialization method. Loads the buffer returned * from `XGBoosterSerializeToBuffer'. * \param handle handle to booster * \return raw byte array */ XGB_DLL SEXP XGBoosterUnserializeFromBuffer_R(SEXP handle, SEXP raw); /*! * \brief dump model into a string * \param handle handle * \param fmap name to fmap can be empty string * \param with_stats whether dump statistics of splits * \param dump_format the format to dump the model in */ XGB_DLL SEXP XGBoosterDumpModel_R(SEXP handle, SEXP fmap, SEXP with_stats, SEXP dump_format); /*! * \brief get learner attribute value * \param handle handle * \param name attribute name * \return character containing attribute value */ XGB_DLL SEXP XGBoosterGetAttr_R(SEXP handle, SEXP name); /*! * \brief set learner attribute value * \param handle handle * \param name attribute name * \param val attribute value; NULL value would delete an attribute * \return R_NilValue */ XGB_DLL SEXP XGBoosterSetAttr_R(SEXP handle, SEXP name, SEXP val); /*! * \brief get the names of learner attributes * \return string vector containing attribute names */ XGB_DLL SEXP XGBoosterGetAttrNames_R(SEXP handle); /*! * \brief Get feature scores from the model. * \param json_config See `XGBoosterFeatureScore` in xgboost c_api.h * \return A vector with the first element as feature names, second element as shape of * feature scores and thrid element as feature scores. */ XGB_DLL SEXP XGBoosterFeatureScore_R(SEXP handle, SEXP json_config); #endif // XGBOOST_WRAPPER_R_H_ // NOLINT(*) xgboost-1.5.2/R-package/src/xgboost_assert.c000066400000000000000000000010641417122711700210030ustar00rootroot00000000000000// Copyright (c) 2014 by Contributors #include #include #include // implements error handling void XGBoostAssert_R(int exp, const char *fmt, ...) { char buf[1024]; if (exp == 0) { va_list args; va_start(args, fmt); vsprintf(buf, fmt, args); va_end(args); error("AssertError:%s\n", buf); } } void XGBoostCheck_R(int exp, const char *fmt, ...) { char buf[1024]; if (exp == 0) { va_list args; va_start(args, fmt); vsprintf(buf, fmt, args); va_end(args); error("%s\n", buf); } } xgboost-1.5.2/R-package/src/xgboost_custom.cc000066400000000000000000000025041417122711700211570ustar00rootroot00000000000000// Copyright (c) 2015 by Contributors // This file contains the customization implementations of R module // to change behavior of libxgboost #include #include "../../src/common/random.h" #include "./xgboost_R.h" // redirect the messages to R's console. namespace dmlc { void CustomLogMessage::Log(const std::string& msg) { Rprintf("%s\n", msg.c_str()); } } // namespace dmlc namespace xgboost { ConsoleLogger::~ConsoleLogger() { if (cur_verbosity_ == LogVerbosity::kIgnore || cur_verbosity_ <= GlobalVerbosity()) { dmlc::CustomLogMessage::Log(log_stream_.str()); } } TrackerLogger::~TrackerLogger() { dmlc::CustomLogMessage::Log(log_stream_.str()); } } // namespace xgboost namespace xgboost { namespace common { // redirect the nath functions. bool CheckNAN(double v) { return ISNAN(v); } #if !defined(XGBOOST_USE_CUDA) double LogGamma(double v) { return lgammafn(v); } #endif // !defined(XGBOOST_USE_CUDA) // customize random engine. void CustomGlobalRandomEngine::seed(CustomGlobalRandomEngine::result_type val) { // ignore the seed } // use R's PRNG to replacd CustomGlobalRandomEngine::result_type CustomGlobalRandomEngine::operator()() { return static_cast( std::floor(unif_rand() * CustomGlobalRandomEngine::max())); } } // namespace common } // namespace xgboost xgboost-1.5.2/R-package/tests/000077500000000000000000000000001417122711700161435ustar00rootroot00000000000000xgboost-1.5.2/R-package/tests/helper_scripts/000077500000000000000000000000001417122711700211715ustar00rootroot00000000000000xgboost-1.5.2/R-package/tests/helper_scripts/generate_models.R000066400000000000000000000073351417122711700244610ustar00rootroot00000000000000# Script to generate reference models. The reference models are used to test backward compatibility # of saved model files from XGBoost version 0.90 and 1.0.x. library(xgboost) library(Matrix) set.seed(0) metadata <- list( kRounds = 2, kRows = 1000, kCols = 4, kForests = 2, kMaxDepth = 2, kClasses = 3 ) X <- Matrix(data = rnorm(metadata$kRows * metadata$kCols), nrow = metadata$kRows, ncol = metadata$kCols, sparse = TRUE) w <- runif(metadata$kRows) version <- packageVersion('xgboost') target_dir <- 'models' save_booster <- function (booster, model_name) { booster_bin <- function (model_name) { return (file.path(target_dir, paste('xgboost-', version, '.', model_name, '.bin', sep = ''))) } booster_json <- function (model_name) { return (file.path(target_dir, paste('xgboost-', version, '.', model_name, '.json', sep = ''))) } booster_rds <- function (model_name) { return (file.path(target_dir, paste('xgboost-', version, '.', model_name, '.rds', sep = ''))) } xgb.save(booster, booster_bin(model_name)) saveRDS(booster, booster_rds(model_name)) if (version >= '1.0.0') { xgb.save(booster, booster_json(model_name)) } } generate_regression_model <- function () { print('Regression') y <- rnorm(metadata$kRows) data <- xgb.DMatrix(X, label = y) params <- list(tree_method = 'hist', num_parallel_tree = metadata$kForests, max_depth = metadata$kMaxDepth) booster <- xgb.train(params, data, nrounds = metadata$kRounds) save_booster(booster, 'reg') } generate_logistic_model <- function () { print('Binary classification with logistic loss') y <- sample(0:1, size = metadata$kRows, replace = TRUE) stopifnot(max(y) == 1, min(y) == 0) objective <- c('binary:logistic', 'binary:logitraw') name <- c('logit', 'logitraw') for (i in seq_len(length(objective))) { data <- xgb.DMatrix(X, label = y, weight = w) params <- list(tree_method = 'hist', num_parallel_tree = metadata$kForests, max_depth = metadata$kMaxDepth, objective = objective[i]) booster <- xgb.train(params, data, nrounds = metadata$kRounds) save_booster(booster, name[i]) } } generate_classification_model <- function () { print('Multi-class classification') y <- sample(0:(metadata$kClasses - 1), size = metadata$kRows, replace = TRUE) stopifnot(max(y) == metadata$kClasses - 1, min(y) == 0) data <- xgb.DMatrix(X, label = y, weight = w) params <- list(num_class = metadata$kClasses, tree_method = 'hist', num_parallel_tree = metadata$kForests, max_depth = metadata$kMaxDepth, objective = 'multi:softmax') booster <- xgb.train(params, data, nrounds = metadata$kRounds) save_booster(booster, 'cls') } generate_ranking_model <- function () { print('Learning to rank') y <- sample(0:4, size = metadata$kRows, replace = TRUE) stopifnot(max(y) == 4, min(y) == 0) kGroups <- 20 w <- runif(kGroups) g <- rep(50, times = kGroups) data <- xgb.DMatrix(X, label = y, group = g) # setinfo(data, 'weight', w) # ^^^ does not work in version <= 1.1.0; see https://github.com/dmlc/xgboost/issues/5942 # So call low-level function XGDMatrixSetInfo_R directly. Since this function is not an exported # symbol, use the triple-colon operator. .Call(xgboost:::XGDMatrixSetInfo_R, data, 'weight', as.numeric(w)) params <- list(objective = 'rank:ndcg', num_parallel_tree = metadata$kForests, tree_method = 'hist', max_depth = metadata$kMaxDepth) booster <- xgb.train(params, data, nrounds = metadata$kRounds) save_booster(booster, 'ltr') } dir.create(target_dir) invisible(generate_regression_model()) invisible(generate_logistic_model()) invisible(generate_classification_model()) invisible(generate_ranking_model()) xgboost-1.5.2/R-package/tests/helper_scripts/run_lint.R000066400000000000000000000046341417122711700231550ustar00rootroot00000000000000library(lintr) library(crayon) my_linters <- list( absolute_path_linter = lintr::absolute_path_linter, assignment_linter = lintr::assignment_linter, closed_curly_linter = lintr::closed_curly_linter, commas_linter = lintr::commas_linter, equals_na = lintr::equals_na_linter, infix_spaces_linter = lintr::infix_spaces_linter, line_length_linter = lintr::line_length_linter, no_tab_linter = lintr::no_tab_linter, object_usage_linter = lintr::object_usage_linter, object_length_linter = lintr::object_length_linter, open_curly_linter = lintr::open_curly_linter, semicolon = lintr::semicolon_terminator_linter, seq = lintr::seq_linter, spaces_inside_linter = lintr::spaces_inside_linter, spaces_left_parentheses_linter = lintr::spaces_left_parentheses_linter, trailing_blank_lines_linter = lintr::trailing_blank_lines_linter, trailing_whitespace_linter = lintr::trailing_whitespace_linter, true_false = lintr::T_and_F_symbol_linter, unneeded_concatenation = lintr::unneeded_concatenation_linter ) results <- lapply( list.files(path = '.', pattern = '\\.[Rr]$', recursive = TRUE), function (r_file) { cat(sprintf("Processing %s ...\n", r_file)) list(r_file = r_file, output = lintr::lint(filename = r_file, linters = my_linters)) }) num_issue <- Reduce(sum, lapply(results, function (e) length(e$output))) lint2str <- function(lint_entry) { color <- function(type) { switch(type, "warning" = crayon::magenta, "error" = crayon::red, "style" = crayon::blue, crayon::bold ) } paste0( lapply(lint_entry$output, function (lint_line) { paste0( crayon::bold(lint_entry$r_file, ":", as.character(lint_line$line_number), ":", as.character(lint_line$column_number), ": ", sep = ""), color(lint_line$type)(lint_line$type, ": ", sep = ""), crayon::bold(lint_line$message), "\n", lint_line$line, "\n", lintr:::highlight_string(lint_line$message, lint_line$column_number, lint_line$ranges), "\n", collapse = "") }), collapse = "") } if (num_issue > 0) { cat(sprintf('R linters found %d issues:\n', num_issue)) for (entry in results) { if (length(entry$output)) { cat(paste0('**** ', crayon::bold(entry$r_file), '\n')) cat(paste0(lint2str(entry), collapse = '')) } } quit(save = 'no', status = 1) # Signal error to parent shell } xgboost-1.5.2/R-package/tests/testthat.R000066400000000000000000000001271417122711700201260ustar00rootroot00000000000000library(testthat) library(xgboost) test_check("xgboost", reporter = ProgressReporter) xgboost-1.5.2/R-package/tests/testthat/000077500000000000000000000000001417122711700200035ustar00rootroot00000000000000xgboost-1.5.2/R-package/tests/testthat/test_basic.R000066400000000000000000000443311417122711700222530ustar00rootroot00000000000000require(xgboost) context("basic functions") data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') train <- agaricus.train test <- agaricus.test set.seed(1994) # disable some tests for Win32 windows_flag <- .Platform$OS.type == "windows" && .Machine$sizeof.pointer != 8 solaris_flag <- (Sys.info()['sysname'] == "SunOS") test_that("train and predict binary classification", { nrounds <- 2 expect_output( bst <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = nrounds, objective = "binary:logistic", eval_metric = "error") , "train-error") expect_equal(class(bst), "xgb.Booster") expect_equal(bst$niter, nrounds) expect_false(is.null(bst$evaluation_log)) expect_equal(nrow(bst$evaluation_log), nrounds) expect_lt(bst$evaluation_log[, min(train_error)], 0.03) pred <- predict(bst, test$data) expect_length(pred, 1611) pred1 <- predict(bst, train$data, ntreelimit = 1) expect_length(pred1, 6513) err_pred1 <- sum((pred1 > 0.5) != train$label) / length(train$label) err_log <- bst$evaluation_log[1, train_error] expect_lt(abs(err_pred1 - err_log), 10e-6) pred2 <- predict(bst, train$data, iterationrange = c(1, 2)) expect_length(pred1, 6513) expect_equal(pred1, pred2) }) test_that("parameter validation works", { p <- list(foo = "bar") nrounds <- 1 set.seed(1994) d <- cbind( x1 = rnorm(10), x2 = rnorm(10), x3 = rnorm(10)) y <- d[, "x1"] + d[, "x2"]^2 + ifelse(d[, "x3"] > .5, d[, "x3"]^2, 2^d[, "x3"]) + rnorm(10) dtrain <- xgb.DMatrix(data = d, info = list(label = y)) correct <- function() { params <- list(max_depth = 2, booster = "dart", rate_drop = 0.5, one_drop = TRUE, objective = "reg:squarederror") xgb.train(params = params, data = dtrain, nrounds = nrounds) } expect_silent(correct()) incorrect <- function() { params <- list(max_depth = 2, booster = "dart", rate_drop = 0.5, one_drop = TRUE, objective = "reg:squarederror", foo = "bar", bar = "foo") output <- capture.output( xgb.train(params = params, data = dtrain, nrounds = nrounds)) print(output) } expect_output(incorrect(), '\\\\"bar\\\\", \\\\"foo\\\\"') }) test_that("dart prediction works", { nrounds <- 32 set.seed(1994) d <- cbind( x1 = rnorm(100), x2 = rnorm(100), x3 = rnorm(100)) y <- d[, "x1"] + d[, "x2"]^2 + ifelse(d[, "x3"] > .5, d[, "x3"]^2, 2^d[, "x3"]) + rnorm(100) set.seed(1994) booster_by_xgboost <- xgboost(data = d, label = y, max_depth = 2, booster = "dart", rate_drop = 0.5, one_drop = TRUE, eta = 1, nthread = 2, nrounds = nrounds, objective = "reg:squarederror") pred_by_xgboost_0 <- predict(booster_by_xgboost, newdata = d, ntreelimit = 0) pred_by_xgboost_1 <- predict(booster_by_xgboost, newdata = d, ntreelimit = nrounds) expect_true(all(matrix(pred_by_xgboost_0, byrow = TRUE) == matrix(pred_by_xgboost_1, byrow = TRUE))) pred_by_xgboost_2 <- predict(booster_by_xgboost, newdata = d, training = TRUE) expect_false(all(matrix(pred_by_xgboost_0, byrow = TRUE) == matrix(pred_by_xgboost_2, byrow = TRUE))) set.seed(1994) dtrain <- xgb.DMatrix(data = d, info = list(label = y)) booster_by_train <- xgb.train(params = list( booster = "dart", max_depth = 2, eta = 1, rate_drop = 0.5, one_drop = TRUE, nthread = 1, tree_method = "exact", objective = "reg:squarederror" ), data = dtrain, nrounds = nrounds ) pred_by_train_0 <- predict(booster_by_train, newdata = dtrain, ntreelimit = 0) pred_by_train_1 <- predict(booster_by_train, newdata = dtrain, ntreelimit = nrounds) pred_by_train_2 <- predict(booster_by_train, newdata = dtrain, training = TRUE) expect_true(all(matrix(pred_by_train_0, byrow = TRUE) == matrix(pred_by_xgboost_0, byrow = TRUE))) expect_true(all(matrix(pred_by_train_1, byrow = TRUE) == matrix(pred_by_xgboost_1, byrow = TRUE))) expect_true(all(matrix(pred_by_train_2, byrow = TRUE) == matrix(pred_by_xgboost_2, byrow = TRUE))) }) test_that("train and predict softprob", { lb <- as.numeric(iris$Species) - 1 set.seed(11) expect_output( bst <- xgboost(data = as.matrix(iris[, -5]), label = lb, max_depth = 3, eta = 0.5, nthread = 2, nrounds = 5, objective = "multi:softprob", num_class = 3, eval_metric = "merror") , "train-merror") expect_false(is.null(bst$evaluation_log)) expect_lt(bst$evaluation_log[, min(train_merror)], 0.025) expect_equal(bst$niter * 3, xgb.ntree(bst)) pred <- predict(bst, as.matrix(iris[, -5])) expect_length(pred, nrow(iris) * 3) # row sums add up to total probability of 1: expect_equal(rowSums(matrix(pred, ncol = 3, byrow = TRUE)), rep(1, nrow(iris)), tolerance = 1e-7) # manually calculate error at the last iteration: mpred <- predict(bst, as.matrix(iris[, -5]), reshape = TRUE) expect_equal(as.numeric(t(mpred)), pred) pred_labels <- max.col(mpred) - 1 err <- sum(pred_labels != lb) / length(lb) expect_equal(bst$evaluation_log[5, train_merror], err, tolerance = 5e-6) # manually calculate error at the 1st iteration: mpred <- predict(bst, as.matrix(iris[, -5]), reshape = TRUE, ntreelimit = 1) pred_labels <- max.col(mpred) - 1 err <- sum(pred_labels != lb) / length(lb) expect_equal(bst$evaluation_log[1, train_merror], err, tolerance = 5e-6) mpred1 <- predict(bst, as.matrix(iris[, -5]), reshape = TRUE, iterationrange = c(1, 2)) expect_equal(mpred, mpred1) d <- cbind( x1 = rnorm(100), x2 = rnorm(100), x3 = rnorm(100) ) y <- sample.int(10, 100, replace = TRUE) - 1 dtrain <- xgb.DMatrix(data = d, info = list(label = y)) booster <- xgb.train( params = list(tree_method = "hist"), data = dtrain, nrounds = 4, num_class = 10, objective = "multi:softprob" ) predt <- predict(booster, as.matrix(d), reshape = TRUE, strict_shape = FALSE) expect_equal(ncol(predt), 10) expect_equal(rowSums(predt), rep(1, 100), tolerance = 1e-7) }) test_that("train and predict softmax", { lb <- as.numeric(iris$Species) - 1 set.seed(11) expect_output( bst <- xgboost(data = as.matrix(iris[, -5]), label = lb, max_depth = 3, eta = 0.5, nthread = 2, nrounds = 5, objective = "multi:softmax", num_class = 3, eval_metric = "merror") , "train-merror") expect_false(is.null(bst$evaluation_log)) expect_lt(bst$evaluation_log[, min(train_merror)], 0.025) expect_equal(bst$niter * 3, xgb.ntree(bst)) pred <- predict(bst, as.matrix(iris[, -5])) expect_length(pred, nrow(iris)) err <- sum(pred != lb) / length(lb) expect_equal(bst$evaluation_log[5, train_merror], err, tolerance = 5e-6) }) test_that("train and predict RF", { set.seed(11) lb <- train$label # single iteration bst <- xgboost(data = train$data, label = lb, max_depth = 5, nthread = 2, nrounds = 1, objective = "binary:logistic", eval_metric = "error", num_parallel_tree = 20, subsample = 0.6, colsample_bytree = 0.1) expect_equal(bst$niter, 1) expect_equal(xgb.ntree(bst), 20) pred <- predict(bst, train$data) pred_err <- sum((pred > 0.5) != lb) / length(lb) expect_lt(abs(bst$evaluation_log[1, train_error] - pred_err), 10e-6) #expect_lt(pred_err, 0.03) pred <- predict(bst, train$data, ntreelimit = 20) pred_err_20 <- sum((pred > 0.5) != lb) / length(lb) expect_equal(pred_err_20, pred_err) pred1 <- predict(bst, train$data, iterationrange = c(1, 2)) expect_equal(pred, pred1) }) test_that("train and predict RF with softprob", { lb <- as.numeric(iris$Species) - 1 nrounds <- 15 set.seed(11) bst <- xgboost(data = as.matrix(iris[, -5]), label = lb, max_depth = 3, eta = 0.9, nthread = 2, nrounds = nrounds, objective = "multi:softprob", eval_metric = "merror", num_class = 3, verbose = 0, num_parallel_tree = 4, subsample = 0.5, colsample_bytree = 0.5) expect_equal(bst$niter, 15) expect_equal(xgb.ntree(bst), 15 * 3 * 4) # predict for all iterations: pred <- predict(bst, as.matrix(iris[, -5]), reshape = TRUE) expect_equal(dim(pred), c(nrow(iris), 3)) pred_labels <- max.col(pred) - 1 err <- sum(pred_labels != lb) / length(lb) expect_equal(bst$evaluation_log[nrounds, train_merror], err, tolerance = 5e-6) # predict for 7 iterations and adjust for 4 parallel trees per iteration pred <- predict(bst, as.matrix(iris[, -5]), reshape = TRUE, ntreelimit = 7 * 4) err <- sum((max.col(pred) - 1) != lb) / length(lb) expect_equal(bst$evaluation_log[7, train_merror], err, tolerance = 5e-6) }) test_that("use of multiple eval metrics works", { expect_output( bst <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic", eval_metric = 'error', eval_metric = 'auc', eval_metric = "logloss") , "train-error.*train-auc.*train-logloss") expect_false(is.null(bst$evaluation_log)) expect_equal(dim(bst$evaluation_log), c(2, 4)) expect_equal(colnames(bst$evaluation_log), c("iter", "train_error", "train_auc", "train_logloss")) }) test_that("training continuation works", { dtrain <- xgb.DMatrix(train$data, label = train$label) watchlist <- list(train = dtrain) param <- list(objective = "binary:logistic", max_depth = 2, eta = 1, nthread = 2) # for the reference, use 4 iterations at once: set.seed(11) bst <- xgb.train(param, dtrain, nrounds = 4, watchlist, verbose = 0) # first two iterations: set.seed(11) bst1 <- xgb.train(param, dtrain, nrounds = 2, watchlist, verbose = 0) # continue for two more: bst2 <- xgb.train(param, dtrain, nrounds = 2, watchlist, verbose = 0, xgb_model = bst1) if (!windows_flag && !solaris_flag) expect_equal(bst$raw, bst2$raw) expect_false(is.null(bst2$evaluation_log)) expect_equal(dim(bst2$evaluation_log), c(4, 2)) expect_equal(bst2$evaluation_log, bst$evaluation_log) # test continuing from raw model data bst2 <- xgb.train(param, dtrain, nrounds = 2, watchlist, verbose = 0, xgb_model = bst1$raw) if (!windows_flag && !solaris_flag) expect_equal(bst$raw, bst2$raw) expect_equal(dim(bst2$evaluation_log), c(2, 2)) # test continuing from a model in file xgb.save(bst1, "xgboost.json") bst2 <- xgb.train(param, dtrain, nrounds = 2, watchlist, verbose = 0, xgb_model = "xgboost.json") if (!windows_flag && !solaris_flag) expect_equal(bst$raw, bst2$raw) expect_equal(dim(bst2$evaluation_log), c(2, 2)) file.remove("xgboost.json") }) test_that("model serialization works", { out_path <- "model_serialization" dtrain <- xgb.DMatrix(train$data, label = train$label) watchlist <- list(train = dtrain) param <- list(objective = "binary:logistic") booster <- xgb.train(param, dtrain, nrounds = 4, watchlist) raw <- xgb.serialize(booster) saveRDS(raw, out_path) raw <- readRDS(out_path) loaded <- xgb.unserialize(raw) raw_from_loaded <- xgb.serialize(loaded) expect_equal(raw, raw_from_loaded) file.remove(out_path) }) test_that("xgb.cv works", { set.seed(11) expect_output( cv <- xgb.cv(data = train$data, label = train$label, max_depth = 2, nfold = 5, eta = 1., nthread = 2, nrounds = 2, objective = "binary:logistic", eval_metric = "error", verbose = TRUE) , "train-error:") expect_is(cv, 'xgb.cv.synchronous') expect_false(is.null(cv$evaluation_log)) expect_lt(cv$evaluation_log[, min(test_error_mean)], 0.03) expect_lt(cv$evaluation_log[, min(test_error_std)], 0.008) expect_equal(cv$niter, 2) expect_false(is.null(cv$folds) && is.list(cv$folds)) expect_length(cv$folds, 5) expect_false(is.null(cv$params) && is.list(cv$params)) expect_false(is.null(cv$callbacks)) expect_false(is.null(cv$call)) }) test_that("xgb.cv works with stratified folds", { dtrain <- xgb.DMatrix(train$data, label = train$label) set.seed(314159) cv <- xgb.cv(data = dtrain, max_depth = 2, nfold = 5, eta = 1., nthread = 2, nrounds = 2, objective = "binary:logistic", verbose = TRUE, stratified = FALSE) set.seed(314159) cv2 <- xgb.cv(data = dtrain, max_depth = 2, nfold = 5, eta = 1., nthread = 2, nrounds = 2, objective = "binary:logistic", verbose = TRUE, stratified = TRUE) # Stratified folds should result in a different evaluation logs expect_true(all(cv$evaluation_log[, test_logloss_mean] != cv2$evaluation_log[, test_logloss_mean])) }) test_that("train and predict with non-strict classes", { # standard dense matrix input train_dense <- as.matrix(train$data) bst <- xgboost(data = train_dense, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic", verbose = 0) pr0 <- predict(bst, train_dense) # dense matrix-like input of non-matrix class class(train_dense) <- 'shmatrix' expect_true(is.matrix(train_dense)) expect_error( bst <- xgboost(data = train_dense, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic", verbose = 0) , regexp = NA) expect_error(pr <- predict(bst, train_dense), regexp = NA) expect_equal(pr0, pr) # dense matrix-like input of non-matrix class with some inheritance class(train_dense) <- c('pphmatrix', 'shmatrix') expect_true(is.matrix(train_dense)) expect_error( bst <- xgboost(data = train_dense, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic", verbose = 0) , regexp = NA) expect_error(pr <- predict(bst, train_dense), regexp = NA) expect_equal(pr0, pr) # when someone inherits from xgb.Booster, it should still be possible to use it as xgb.Booster class(bst) <- c('super.Booster', 'xgb.Booster') expect_error(pr <- predict(bst, train_dense), regexp = NA) expect_equal(pr0, pr) }) test_that("max_delta_step works", { dtrain <- xgb.DMatrix(agaricus.train$data, label = agaricus.train$label) watchlist <- list(train = dtrain) param <- list(objective = "binary:logistic", eval_metric = "logloss", max_depth = 2, nthread = 2, eta = 0.5) nrounds <- 5 # model with no restriction on max_delta_step bst1 <- xgb.train(param, dtrain, nrounds, watchlist, verbose = 1) # model with restricted max_delta_step bst2 <- xgb.train(param, dtrain, nrounds, watchlist, verbose = 1, max_delta_step = 1) # the no-restriction model is expected to have consistently lower loss during the initial iterations expect_true(all(bst1$evaluation_log$train_logloss < bst2$evaluation_log$train_logloss)) expect_lt(mean(bst1$evaluation_log$train_logloss) / mean(bst2$evaluation_log$train_logloss), 0.8) }) test_that("colsample_bytree works", { # Randomly generate data matrix by sampling from uniform distribution [-1, 1] set.seed(1) train_x <- matrix(runif(1000, min = -1, max = 1), ncol = 100) train_y <- as.numeric(rowSums(train_x) > 0) test_x <- matrix(runif(1000, min = -1, max = 1), ncol = 100) test_y <- as.numeric(rowSums(test_x) > 0) colnames(train_x) <- paste0("Feature_", sprintf("%03d", 1:100)) colnames(test_x) <- paste0("Feature_", sprintf("%03d", 1:100)) dtrain <- xgb.DMatrix(train_x, label = train_y) dtest <- xgb.DMatrix(test_x, label = test_y) watchlist <- list(train = dtrain, eval = dtest) ## Use colsample_bytree = 0.01, so that roughly one out of 100 features is chosen for ## each tree param <- list(max_depth = 2, eta = 0, nthread = 2, colsample_bytree = 0.01, objective = "binary:logistic", eval_metric = "auc") set.seed(2) bst <- xgb.train(param, dtrain, nrounds = 100, watchlist, verbose = 0) xgb.importance(model = bst) # If colsample_bytree works properly, a variety of features should be used # in the 100 trees expect_gte(nrow(xgb.importance(model = bst)), 30) }) test_that("Configuration works", { bst <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic", eval_metric = 'error', eval_metric = 'auc', eval_metric = "logloss") config <- xgb.config(bst) xgb.config(bst) <- config reloaded_config <- xgb.config(bst) expect_equal(config, reloaded_config); }) test_that("strict_shape works", { n_rounds <- 2 test_strict_shape <- function(bst, X, n_groups) { predt <- predict(bst, X, strict_shape = TRUE) margin <- predict(bst, X, outputmargin = TRUE, strict_shape = TRUE) contri <- predict(bst, X, predcontrib = TRUE, strict_shape = TRUE) interact <- predict(bst, X, predinteraction = TRUE, strict_shape = TRUE) leaf <- predict(bst, X, predleaf = TRUE, strict_shape = TRUE) n_rows <- nrow(X) n_cols <- ncol(X) expect_equal(dim(predt), c(n_groups, n_rows)) expect_equal(dim(margin), c(n_groups, n_rows)) expect_equal(dim(contri), c(n_cols + 1, n_groups, n_rows)) expect_equal(dim(interact), c(n_cols + 1, n_cols + 1, n_groups, n_rows)) expect_equal(dim(leaf), c(1, n_groups, n_rounds, n_rows)) if (n_groups != 1) { for (g in seq_len(n_groups)) { expect_lt(max(abs(colSums(contri[, g, ]) - margin[g, ])), 1e-5) } } } test_iris <- function() { y <- as.numeric(iris$Species) - 1 X <- as.matrix(iris[, -5]) bst <- xgboost(data = X, label = y, max_depth = 2, nrounds = n_rounds, objective = "multi:softprob", num_class = 3, eval_metric = "merror") test_strict_shape(bst, X, 3) } test_agaricus <- function() { data(agaricus.train, package = 'xgboost') X <- agaricus.train$data y <- agaricus.train$label bst <- xgboost(data = X, label = y, max_depth = 2, nrounds = n_rounds, objective = "binary:logistic", eval_metric = 'error', eval_metric = 'auc', eval_metric = "logloss") test_strict_shape(bst, X, 1) } test_iris() test_agaricus() }) xgboost-1.5.2/R-package/tests/testthat/test_callbacks.R000066400000000000000000000311241417122711700231050ustar00rootroot00000000000000# More specific testing of callbacks require(xgboost) require(data.table) require(titanic) context("callbacks") data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') train <- agaricus.train test <- agaricus.test # add some label noise for early stopping tests add.noise <- function(label, frac) { inoise <- sample(length(label), length(label) * frac) label[inoise] <- !label[inoise] label } set.seed(11) ltrain <- add.noise(train$label, 0.2) ltest <- add.noise(test$label, 0.2) dtrain <- xgb.DMatrix(train$data, label = ltrain) dtest <- xgb.DMatrix(test$data, label = ltest) watchlist <- list(train = dtrain, test = dtest) err <- function(label, pr) sum((pr > 0.5) != label) / length(label) param <- list(objective = "binary:logistic", eval_metric = "error", max_depth = 2, nthread = 2) test_that("cb.print.evaluation works as expected", { bst_evaluation <- c('train-auc' = 0.9, 'test-auc' = 0.8) bst_evaluation_err <- NULL begin_iteration <- 1 end_iteration <- 7 f0 <- cb.print.evaluation(period = 0) f1 <- cb.print.evaluation(period = 1) f5 <- cb.print.evaluation(period = 5) expect_false(is.null(attr(f1, 'call'))) expect_equal(attr(f1, 'name'), 'cb.print.evaluation') iteration <- 1 expect_silent(f0()) expect_output(f1(), "\\[1\\]\ttrain-auc:0.900000\ttest-auc:0.800000") expect_output(f5(), "\\[1\\]\ttrain-auc:0.900000\ttest-auc:0.800000") expect_null(f1()) iteration <- 2 expect_output(f1(), "\\[2\\]\ttrain-auc:0.900000\ttest-auc:0.800000") expect_silent(f5()) iteration <- 7 expect_output(f1(), "\\[7\\]\ttrain-auc:0.900000\ttest-auc:0.800000") expect_output(f5(), "\\[7\\]\ttrain-auc:0.900000\ttest-auc:0.800000") bst_evaluation_err <- c('train-auc' = 0.1, 'test-auc' = 0.2) expect_output(f1(), "\\[7\\]\ttrain-auc:0.900000\\+0.100000\ttest-auc:0.800000\\+0.200000") }) test_that("cb.evaluation.log works as expected", { bst_evaluation <- c('train-auc' = 0.9, 'test-auc' = 0.8) bst_evaluation_err <- NULL evaluation_log <- list() f <- cb.evaluation.log() expect_false(is.null(attr(f, 'call'))) expect_equal(attr(f, 'name'), 'cb.evaluation.log') iteration <- 1 expect_silent(f()) expect_equal(evaluation_log, list(c(iter = 1, bst_evaluation))) iteration <- 2 expect_silent(f()) expect_equal(evaluation_log, list(c(iter = 1, bst_evaluation), c(iter = 2, bst_evaluation))) expect_silent(f(finalize = TRUE)) expect_equal(evaluation_log, data.table(iter = 1:2, train_auc = c(0.9, 0.9), test_auc = c(0.8, 0.8))) bst_evaluation_err <- c('train-auc' = 0.1, 'test-auc' = 0.2) evaluation_log <- list() f <- cb.evaluation.log() iteration <- 1 expect_silent(f()) expect_equal(evaluation_log, list(c(iter = 1, c(bst_evaluation, bst_evaluation_err)))) iteration <- 2 expect_silent(f()) expect_equal(evaluation_log, list(c(iter = 1, c(bst_evaluation, bst_evaluation_err)), c(iter = 2, c(bst_evaluation, bst_evaluation_err)))) expect_silent(f(finalize = TRUE)) expect_equal(evaluation_log, data.table(iter = 1:2, train_auc_mean = c(0.9, 0.9), train_auc_std = c(0.1, 0.1), test_auc_mean = c(0.8, 0.8), test_auc_std = c(0.2, 0.2))) }) param <- list(objective = "binary:logistic", eval_metric = "error", max_depth = 4, nthread = 2) test_that("can store evaluation_log without printing", { expect_silent( bst <- xgb.train(param, dtrain, nrounds = 10, watchlist, eta = 1, verbose = 0) ) expect_false(is.null(bst$evaluation_log)) expect_false(is.null(bst$evaluation_log$train_error)) expect_lt(bst$evaluation_log[, min(train_error)], 0.2) }) test_that("cb.reset.parameters works as expected", { # fixed eta set.seed(111) bst0 <- xgb.train(param, dtrain, nrounds = 2, watchlist, eta = 0.9, verbose = 0) expect_false(is.null(bst0$evaluation_log)) expect_false(is.null(bst0$evaluation_log$train_error)) # same eta but re-set as a vector parameter in the callback set.seed(111) my_par <- list(eta = c(0.9, 0.9)) bst1 <- xgb.train(param, dtrain, nrounds = 2, watchlist, verbose = 0, callbacks = list(cb.reset.parameters(my_par))) expect_false(is.null(bst1$evaluation_log$train_error)) expect_equal(bst0$evaluation_log$train_error, bst1$evaluation_log$train_error) # same eta but re-set via a function in the callback set.seed(111) my_par <- list(eta = function(itr, itr_end) 0.9) bst2 <- xgb.train(param, dtrain, nrounds = 2, watchlist, verbose = 0, callbacks = list(cb.reset.parameters(my_par))) expect_false(is.null(bst2$evaluation_log$train_error)) expect_equal(bst0$evaluation_log$train_error, bst2$evaluation_log$train_error) # different eta re-set as a vector parameter in the callback set.seed(111) my_par <- list(eta = c(0.6, 0.5)) bst3 <- xgb.train(param, dtrain, nrounds = 2, watchlist, verbose = 0, callbacks = list(cb.reset.parameters(my_par))) expect_false(is.null(bst3$evaluation_log$train_error)) expect_false(all(bst0$evaluation_log$train_error == bst3$evaluation_log$train_error)) # resetting multiple parameters at the same time runs with no error my_par <- list(eta = c(1., 0.5), gamma = c(1, 2), max_depth = c(4, 8)) expect_error( bst4 <- xgb.train(param, dtrain, nrounds = 2, watchlist, verbose = 0, callbacks = list(cb.reset.parameters(my_par))) , NA) # NA = no error # CV works as well expect_error( bst4 <- xgb.cv(param, dtrain, nfold = 2, nrounds = 2, verbose = 0, callbacks = list(cb.reset.parameters(my_par))) , NA) # NA = no error # expect no learning with 0 learning rate my_par <- list(eta = c(0., 0.)) bstX <- xgb.train(param, dtrain, nrounds = 2, watchlist, verbose = 0, callbacks = list(cb.reset.parameters(my_par))) expect_false(is.null(bstX$evaluation_log$train_error)) er <- unique(bstX$evaluation_log$train_error) expect_length(er, 1) expect_gt(er, 0.4) }) test_that("cb.save.model works as expected", { files <- c('xgboost_01.json', 'xgboost_02.json', 'xgboost.json') for (f in files) if (file.exists(f)) file.remove(f) bst <- xgb.train(param, dtrain, nrounds = 2, watchlist, eta = 1, verbose = 0, save_period = 1, save_name = "xgboost_%02d.json") expect_true(file.exists('xgboost_01.json')) expect_true(file.exists('xgboost_02.json')) b1 <- xgb.load('xgboost_01.json') expect_equal(xgb.ntree(b1), 1) b2 <- xgb.load('xgboost_02.json') expect_equal(xgb.ntree(b2), 2) xgb.config(b2) <- xgb.config(bst) expect_equal(xgb.config(bst), xgb.config(b2)) expect_equal(bst$raw, b2$raw) # save_period = 0 saves the last iteration's model bst <- xgb.train(param, dtrain, nrounds = 2, watchlist, eta = 1, verbose = 0, save_period = 0, save_name = 'xgboost.json') expect_true(file.exists('xgboost.json')) b2 <- xgb.load('xgboost.json') xgb.config(b2) <- xgb.config(bst) expect_equal(bst$raw, b2$raw) for (f in files) if (file.exists(f)) file.remove(f) }) test_that("early stopping xgb.train works", { set.seed(11) expect_output( bst <- xgb.train(param, dtrain, nrounds = 20, watchlist, eta = 0.3, early_stopping_rounds = 3, maximize = FALSE) , "Stopping. Best iteration") expect_false(is.null(bst$best_iteration)) expect_lt(bst$best_iteration, 19) expect_equal(bst$best_iteration, bst$best_ntreelimit) pred <- predict(bst, dtest) expect_equal(length(pred), 1611) err_pred <- err(ltest, pred) err_log <- bst$evaluation_log[bst$best_iteration, test_error] expect_equal(err_log, err_pred, tolerance = 5e-6) set.seed(11) expect_silent( bst0 <- xgb.train(param, dtrain, nrounds = 20, watchlist, eta = 0.3, early_stopping_rounds = 3, maximize = FALSE, verbose = 0) ) expect_equal(bst$evaluation_log, bst0$evaluation_log) xgb.save(bst, "model.bin") loaded <- xgb.load("model.bin") expect_false(is.null(loaded$best_iteration)) expect_equal(loaded$best_iteration, bst$best_ntreelimit) expect_equal(loaded$best_ntreelimit, bst$best_ntreelimit) file.remove("model.bin") }) test_that("early stopping using a specific metric works", { set.seed(11) expect_output( bst <- xgb.train(param[-2], dtrain, nrounds = 20, watchlist, eta = 0.6, eval_metric = "logloss", eval_metric = "auc", callbacks = list(cb.early.stop(stopping_rounds = 3, maximize = FALSE, metric_name = 'test_logloss'))) , "Stopping. Best iteration") expect_false(is.null(bst$best_iteration)) expect_lt(bst$best_iteration, 19) expect_equal(bst$best_iteration, bst$best_ntreelimit) pred <- predict(bst, dtest, ntreelimit = bst$best_ntreelimit) expect_equal(length(pred), 1611) logloss_pred <- sum(-ltest * log(pred) - (1 - ltest) * log(1 - pred)) / length(ltest) logloss_log <- bst$evaluation_log[bst$best_iteration, test_logloss] expect_equal(logloss_log, logloss_pred, tolerance = 1e-5) }) test_that("early stopping works with titanic", { # This test was inspired by https://github.com/dmlc/xgboost/issues/5935 # It catches possible issues on noLD R titanic <- titanic::titanic_train titanic$Pclass <- as.factor(titanic$Pclass) dtx <- model.matrix(~ 0 + ., data = titanic[, c("Pclass", "Sex")]) dty <- titanic$Survived xgboost::xgboost( data = dtx, label = dty, objective = "binary:logistic", eval_metric = "auc", nrounds = 100, early_stopping_rounds = 3 ) expect_true(TRUE) # should not crash }) test_that("early stopping xgb.cv works", { set.seed(11) expect_output( cv <- xgb.cv(param, dtrain, nfold = 5, eta = 0.3, nrounds = 20, early_stopping_rounds = 3, maximize = FALSE) , "Stopping. Best iteration") expect_false(is.null(cv$best_iteration)) expect_lt(cv$best_iteration, 19) expect_equal(cv$best_iteration, cv$best_ntreelimit) # the best error is min error: expect_true(cv$evaluation_log[, test_error_mean[cv$best_iteration] == min(test_error_mean)]) }) test_that("prediction in xgb.cv works", { set.seed(11) nrounds <- 4 cv <- xgb.cv(param, dtrain, nfold = 5, eta = 0.5, nrounds = nrounds, prediction = TRUE, verbose = 0) expect_false(is.null(cv$evaluation_log)) expect_false(is.null(cv$pred)) expect_length(cv$pred, nrow(train$data)) err_pred <- mean(sapply(cv$folds, function(f) mean(err(ltrain[f], cv$pred[f])))) err_log <- cv$evaluation_log[nrounds, test_error_mean] expect_equal(err_pred, err_log, tolerance = 1e-6) # save CV models set.seed(11) cvx <- xgb.cv(param, dtrain, nfold = 5, eta = 0.5, nrounds = nrounds, prediction = TRUE, verbose = 0, callbacks = list(cb.cv.predict(save_models = TRUE))) expect_equal(cv$evaluation_log, cvx$evaluation_log) expect_length(cvx$models, 5) expect_true(all(sapply(cvx$models, class) == 'xgb.Booster')) }) test_that("prediction in xgb.cv works for gblinear too", { set.seed(11) p <- list(booster = 'gblinear', objective = "reg:logistic", nthread = 2) cv <- xgb.cv(p, dtrain, nfold = 5, eta = 0.5, nrounds = 2, prediction = TRUE, verbose = 0) expect_false(is.null(cv$evaluation_log)) expect_false(is.null(cv$pred)) expect_length(cv$pred, nrow(train$data)) }) test_that("prediction in early-stopping xgb.cv works", { set.seed(11) expect_output( cv <- xgb.cv(param, dtrain, nfold = 5, eta = 0.1, nrounds = 20, early_stopping_rounds = 5, maximize = FALSE, stratified = FALSE, prediction = TRUE) , "Stopping. Best iteration") expect_false(is.null(cv$best_iteration)) expect_lt(cv$best_iteration, 19) expect_false(is.null(cv$evaluation_log)) expect_false(is.null(cv$pred)) expect_length(cv$pred, nrow(train$data)) err_pred <- mean(sapply(cv$folds, function(f) mean(err(ltrain[f], cv$pred[f])))) err_log <- cv$evaluation_log[cv$best_iteration, test_error_mean] expect_equal(err_pred, err_log, tolerance = 1e-6) err_log_last <- cv$evaluation_log[cv$niter, test_error_mean] expect_gt(abs(err_pred - err_log_last), 1e-4) }) test_that("prediction in xgb.cv for softprob works", { lb <- as.numeric(iris$Species) - 1 set.seed(11) expect_warning( cv <- xgb.cv(data = as.matrix(iris[, -5]), label = lb, nfold = 4, eta = 0.5, nrounds = 5, max_depth = 3, nthread = 2, subsample = 0.8, gamma = 2, verbose = 0, prediction = TRUE, objective = "multi:softprob", num_class = 3) , NA) expect_false(is.null(cv$pred)) expect_equal(dim(cv$pred), c(nrow(iris), 3)) expect_lt(diff(range(rowSums(cv$pred))), 1e-6) }) xgboost-1.5.2/R-package/tests/testthat/test_config.R000066400000000000000000000012601417122711700224310ustar00rootroot00000000000000context('Test global configuration') test_that('Global configuration works with verbosity', { old_verbosity <- xgb.get.config()$verbosity for (v in c(0, 1, 2, 3)) { xgb.set.config(verbosity = v) expect_equal(xgb.get.config()$verbosity, v) } xgb.set.config(verbosity = old_verbosity) expect_equal(xgb.get.config()$verbosity, old_verbosity) }) test_that('Global configuration works with use_rmm flag', { old_use_rmm_flag <- xgb.get.config()$use_rmm for (v in c(TRUE, FALSE)) { xgb.set.config(use_rmm = v) expect_equal(xgb.get.config()$use_rmm, v) } xgb.set.config(use_rmm = old_use_rmm_flag) expect_equal(xgb.get.config()$use_rmm, old_use_rmm_flag) }) xgboost-1.5.2/R-package/tests/testthat/test_custom_objective.R000066400000000000000000000055241417122711700245370ustar00rootroot00000000000000context('Test models with custom objective') require(xgboost) set.seed(1994) data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') dtrain <- xgb.DMatrix(agaricus.train$data, label = agaricus.train$label) dtest <- xgb.DMatrix(agaricus.test$data, label = agaricus.test$label) watchlist <- list(eval = dtest, train = dtrain) logregobj <- function(preds, dtrain) { labels <- getinfo(dtrain, "label") preds <- 1 / (1 + exp(-preds)) grad <- preds - labels hess <- preds * (1 - preds) return(list(grad = grad, hess = hess)) } evalerror <- function(preds, dtrain) { labels <- getinfo(dtrain, "label") err <- as.numeric(sum(labels != (preds > 0.5))) / length(labels) return(list(metric = "error", value = err)) } param <- list(max_depth = 2, eta = 1, nthread = 2, objective = logregobj, eval_metric = evalerror) num_round <- 2 test_that("custom objective works", { bst <- xgb.train(param, dtrain, num_round, watchlist) expect_equal(class(bst), "xgb.Booster") expect_false(is.null(bst$evaluation_log)) expect_false(is.null(bst$evaluation_log$eval_error)) expect_lt(bst$evaluation_log[num_round, eval_error], 0.03) }) test_that("custom objective in CV works", { cv <- xgb.cv(param, dtrain, num_round, nfold = 10, verbose = FALSE) expect_false(is.null(cv$evaluation_log)) expect_equal(dim(cv$evaluation_log), c(2, 5)) expect_lt(cv$evaluation_log[num_round, test_error_mean], 0.03) }) test_that("custom objective with early stop works", { bst <- xgb.train(param, dtrain, 10, watchlist) expect_equal(class(bst), "xgb.Booster") train_log <- bst$evaluation_log$train_error expect_true(all(diff(train_log) <= 0)) }) test_that("custom objective using DMatrix attr works", { attr(dtrain, 'label') <- getinfo(dtrain, 'label') logregobjattr <- function(preds, dtrain) { labels <- attr(dtrain, 'label') preds <- 1 / (1 + exp(-preds)) grad <- preds - labels hess <- preds * (1 - preds) return(list(grad = grad, hess = hess)) } param$objective <- logregobjattr bst <- xgb.train(param, dtrain, num_round, watchlist) expect_equal(class(bst), "xgb.Booster") }) test_that("custom objective with multi-class works", { data <- as.matrix(iris[, -5]) label <- as.numeric(iris$Species) - 1 dtrain <- xgb.DMatrix(data = data, label = label) nclasses <- 3 fake_softprob <- function(preds, dtrain) { expect_true(all(matrix(preds) == 0.5)) grad <- rnorm(dim(as.matrix(preds))[1]) expect_equal(dim(data)[1] * nclasses, dim(as.matrix(preds))[1]) hess <- rnorm(dim(as.matrix(preds))[1]) return (list(grad = grad, hess = hess)) } fake_merror <- function(preds, dtrain) { expect_equal(dim(data)[1] * nclasses, dim(as.matrix(preds))[1]) } param$objective <- fake_softprob param$eval_metric <- fake_merror bst <- xgb.train(param, dtrain, 1, num_class = nclasses) }) xgboost-1.5.2/R-package/tests/testthat/test_dmatrix.R000066400000000000000000000076111417122711700226420ustar00rootroot00000000000000require(xgboost) require(Matrix) context("testing xgb.DMatrix functionality") data(agaricus.test, package = 'xgboost') test_data <- agaricus.test$data[1:100, ] test_label <- agaricus.test$label[1:100] test_that("xgb.DMatrix: basic construction", { # from sparse matrix dtest1 <- xgb.DMatrix(test_data, label = test_label) # from dense matrix dtest2 <- xgb.DMatrix(as.matrix(test_data), label = test_label) expect_equal(getinfo(dtest1, 'label'), getinfo(dtest2, 'label')) expect_equal(dim(dtest1), dim(dtest2)) #from dense integer matrix int_data <- as.matrix(test_data) storage.mode(int_data) <- "integer" dtest3 <- xgb.DMatrix(int_data, label = test_label) expect_equal(dim(dtest1), dim(dtest3)) }) test_that("xgb.DMatrix: saving, loading", { # save to a local file dtest1 <- xgb.DMatrix(test_data, label = test_label) tmp_file <- tempfile('xgb.DMatrix_') expect_true(xgb.DMatrix.save(dtest1, tmp_file)) # read from a local file expect_output(dtest3 <- xgb.DMatrix(tmp_file), "entries loaded from") expect_output(dtest3 <- xgb.DMatrix(tmp_file, silent = TRUE), NA) unlink(tmp_file) expect_equal(getinfo(dtest1, 'label'), getinfo(dtest3, 'label')) # from a libsvm text file tmp <- c("0 1:1 2:1", "1 3:1", "0 1:1") tmp_file <- 'tmp.libsvm' writeLines(tmp, tmp_file) dtest4 <- xgb.DMatrix(tmp_file, silent = TRUE) expect_equal(dim(dtest4), c(3, 4)) expect_equal(getinfo(dtest4, 'label'), c(0, 1, 0)) unlink(tmp_file) }) test_that("xgb.DMatrix: getinfo & setinfo", { dtest <- xgb.DMatrix(test_data) expect_true(setinfo(dtest, 'label', test_label)) labels <- getinfo(dtest, 'label') expect_equal(test_label, getinfo(dtest, 'label')) expect_true(setinfo(dtest, 'label_lower_bound', test_label)) expect_equal(test_label, getinfo(dtest, 'label_lower_bound')) expect_true(setinfo(dtest, 'label_upper_bound', test_label)) expect_equal(test_label, getinfo(dtest, 'label_upper_bound')) expect_true(length(getinfo(dtest, 'weight')) == 0) expect_true(length(getinfo(dtest, 'base_margin')) == 0) expect_true(setinfo(dtest, 'weight', test_label)) expect_true(setinfo(dtest, 'base_margin', test_label)) expect_true(setinfo(dtest, 'group', c(50, 50))) expect_error(setinfo(dtest, 'group', test_label)) # providing character values will give an error expect_error(setinfo(dtest, 'weight', rep('a', nrow(test_data)))) # any other label should error expect_error(setinfo(dtest, 'asdf', test_label)) }) test_that("xgb.DMatrix: slice, dim", { dtest <- xgb.DMatrix(test_data, label = test_label) expect_equal(dim(dtest), dim(test_data)) dsub1 <- slice(dtest, 1:42) expect_equal(nrow(dsub1), 42) expect_equal(ncol(dsub1), ncol(test_data)) dsub2 <- dtest[1:42, ] expect_equal(dim(dtest), dim(test_data)) expect_equal(getinfo(dsub1, 'label'), getinfo(dsub2, 'label')) }) test_that("xgb.DMatrix: slice, trailing empty rows", { data(agaricus.train, package = 'xgboost') train_data <- agaricus.train$data train_label <- agaricus.train$label dtrain <- xgb.DMatrix(data = train_data, label = train_label) slice(dtrain, 6513L) train_data[6513, ] <- 0 dtrain <- xgb.DMatrix(data = train_data, label = train_label) slice(dtrain, 6513L) expect_equal(nrow(dtrain), 6513) }) test_that("xgb.DMatrix: colnames", { dtest <- xgb.DMatrix(test_data, label = test_label) expect_equal(colnames(dtest), colnames(test_data)) expect_error(colnames(dtest) <- 'asdf') new_names <- make.names(seq_len(ncol(test_data))) expect_silent(colnames(dtest) <- new_names) expect_equal(colnames(dtest), new_names) expect_silent(colnames(dtest) <- NULL) expect_null(colnames(dtest)) }) test_that("xgb.DMatrix: nrow is correct for a very sparse matrix", { set.seed(123) nr <- 1000 x <- rsparsematrix(nr, 100, density = 0.0005) # we want it very sparse, so that last rows are empty expect_lt(max(x@i), nr) dtest <- xgb.DMatrix(x) expect_equal(dim(dtest), dim(x)) }) xgboost-1.5.2/R-package/tests/testthat/test_gc_safety.R000066400000000000000000000010171417122711700231300ustar00rootroot00000000000000require(xgboost) context("Garbage Collection Safety Check") test_that("train and prediction when gctorture is on", { data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') train <- agaricus.train test <- agaricus.test gctorture(TRUE) bst <- xgboost(data = train$data, label = train$label, max.depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") pred <- predict(bst, test$data) gctorture(FALSE) expect_length(pred, length(test$label)) }) xgboost-1.5.2/R-package/tests/testthat/test_glm.R000066400000000000000000000056731417122711700217570ustar00rootroot00000000000000context('Test generalized linear models') require(xgboost) test_that("gblinear works", { data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') dtrain <- xgb.DMatrix(agaricus.train$data, label = agaricus.train$label) dtest <- xgb.DMatrix(agaricus.test$data, label = agaricus.test$label) param <- list(objective = "binary:logistic", eval_metric = "error", booster = "gblinear", nthread = 2, eta = 0.8, alpha = 0.0001, lambda = 0.0001) watchlist <- list(eval = dtest, train = dtrain) n <- 5 # iterations ERR_UL <- 0.005 # upper limit for the test set error VERB <- 0 # chatterbox switch param$updater <- 'shotgun' bst <- xgb.train(param, dtrain, n, watchlist, verbose = VERB, feature_selector = 'shuffle') ypred <- predict(bst, dtest) expect_equal(length(getinfo(dtest, 'label')), 1611) expect_lt(bst$evaluation_log$eval_error[n], ERR_UL) bst <- xgb.train(param, dtrain, n, watchlist, verbose = VERB, feature_selector = 'cyclic', callbacks = list(cb.gblinear.history())) expect_lt(bst$evaluation_log$eval_error[n], ERR_UL) h <- xgb.gblinear.history(bst) expect_equal(dim(h), c(n, ncol(dtrain) + 1)) expect_is(h, "matrix") param$updater <- 'coord_descent' bst <- xgb.train(param, dtrain, n, watchlist, verbose = VERB, feature_selector = 'cyclic') expect_lt(bst$evaluation_log$eval_error[n], ERR_UL) bst <- xgb.train(param, dtrain, n, watchlist, verbose = VERB, feature_selector = 'shuffle') expect_lt(bst$evaluation_log$eval_error[n], ERR_UL) bst <- xgb.train(param, dtrain, 2, watchlist, verbose = VERB, feature_selector = 'greedy') expect_lt(bst$evaluation_log$eval_error[2], ERR_UL) bst <- xgb.train(param, dtrain, n, watchlist, verbose = VERB, feature_selector = 'thrifty', top_k = 50, callbacks = list(cb.gblinear.history(sparse = TRUE))) expect_lt(bst$evaluation_log$eval_error[n], ERR_UL) h <- xgb.gblinear.history(bst) expect_equal(dim(h), c(n, ncol(dtrain) + 1)) expect_s4_class(h, "dgCMatrix") }) test_that("gblinear early stopping works", { data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') dtrain <- xgb.DMatrix(agaricus.train$data, label = agaricus.train$label) dtest <- xgb.DMatrix(agaricus.test$data, label = agaricus.test$label) param <- list( objective = "binary:logistic", eval_metric = "error", booster = "gblinear", nthread = 2, eta = 0.8, alpha = 0.0001, lambda = 0.0001, updater = "coord_descent" ) es_round <- 1 n <- 10 booster <- xgb.train( param, dtrain, n, list(eval = dtest, train = dtrain), early_stopping_rounds = es_round ) expect_equal(booster$best_iteration, 5) predt_es <- predict(booster, dtrain) n <- booster$best_iteration + es_round booster <- xgb.train( param, dtrain, n, list(eval = dtest, train = dtrain), early_stopping_rounds = es_round ) predt <- predict(booster, dtrain) expect_equal(predt_es, predt) }) xgboost-1.5.2/R-package/tests/testthat/test_helpers.R000066400000000000000000000446571417122711700226470ustar00rootroot00000000000000library(testthat) context('Test helper functions') require(xgboost) require(data.table) require(Matrix) require(vcd, quietly = TRUE) float_tolerance <- 5e-6 # disable some tests for 32-bit environment flag_32bit <- .Machine$sizeof.pointer != 8 set.seed(1982) data(Arthritis) df <- data.table(Arthritis, keep.rownames = FALSE) df[, AgeDiscret := as.factor(round(Age / 10, 0))] df[, AgeCat := as.factor(ifelse(Age > 30, "Old", "Young"))] df[, ID := NULL] sparse_matrix <- sparse.model.matrix(Improved~.-1, data = df) # nolint label <- df[, ifelse(Improved == "Marked", 1, 0)] # binary nrounds <- 12 bst.Tree <- xgboost(data = sparse_matrix, label = label, max_depth = 9, eta = 1, nthread = 2, nrounds = nrounds, verbose = 0, objective = "binary:logistic", booster = "gbtree") bst.GLM <- xgboost(data = sparse_matrix, label = label, eta = 1, nthread = 1, nrounds = nrounds, verbose = 0, objective = "binary:logistic", booster = "gblinear") feature.names <- colnames(sparse_matrix) # multiclass mlabel <- as.numeric(iris$Species) - 1 nclass <- 3 mbst.Tree <- xgboost(data = as.matrix(iris[, -5]), label = mlabel, verbose = 0, max_depth = 3, eta = 0.5, nthread = 2, nrounds = nrounds, objective = "multi:softprob", num_class = nclass, base_score = 0) mbst.GLM <- xgboost(data = as.matrix(iris[, -5]), label = mlabel, verbose = 0, booster = "gblinear", eta = 0.1, nthread = 1, nrounds = nrounds, objective = "multi:softprob", num_class = nclass, base_score = 0) test_that("xgb.dump works", { if (!flag_32bit) expect_length(xgb.dump(bst.Tree), 200) dump_file <- file.path(tempdir(), 'xgb.model.dump') expect_true(xgb.dump(bst.Tree, dump_file, with_stats = TRUE)) expect_true(file.exists(dump_file)) expect_gt(file.size(dump_file), 8000) # JSON format dmp <- xgb.dump(bst.Tree, dump_format = "json") expect_length(dmp, 1) if (!flag_32bit) expect_length(grep('nodeid', strsplit(dmp, '\n')[[1]]), 188) }) test_that("xgb.dump works for gblinear", { expect_length(xgb.dump(bst.GLM), 14) # also make sure that it works properly for a sparse model where some coefficients # are 0 from setting large L1 regularization: bst.GLM.sp <- xgboost(data = sparse_matrix, label = label, eta = 1, nthread = 2, nrounds = 1, alpha = 2, objective = "binary:logistic", booster = "gblinear") d.sp <- xgb.dump(bst.GLM.sp) expect_length(d.sp, 14) expect_gt(sum(d.sp == "0"), 0) # JSON format dmp <- xgb.dump(bst.GLM.sp, dump_format = "json") expect_length(dmp, 1) expect_length(grep('\\d', strsplit(dmp, '\n')[[1]]), 11) }) test_that("predict leafs works", { # no error for gbtree expect_error(pred_leaf <- predict(bst.Tree, sparse_matrix, predleaf = TRUE), regexp = NA) expect_equal(dim(pred_leaf), c(nrow(sparse_matrix), nrounds)) # error for gblinear expect_error(predict(bst.GLM, sparse_matrix, predleaf = TRUE)) }) test_that("predict feature contributions works", { # gbtree binary classifier expect_error(pred_contr <- predict(bst.Tree, sparse_matrix, predcontrib = TRUE), regexp = NA) expect_equal(dim(pred_contr), c(nrow(sparse_matrix), ncol(sparse_matrix) + 1)) expect_equal(colnames(pred_contr), c(colnames(sparse_matrix), "BIAS")) pred <- predict(bst.Tree, sparse_matrix, outputmargin = TRUE) expect_lt(max(abs(rowSums(pred_contr) - pred)), 1e-5) # must work with data that has no column names X <- sparse_matrix colnames(X) <- NULL expect_error(pred_contr_ <- predict(bst.Tree, X, predcontrib = TRUE), regexp = NA) expect_equal(pred_contr, pred_contr_, check.attributes = FALSE, tolerance = float_tolerance) # gbtree binary classifier (approximate method) expect_error(pred_contr <- predict(bst.Tree, sparse_matrix, predcontrib = TRUE, approxcontrib = TRUE), regexp = NA) expect_equal(dim(pred_contr), c(nrow(sparse_matrix), ncol(sparse_matrix) + 1)) expect_equal(colnames(pred_contr), c(colnames(sparse_matrix), "BIAS")) pred <- predict(bst.Tree, sparse_matrix, outputmargin = TRUE) expect_lt(max(abs(rowSums(pred_contr) - pred)), 1e-5) # gblinear binary classifier expect_error(pred_contr <- predict(bst.GLM, sparse_matrix, predcontrib = TRUE), regexp = NA) expect_equal(dim(pred_contr), c(nrow(sparse_matrix), ncol(sparse_matrix) + 1)) expect_equal(colnames(pred_contr), c(colnames(sparse_matrix), "BIAS")) pred <- predict(bst.GLM, sparse_matrix, outputmargin = TRUE) expect_lt(max(abs(rowSums(pred_contr) - pred)), 1e-5) # manual calculation of linear terms coefs <- as.numeric(xgb.dump(bst.GLM)[-c(1, 2, 4)]) coefs <- c(coefs[-1], coefs[1]) # intercept must be the last pred_contr_manual <- sweep(cbind(sparse_matrix, 1), 2, coefs, FUN = "*") expect_equal(as.numeric(pred_contr), as.numeric(pred_contr_manual), tolerance = float_tolerance) # gbtree multiclass pred <- predict(mbst.Tree, as.matrix(iris[, -5]), outputmargin = TRUE, reshape = TRUE) pred_contr <- predict(mbst.Tree, as.matrix(iris[, -5]), predcontrib = TRUE) expect_is(pred_contr, "list") expect_length(pred_contr, 3) for (g in seq_along(pred_contr)) { expect_equal(colnames(pred_contr[[g]]), c(colnames(iris[, -5]), "BIAS")) expect_lt(max(abs(rowSums(pred_contr[[g]]) - pred[, g])), 1e-5) } # gblinear multiclass (set base_score = 0, which is base margin in multiclass) pred <- predict(mbst.GLM, as.matrix(iris[, -5]), outputmargin = TRUE, reshape = TRUE) pred_contr <- predict(mbst.GLM, as.matrix(iris[, -5]), predcontrib = TRUE) expect_length(pred_contr, 3) coefs_all <- matrix( data = as.numeric(xgb.dump(mbst.GLM)[-c(1, 2, 6)]), ncol = 3, byrow = TRUE ) for (g in seq_along(pred_contr)) { expect_equal(colnames(pred_contr[[g]]), c(colnames(iris[, -5]), "BIAS")) expect_lt(max(abs(rowSums(pred_contr[[g]]) - pred[, g])), float_tolerance) # manual calculation of linear terms coefs <- c(coefs_all[-1, g], coefs_all[1, g]) # intercept needs to be the last pred_contr_manual <- sweep(as.matrix(cbind(iris[, -5], 1)), 2, coefs, FUN = "*") expect_equal(as.numeric(pred_contr[[g]]), as.numeric(pred_contr_manual), tolerance = float_tolerance) } }) test_that("SHAPs sum to predictions, with or without DART", { d <- cbind( x1 = rnorm(100), x2 = rnorm(100), x3 = rnorm(100)) y <- d[, "x1"] + d[, "x2"]^2 + ifelse(d[, "x3"] > .5, d[, "x3"]^2, 2^d[, "x3"]) + rnorm(100) nrounds <- 30 for (booster in list("gbtree", "dart")) { fit <- xgboost( params = c( list( booster = booster, objective = "reg:squarederror", eval_metric = "rmse"), if (booster == "dart") list(rate_drop = .01, one_drop = TRUE)), data = d, label = y, nrounds = nrounds) pr <- function(...) predict(fit, newdata = d, ...) pred <- pr() shap <- pr(predcontrib = TRUE) shapi <- pr(predinteraction = TRUE) tol <- 1e-5 expect_equal(rowSums(shap), pred, tol = tol) expect_equal(apply(shapi, 1, sum), pred, tol = tol) for (i in seq_len(nrow(d))) for (f in list(rowSums, colSums)) expect_equal(f(shapi[i, , ]), shap[i, ], tol = tol) } }) test_that("xgb-attribute functionality", { val <- "my attribute value" list.val <- list(my_attr = val, a = 123, b = 'ok') list.ch <- list.val[order(names(list.val))] list.ch <- lapply(list.ch, as.character) # note: iter is 0-index in xgb attributes list.default <- list(niter = as.character(nrounds - 1)) list.ch <- c(list.ch, list.default) # proper input: expect_error(xgb.attr(bst.Tree, NULL)) expect_error(xgb.attr(val, val)) # set & get: expect_null(xgb.attr(bst.Tree, "asdf")) expect_equal(xgb.attributes(bst.Tree), list.default) xgb.attr(bst.Tree, "my_attr") <- val expect_equal(xgb.attr(bst.Tree, "my_attr"), val) xgb.attributes(bst.Tree) <- list.val expect_equal(xgb.attributes(bst.Tree), list.ch) # serializing: xgb.save(bst.Tree, 'xgb.model') bst <- xgb.load('xgb.model') if (file.exists('xgb.model')) file.remove('xgb.model') expect_equal(xgb.attr(bst, "my_attr"), val) expect_equal(xgb.attributes(bst), list.ch) # deletion: xgb.attr(bst, "my_attr") <- NULL expect_null(xgb.attr(bst, "my_attr")) expect_equal(xgb.attributes(bst), list.ch[c("a", "b", "niter")]) xgb.attributes(bst) <- list(a = NULL, b = NULL) expect_equal(xgb.attributes(bst), list.default) xgb.attributes(bst) <- list(niter = NULL) expect_null(xgb.attributes(bst)) }) if (grepl('Windows', Sys.info()[['sysname']]) || grepl('Linux', Sys.info()[['sysname']]) || grepl('Darwin', Sys.info()[['sysname']])) { test_that("xgb-attribute numeric precision", { # check that lossless conversion works with 17 digits # numeric -> character -> numeric X <- 10^runif(100, -20, 20) if (capabilities('long.double')) { X2X <- as.numeric(format(X, digits = 17)) expect_equal(X, X2X, tolerance = float_tolerance) } # retrieved attributes to be the same as written for (x in X) { xgb.attr(bst.Tree, "x") <- x expect_equal(as.numeric(xgb.attr(bst.Tree, "x")), x, tolerance = float_tolerance) xgb.attributes(bst.Tree) <- list(a = "A", b = x) expect_equal(as.numeric(xgb.attr(bst.Tree, "b")), x, tolerance = float_tolerance) } }) } test_that("xgb.Booster serializing as R object works", { saveRDS(bst.Tree, 'xgb.model.rds') bst <- readRDS('xgb.model.rds') dtrain <- xgb.DMatrix(sparse_matrix, label = label) expect_equal(predict(bst.Tree, dtrain), predict(bst, dtrain), tolerance = float_tolerance) expect_equal(xgb.dump(bst.Tree), xgb.dump(bst)) xgb.save(bst, 'xgb.model') if (file.exists('xgb.model')) file.remove('xgb.model') bst <- readRDS('xgb.model.rds') if (file.exists('xgb.model.rds')) file.remove('xgb.model.rds') nil_ptr <- new("externalptr") class(nil_ptr) <- "xgb.Booster.handle" expect_true(identical(bst$handle, nil_ptr)) bst <- xgb.Booster.complete(bst) expect_true(!identical(bst$handle, nil_ptr)) expect_equal(predict(bst.Tree, dtrain), predict(bst, dtrain), tolerance = float_tolerance) }) test_that("xgb.model.dt.tree works with and without feature names", { names.dt.trees <- c("Tree", "Node", "ID", "Feature", "Split", "Yes", "No", "Missing", "Quality", "Cover") dt.tree <- xgb.model.dt.tree(feature_names = feature.names, model = bst.Tree) expect_equal(names.dt.trees, names(dt.tree)) if (!flag_32bit) expect_equal(dim(dt.tree), c(188, 10)) expect_output(str(dt.tree), 'Feature.*\\"Age\\"') dt.tree.0 <- xgb.model.dt.tree(model = bst.Tree) expect_equal(dt.tree, dt.tree.0) # when model contains no feature names: bst.Tree.x <- bst.Tree bst.Tree.x$feature_names <- NULL dt.tree.x <- xgb.model.dt.tree(model = bst.Tree.x) expect_output(str(dt.tree.x), 'Feature.*\\"3\\"') expect_equal(dt.tree[, -4, with = FALSE], dt.tree.x[, -4, with = FALSE]) # using integer node ID instead of character dt.tree.int <- xgb.model.dt.tree(model = bst.Tree, use_int_id = TRUE) expect_equal(as.integer(tstrsplit(dt.tree$Yes, '-')[[2]]), dt.tree.int$Yes) expect_equal(as.integer(tstrsplit(dt.tree$No, '-')[[2]]), dt.tree.int$No) expect_equal(as.integer(tstrsplit(dt.tree$Missing, '-')[[2]]), dt.tree.int$Missing) }) test_that("xgb.model.dt.tree throws error for gblinear", { expect_error(xgb.model.dt.tree(model = bst.GLM)) }) test_that("xgb.importance works with and without feature names", { importance.Tree <- xgb.importance(feature_names = feature.names, model = bst.Tree) if (!flag_32bit) expect_equal(dim(importance.Tree), c(7, 4)) expect_equal(colnames(importance.Tree), c("Feature", "Gain", "Cover", "Frequency")) expect_output(str(importance.Tree), 'Feature.*\\"Age\\"') importance.Tree.0 <- xgb.importance(model = bst.Tree) expect_equal(importance.Tree, importance.Tree.0, tolerance = float_tolerance) # when model contains no feature names: bst.Tree.x <- bst.Tree bst.Tree.x$feature_names <- NULL importance.Tree.x <- xgb.importance(model = bst.Tree) expect_equal(importance.Tree[, -1, with = FALSE], importance.Tree.x[, -1, with = FALSE], tolerance = float_tolerance) imp2plot <- xgb.plot.importance(importance_matrix = importance.Tree) expect_equal(colnames(imp2plot), c("Feature", "Gain", "Cover", "Frequency", "Importance")) xgb.ggplot.importance(importance_matrix = importance.Tree) # for multiclass imp.Tree <- xgb.importance(model = mbst.Tree) expect_equal(dim(imp.Tree), c(4, 4)) trees <- seq(from = 0, by = 2, length.out = 2) importance <- xgb.importance(feature_names = feature.names, model = bst.Tree, trees = trees) importance_from_dump <- function() { model_text_dump <- xgb.dump(model = bst.Tree, with_stats = TRUE, trees = trees) imp <- xgb.model.dt.tree( feature_names = feature.names, text = model_text_dump, trees = trees )[ Feature != "Leaf", .( Gain = sum(Quality), Cover = sum(Cover), Frequency = .N ), by = Feature ][ , `:=`( Gain = Gain / sum(Gain), Cover = Cover / sum(Cover), Frequency = Frequency / sum(Frequency) ) ][ order(Gain, decreasing = TRUE) ] imp } expect_equal(importance_from_dump(), importance, tolerance = 1e-6) }) test_that("xgb.importance works with GLM model", { importance.GLM <- xgb.importance(feature_names = feature.names, model = bst.GLM) expect_equal(dim(importance.GLM), c(10, 2)) expect_equal(colnames(importance.GLM), c("Feature", "Weight")) xgb.importance(model = bst.GLM) imp2plot <- xgb.plot.importance(importance.GLM) expect_equal(colnames(imp2plot), c("Feature", "Weight", "Importance")) xgb.ggplot.importance(importance.GLM) # for multiclass imp.GLM <- xgb.importance(model = mbst.GLM) expect_equal(dim(imp.GLM), c(12, 3)) expect_equal(imp.GLM$Class, rep(0:2, each = 4)) }) test_that("xgb.model.dt.tree and xgb.importance work with a single split model", { bst1 <- xgboost(data = sparse_matrix, label = label, max_depth = 1, eta = 1, nthread = 2, nrounds = 1, verbose = 0, objective = "binary:logistic") expect_error(dt <- xgb.model.dt.tree(model = bst1), regexp = NA) # no error expect_equal(nrow(dt), 3) expect_error(imp <- xgb.importance(model = bst1), regexp = NA) # no error expect_equal(nrow(imp), 1) expect_equal(imp$Gain, 1) }) test_that("xgb.plot.tree works with and without feature names", { expect_silent(xgb.plot.tree(feature_names = feature.names, model = bst.Tree)) expect_silent(xgb.plot.tree(model = bst.Tree)) }) test_that("xgb.plot.multi.trees works with and without feature names", { xgb.plot.multi.trees(model = bst.Tree, feature_names = feature.names, features_keep = 3) xgb.plot.multi.trees(model = bst.Tree, features_keep = 3) }) test_that("xgb.plot.deepness works", { d2p <- xgb.plot.deepness(model = bst.Tree) expect_equal(colnames(d2p), c("ID", "Tree", "Depth", "Cover", "Weight")) xgb.plot.deepness(model = bst.Tree, which = "med.depth") xgb.ggplot.deepness(model = bst.Tree) }) test_that("xgb.shap.data works when top_n is provided", { data_list <- xgb.shap.data(data = sparse_matrix, model = bst.Tree, top_n = 2) expect_equal(names(data_list), c("data", "shap_contrib")) expect_equal(NCOL(data_list$data), 2) expect_equal(NCOL(data_list$shap_contrib), 2) expect_equal(NROW(data_list$data), NROW(data_list$shap_contrib)) expect_gt(length(colnames(data_list$data)), 0) expect_gt(length(colnames(data_list$shap_contrib)), 0) # for multiclass without target class provided data_list <- xgb.shap.data(data = as.matrix(iris[, -5]), model = mbst.Tree, top_n = 2) expect_equal(dim(data_list$shap_contrib), c(nrow(iris), 2)) # for multiclass with target class provided data_list <- xgb.shap.data(data = as.matrix(iris[, -5]), model = mbst.Tree, top_n = 2, target_class = 0) expect_equal(dim(data_list$shap_contrib), c(nrow(iris), 2)) }) test_that("xgb.shap.data works with subsampling", { data_list <- xgb.shap.data(data = sparse_matrix, model = bst.Tree, top_n = 2, subsample = 0.8) expect_equal(NROW(data_list$data), as.integer(0.8 * nrow(sparse_matrix))) expect_equal(NROW(data_list$data), NROW(data_list$shap_contrib)) }) test_that("prepare.ggplot.shap.data works", { data_list <- xgb.shap.data(data = sparse_matrix, model = bst.Tree, top_n = 2) plot_data <- prepare.ggplot.shap.data(data_list, normalize = TRUE) expect_s3_class(plot_data, "data.frame") expect_equal(names(plot_data), c("id", "feature", "feature_value", "shap_value")) expect_s3_class(plot_data$feature, "factor") # Each observation should have 1 row for each feature expect_equal(nrow(plot_data), nrow(sparse_matrix) * 2) }) test_that("xgb.plot.shap works", { sh <- xgb.plot.shap(data = sparse_matrix, model = bst.Tree, top_n = 2, col = 4) expect_equal(names(sh), c("data", "shap_contrib")) }) test_that("xgb.plot.shap.summary works", { expect_silent(xgb.plot.shap.summary(data = sparse_matrix, model = bst.Tree, top_n = 2)) expect_silent(xgb.ggplot.shap.summary(data = sparse_matrix, model = bst.Tree, top_n = 2)) }) test_that("check.deprecation works", { ttt <- function(a = NNULL, DUMMY=NULL, ...) { check.deprecation(...) as.list((environment())) } res <- ttt(a = 1, DUMMY = 2, z = 3) expect_equal(res, list(a = 1, DUMMY = 2)) expect_warning( res <- ttt(a = 1, dummy = 22, z = 3) , "\'dummy\' is deprecated") expect_equal(res, list(a = 1, DUMMY = 22)) expect_warning( res <- ttt(a = 1, dumm = 22, z = 3) , "\'dumm\' was partially matched to \'dummy\'") expect_equal(res, list(a = 1, DUMMY = 22)) }) test_that('convert.labels works', { y <- c(0, 1, 0, 0, 1) for (objective in c('binary:logistic', 'binary:logitraw', 'binary:hinge')) { res <- xgboost:::convert.labels(y, objective_name = objective) expect_s3_class(res, 'factor') expect_equal(res, factor(res)) } y <- c(0, 1, 3, 2, 1, 4) for (objective in c('multi:softmax', 'multi:softprob', 'rank:pairwise', 'rank:ndcg', 'rank:map')) { res <- xgboost:::convert.labels(y, objective_name = objective) expect_s3_class(res, 'factor') expect_equal(res, factor(res)) } y <- c(1.2, 3.0, -1.0, 10.0) for (objective in c('reg:squarederror', 'reg:squaredlogerror', 'reg:logistic', 'reg:pseudohubererror', 'count:poisson', 'survival:cox', 'survival:aft', 'reg:gamma', 'reg:tweedie')) { res <- xgboost:::convert.labels(y, objective_name = objective) expect_equal(class(res), 'numeric') } }) xgboost-1.5.2/R-package/tests/testthat/test_interaction_constraints.R000066400000000000000000000036161417122711700261410ustar00rootroot00000000000000require(xgboost) context("interaction constraints") set.seed(1024) x1 <- rnorm(1000, 1) x2 <- rnorm(1000, 1) x3 <- sample(c(1, 2, 3), size = 1000, replace = TRUE) y <- x1 + x2 + x3 + x1 * x2 * x3 + rnorm(1000, 0.001) + 3 * sin(x1) train <- matrix(c(x1, x2, x3), ncol = 3) test_that("interaction constraints for regression", { # Fit a model that only allows interaction between x1 and x2 bst <- xgboost(data = train, label = y, max_depth = 3, eta = 0.1, nthread = 2, nrounds = 100, verbose = 0, interaction_constraints = list(c(0, 1))) # Set all observations to have the same x3 values then increment # by the same amount preds <- lapply(c(1, 2, 3), function(x){ tmat <- matrix(c(x1, x2, rep(x, 1000)), ncol = 3) return(predict(bst, tmat)) }) # Check incrementing x3 has the same effect on all observations # since x3 is constrained to be independent of x1 and x2 # and all observations start off from the same x3 value diff1 <- preds[[2]] - preds[[1]] test1 <- all(abs(diff1 - diff1[1]) < 1e-4) diff2 <- preds[[3]] - preds[[2]] test2 <- all(abs(diff2 - diff2[1]) < 1e-4) expect_true({ test1 & test2 }, "Interaction Contraint Satisfied") }) test_that("interaction constraints scientific representation", { rows <- 10 ## When number exceeds 1e5, R paste function uses scientific representation. ## See: https://github.com/dmlc/xgboost/issues/5179 cols <- 1e5 + 10 d <- matrix(rexp(rows, rate = .1), nrow = rows, ncol = cols) y <- rnorm(rows) dtrain <- xgb.DMatrix(data = d, info = list(label = y)) inc <- list(c(seq.int(from = 0, to = cols, by = 1))) with_inc <- xgb.train(data = dtrain, tree_method = 'hist', interaction_constraints = inc, nrounds = 10) without_inc <- xgb.train(data = dtrain, tree_method = 'hist', nrounds = 10) expect_equal(xgb.save.raw(with_inc), xgb.save.raw(without_inc)) }) xgboost-1.5.2/R-package/tests/testthat/test_interactions.R000066400000000000000000000137641417122711700237020ustar00rootroot00000000000000context('Test prediction of feature interactions') require(xgboost) set.seed(123) test_that("predict feature interactions works", { # simulate some binary data and a linear outcome with an interaction term N <- 1000 P <- 5 X <- matrix(rbinom(N * P, 1, 0.5), ncol = P, dimnames = list(NULL, letters[1:P])) # center the data (as contributions are computed WRT feature means) X <- scale(X, scale = FALSE) # outcome without any interactions, without any noise: f <- function(x) 2 * x[, 1] - 3 * x[, 2] # outcome with interactions, without noise: f_int <- function(x) f(x) + 2 * x[, 2] * x[, 3] # outcome with interactions, with noise: #f_int_noise <- function(x) f_int(x) + rnorm(N, 0, 0.3) y <- f_int(X) dm <- xgb.DMatrix(X, label = y) param <- list(eta = 0.1, max_depth = 4, base_score = mean(y), lambda = 0, nthread = 2) b <- xgb.train(param, dm, 100) pred <- predict(b, dm, outputmargin = TRUE) # SHAP contributions: cont <- predict(b, dm, predcontrib = TRUE) expect_equal(dim(cont), c(N, P + 1)) # make sure for each row they add up to marginal predictions expect_lt(max(abs(rowSums(cont) - pred)), 0.001) # Hand-construct the 'ground truth' feature contributions: gt_cont <- cbind( 2. * X[, 1], -3. * X[, 2] + 1. * X[, 2] * X[, 3], # attribute a HALF of the interaction term to feature #2 1. * X[, 2] * X[, 3] # and another HALF of the interaction term to feature #3 ) gt_cont <- cbind(gt_cont, matrix(0, nrow = N, ncol = P + 1 - 3)) # These should be relatively close: expect_lt(max(abs(cont - gt_cont)), 0.05) # SHAP interaction contributions: intr <- predict(b, dm, predinteraction = TRUE) expect_equal(dim(intr), c(N, P + 1, P + 1)) # check assigned colnames cn <- c(letters[1:P], "BIAS") expect_equal(dimnames(intr), list(NULL, cn, cn)) # check the symmetry expect_lt(max(abs(aperm(intr, c(1, 3, 2)) - intr)), 0.00001) # sums WRT columns must be close to feature contributions expect_lt(max(abs(apply(intr, c(1, 2), sum) - cont)), 0.00001) # diagonal terms for features 3,4,5 must be close to zero expect_lt(Reduce(max, sapply(3:P, function(i) max(abs(intr[, i, i])))), 0.05) # BIAS must have no interactions expect_lt(max(abs(intr[, 1:P, P + 1])), 0.00001) # interactions other than 2 x 3 must be close to zero intr23 <- intr intr23[, 2, 3] <- 0 expect_lt( Reduce(max, sapply(1:P, function(i) max(abs(intr23[, i, (i + 1):(P + 1)])))), 0.05 ) # Construct the 'ground truth' contributions of interactions directly from the linear terms: gt_intr <- array(0, c(N, P + 1, P + 1)) gt_intr[, 2, 3] <- 1. * X[, 2] * X[, 3] # attribute a HALF of the interaction term to each symmetric element gt_intr[, 3, 2] <- gt_intr[, 2, 3] # merge-in the diagonal based on 'ground truth' feature contributions intr_diag <- gt_cont - apply(gt_intr, c(1, 2), sum) for (j in seq_len(P)) { gt_intr[, j, j] <- intr_diag[, j] } # These should be relatively close: expect_lt(max(abs(intr - gt_intr)), 0.1) }) test_that("SHAP contribution values are not NAN", { d <- data.frame( x1 = c(-2.3, 1.4, 5.9, 2, 2.5, 0.3, -3.6, -0.2, 0.5, -2.8, -4.6, 3.3, -1.2, -1.1, -2.3, 0.4, -1.5, -0.2, -1, 3.7), x2 = c(291.179171, 269.198331, 289.942097, 283.191669, 269.673332, 294.158346, 287.255835, 291.530838, 285.899586, 269.290833, 268.649586, 291.530841, 280.074593, 269.484168, 293.94042, 294.327506, 296.20709, 295.441669, 283.16792, 270.227085), y = c(9, 15, 5.7, 9.2, 22.4, 5, 9, 3.2, 7.2, 13.1, 7.8, 16.9, 6.5, 22.1, 5.3, 10.4, 11.1, 13.9, 11, 20.5), fold = c(2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2)) ivs <- c("x1", "x2") fit <- xgboost( verbose = 0, params = list( objective = "reg:squarederror", eval_metric = "rmse"), data = as.matrix(subset(d, fold == 2)[, ivs]), label = subset(d, fold == 2)$y, nthread = 1, nrounds = 3) shaps <- as.data.frame(predict(fit, newdata = as.matrix(subset(d, fold == 1)[, ivs]), predcontrib = TRUE)) result <- cbind(shaps, sum = rowSums(shaps), pred = predict(fit, newdata = as.matrix(subset(d, fold == 1)[, ivs]))) expect_true(identical(TRUE, all.equal(result$sum, result$pred, tol = 1e-6))) }) test_that("multiclass feature interactions work", { dm <- xgb.DMatrix(as.matrix(iris[, -5]), label = as.numeric(iris$Species) - 1) param <- list(eta = 0.1, max_depth = 4, objective = 'multi:softprob', num_class = 3) b <- xgb.train(param, dm, 40) pred <- t( array( data = predict(b, dm, outputmargin = TRUE), dim = c(3, 150) ) ) # SHAP contributions: cont <- predict(b, dm, predcontrib = TRUE) expect_length(cont, 3) # rewrap them as a 3d array cont <- array( data = unlist(cont), dim = c(150, 5, 3) ) # make sure for each row they add up to marginal predictions expect_lt(max(abs(apply(cont, c(1, 3), sum) - pred)), 0.001) # SHAP interaction contributions: intr <- predict(b, dm, predinteraction = TRUE) expect_length(intr, 3) # rewrap them as a 4d array intr <- aperm( a = array( data = unlist(intr), dim = c(150, 5, 5, 3) ), perm = c(4, 1, 2, 3) # [grp, row, col, col] ) # check the symmetry expect_lt(max(abs(aperm(intr, c(1, 2, 4, 3)) - intr)), 0.00001) # sums WRT columns must be close to feature contributions expect_lt(max(abs(apply(intr, c(1, 2, 3), sum) - aperm(cont, c(3, 1, 2)))), 0.00001) }) test_that("SHAP single sample works", { train <- agaricus.train test <- agaricus.test booster <- xgboost( data = train$data, label = train$label, max_depth = 2, nrounds = 4, objective = "binary:logistic", ) predt <- predict( booster, newdata = train$data[1, , drop = FALSE], predcontrib = TRUE ) expect_equal(dim(predt), c(1, dim(train$data)[2] + 1)) predt <- predict( booster, newdata = train$data[1, , drop = FALSE], predinteraction = TRUE ) expect_equal(dim(predt), c(1, dim(train$data)[2] + 1, dim(train$data)[2] + 1)) }) xgboost-1.5.2/R-package/tests/testthat/test_model_compatibility.R000066400000000000000000000113761417122711700252260ustar00rootroot00000000000000require(xgboost) require(jsonlite) context("Models from previous versions of XGBoost can be loaded") metadata <- list( kRounds = 2, kRows = 1000, kCols = 4, kForests = 2, kMaxDepth = 2, kClasses = 3 ) run_model_param_check <- function (config) { testthat::expect_equal(config$learner$learner_model_param$num_feature, '4') testthat::expect_equal(config$learner$learner_train_param$booster, 'gbtree') } get_num_tree <- function (booster) { dump <- xgb.dump(booster) m <- regexec('booster\\[[0-9]+\\]', dump, perl = TRUE) m <- regmatches(dump, m) num_tree <- Reduce('+', lapply(m, length)) return (num_tree) } run_booster_check <- function (booster, name) { # If given a handle, we need to call xgb.Booster.complete() prior to using xgb.config(). if (inherits(booster, "xgb.Booster") && xgboost:::is.null.handle(booster$handle)) { booster <- xgb.Booster.complete(booster) } config <- jsonlite::fromJSON(xgb.config(booster)) run_model_param_check(config) if (name == 'cls') { testthat::expect_equal(get_num_tree(booster), metadata$kForests * metadata$kRounds * metadata$kClasses) testthat::expect_equal(as.numeric(config$learner$learner_model_param$base_score), 0.5) testthat::expect_equal(config$learner$learner_train_param$objective, 'multi:softmax') testthat::expect_equal(as.numeric(config$learner$learner_model_param$num_class), metadata$kClasses) } else if (name == 'logitraw') { testthat::expect_equal(get_num_tree(booster), metadata$kForests * metadata$kRounds) testthat::expect_equal(as.numeric(config$learner$learner_model_param$num_class), 0) testthat::expect_equal(config$learner$learner_train_param$objective, 'binary:logitraw') } else if (name == 'logit') { testthat::expect_equal(get_num_tree(booster), metadata$kForests * metadata$kRounds) testthat::expect_equal(as.numeric(config$learner$learner_model_param$num_class), 0) testthat::expect_equal(config$learner$learner_train_param$objective, 'binary:logistic') } else if (name == 'ltr') { testthat::expect_equal(get_num_tree(booster), metadata$kForests * metadata$kRounds) testthat::expect_equal(config$learner$learner_train_param$objective, 'rank:ndcg') } else { testthat::expect_equal(name, 'reg') testthat::expect_equal(get_num_tree(booster), metadata$kForests * metadata$kRounds) testthat::expect_equal(as.numeric(config$learner$learner_model_param$base_score), 0.5) testthat::expect_equal(config$learner$learner_train_param$objective, 'reg:squarederror') } } test_that("Models from previous versions of XGBoost can be loaded", { bucket <- 'xgboost-ci-jenkins-artifacts' region <- 'us-west-2' file_name <- 'xgboost_r_model_compatibility_test.zip' zipfile <- file.path(getwd(), file_name) model_dir <- file.path(getwd(), 'models') download.file(paste('https://', bucket, '.s3-', region, '.amazonaws.com/', file_name, sep = ''), destfile = zipfile, mode = 'wb', quiet = TRUE) unzip(zipfile, overwrite = TRUE) pred_data <- xgb.DMatrix(matrix(c(0, 0, 0, 0), nrow = 1, ncol = 4)) lapply(list.files(model_dir), function (x) { model_file <- file.path(model_dir, x) m <- regexec("xgboost-([0-9\\.]+)\\.([a-z]+)\\.[a-z]+", model_file, perl = TRUE) m <- regmatches(model_file, m)[[1]] model_xgb_ver <- m[2] name <- m[3] is_rds <- endsWith(model_file, '.rds') cpp_warning <- capture.output({ # Expect an R warning when a model is loaded from RDS and it was generated by version < 1.1.x if (is_rds && compareVersion(model_xgb_ver, '1.1.1.1') < 0) { booster <- readRDS(model_file) expect_warning(predict(booster, newdata = pred_data)) booster <- readRDS(model_file) expect_warning(run_booster_check(booster, name)) } else { if (is_rds) { booster <- readRDS(model_file) } else { booster <- xgb.load(model_file) } predict(booster, newdata = pred_data) run_booster_check(booster, name) } }) if (compareVersion(model_xgb_ver, '1.0.0.0') < 0) { # Expect a C++ warning when a model was generated in version < 1.0.x m <- grepl(paste0('.*Loading model from XGBoost < 1\\.0\\.0, consider saving it again for ', 'improved compatibility.*'), cpp_warning, perl = TRUE) expect_true(length(m) > 0 && all(m)) } else if (is_rds && model_xgb_ver == '1.1.1.1') { # Expect a C++ warning when a model is loaded from RDS and it was generated by version 1.1.x m <- grepl(paste0('.*Attempted to load internal configuration for a model file that was ', 'generated by a previous version of XGBoost.*'), cpp_warning, perl = TRUE) expect_true(length(m) > 0 && all(m)) } }) }) xgboost-1.5.2/R-package/tests/testthat/test_monotone.R000066400000000000000000000010761417122711700230270ustar00rootroot00000000000000require(xgboost) context("monotone constraints") set.seed(1024) x <- rnorm(1000, 10) y <- -1 * x + rnorm(1000, 0.001) + 3 * sin(x) train <- matrix(x, ncol = 1) test_that("monotone constraints for regression", { bst <- xgboost(data = train, label = y, max_depth = 2, eta = 0.1, nthread = 2, nrounds = 100, verbose = 0, monotone_constraints = -1) pred <- predict(bst, train) ind <- order(train[, 1]) pred.ord <- pred[ind] expect_true({ !any(diff(pred.ord) > 0) }, "Monotone constraint satisfied") }) xgboost-1.5.2/R-package/tests/testthat/test_parameter_exposure.R000066400000000000000000000015361417122711700251040ustar00rootroot00000000000000context('Test model params and call are exposed to R') require(xgboost) data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') dtrain <- xgb.DMatrix(agaricus.train$data, label = agaricus.train$label) dtest <- xgb.DMatrix(agaricus.test$data, label = agaricus.test$label) bst <- xgboost(data = dtrain, max_depth = 2, eta = 1, nrounds = 10, nthread = 1, verbose = 0, objective = "binary:logistic") test_that("call is exposed to R", { expect_false(is.null(bst$call)) expect_is(bst$call, "call") }) test_that("params is exposed to R", { model_params <- bst$params expect_is(model_params, "list") expect_equal(model_params$eta, 1) expect_equal(model_params$max_depth, 2) expect_equal(model_params$objective, "binary:logistic") }) xgboost-1.5.2/R-package/tests/testthat/test_poisson_regression.R000066400000000000000000000007071417122711700251230ustar00rootroot00000000000000context('Test Poisson regression model') require(xgboost) set.seed(1994) test_that("Poisson regression works", { data(mtcars) bst <- xgboost(data = as.matrix(mtcars[, -11]), label = mtcars[, 11], objective = 'count:poisson', nrounds = 10, verbose = 0) expect_equal(class(bst), "xgb.Booster") pred <- predict(bst, as.matrix(mtcars[, -11])) expect_equal(length(pred), 32) expect_lt(sqrt(mean((pred - mtcars[, 11])^2)), 1.2) }) xgboost-1.5.2/R-package/tests/testthat/test_ranking.R000066400000000000000000000043321417122711700226200ustar00rootroot00000000000000require(xgboost) require(Matrix) context('Learning to rank') test_that('Test ranking with unweighted data', { X <- sparseMatrix(i = c(2, 3, 7, 9, 12, 15, 17, 18), j = c(1, 1, 2, 2, 3, 3, 4, 4), x = rep(1.0, 8), dims = c(20, 4)) y <- c(0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0) group <- c(5, 5, 5, 5) dtrain <- xgb.DMatrix(X, label = y, group = group) params <- list(eta = 1, tree_method = 'exact', objective = 'rank:pairwise', max_depth = 1, eval_metric = 'auc', eval_metric = 'aucpr') bst <- xgb.train(params, dtrain, nrounds = 10, watchlist = list(train = dtrain)) # Check if the metric is monotone increasing expect_true(all(diff(bst$evaluation_log$train_auc) >= 0)) expect_true(all(diff(bst$evaluation_log$train_aucpr) >= 0)) }) test_that('Test ranking with weighted data', { X <- sparseMatrix(i = c(2, 3, 7, 9, 12, 15, 17, 18), j = c(1, 1, 2, 2, 3, 3, 4, 4), x = rep(1.0, 8), dims = c(20, 4)) y <- c(0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0) group <- c(5, 5, 5, 5) weight <- c(1.0, 2.0, 3.0, 4.0) dtrain <- xgb.DMatrix(X, label = y, group = group, weight = weight) params <- list(eta = 1, tree_method = 'exact', objective = 'rank:pairwise', max_depth = 1, eval_metric = 'auc', eval_metric = 'aucpr') bst <- xgb.train(params, dtrain, nrounds = 10, watchlist = list(train = dtrain)) # Check if the metric is monotone increasing expect_true(all(diff(bst$evaluation_log$train_auc) >= 0)) expect_true(all(diff(bst$evaluation_log$train_aucpr) >= 0)) for (i in 1:10) { pred <- predict(bst, newdata = dtrain, ntreelimit = i) # is_sorted[i]: is i-th group correctly sorted by the ranking predictor? is_sorted <- lapply(seq(1, 20, by = 5), function (k) { ind <- order(-pred[k:(k + 4)]) z <- y[ind + (k - 1)] all(diff(z) <= 0) # Check if z is monotone decreasing }) # Since we give weights 1, 2, 3, 4 to the four query groups, # the ranking predictor will first try to correctly sort the last query group # before correctly sorting other groups. expect_true(all(diff(as.numeric(is_sorted)) >= 0)) } }) xgboost-1.5.2/R-package/tests/testthat/test_update.R000066400000000000000000000125031417122711700224500ustar00rootroot00000000000000require(xgboost) context("update trees in an existing model") data(agaricus.train, package = 'xgboost') data(agaricus.test, package = 'xgboost') dtrain <- xgb.DMatrix(agaricus.train$data, label = agaricus.train$label) dtest <- xgb.DMatrix(agaricus.test$data, label = agaricus.test$label) # Disable flaky tests for 32-bit Windows. # See https://github.com/dmlc/xgboost/issues/3720 win32_flag <- .Platform$OS.type == "windows" && .Machine$sizeof.pointer != 8 test_that("updating the model works", { watchlist <- list(train = dtrain, test = dtest) # no-subsampling p1 <- list(objective = "binary:logistic", max_depth = 2, eta = 0.05, nthread = 2) set.seed(11) bst1 <- xgb.train(p1, dtrain, nrounds = 10, watchlist, verbose = 0) tr1 <- xgb.model.dt.tree(model = bst1) # with subsampling p2 <- modifyList(p1, list(subsample = 0.1)) set.seed(11) bst2 <- xgb.train(p2, dtrain, nrounds = 10, watchlist, verbose = 0) tr2 <- xgb.model.dt.tree(model = bst2) # the same no-subsampling boosting with an extra 'refresh' updater: p1r <- modifyList(p1, list(updater = 'grow_colmaker,prune,refresh', refresh_leaf = FALSE)) set.seed(11) bst1r <- xgb.train(p1r, dtrain, nrounds = 10, watchlist, verbose = 0) tr1r <- xgb.model.dt.tree(model = bst1r) # all should be the same when no subsampling expect_equal(bst1$evaluation_log, bst1r$evaluation_log) if (!win32_flag) { expect_equal(tr1, tr1r, tolerance = 0.00001, check.attributes = FALSE) } # the same boosting with subsampling with an extra 'refresh' updater: p2r <- modifyList(p2, list(updater = 'grow_colmaker,prune,refresh', refresh_leaf = FALSE)) set.seed(11) bst2r <- xgb.train(p2r, dtrain, nrounds = 10, watchlist, verbose = 0) tr2r <- xgb.model.dt.tree(model = bst2r) # should be the same evaluation but different gains and larger cover expect_equal(bst2$evaluation_log, bst2r$evaluation_log) if (!win32_flag) { expect_equal(tr2[Feature == 'Leaf']$Quality, tr2r[Feature == 'Leaf']$Quality) } expect_gt(sum(abs(tr2[Feature != 'Leaf']$Quality - tr2r[Feature != 'Leaf']$Quality)), 100) expect_gt(sum(tr2r$Cover) / sum(tr2$Cover), 1.5) # process type 'update' for no-subsampling model, refreshing the tree stats AND leaves from training data: p1u <- modifyList(p1, list(process_type = 'update', updater = 'refresh', refresh_leaf = TRUE)) bst1u <- xgb.train(p1u, dtrain, nrounds = 10, watchlist, verbose = 0, xgb_model = bst1) tr1u <- xgb.model.dt.tree(model = bst1u) # all should be the same when no subsampling expect_equal(bst1$evaluation_log, bst1u$evaluation_log) expect_equal(tr1, tr1u, tolerance = 0.00001, check.attributes = FALSE) # process type 'update' for model with subsampling, refreshing only the tree stats from training data: p2u <- modifyList(p2, list(process_type = 'update', updater = 'refresh', refresh_leaf = FALSE)) bst2u <- xgb.train(p2u, dtrain, nrounds = 10, watchlist, verbose = 0, xgb_model = bst2) tr2u <- xgb.model.dt.tree(model = bst2u) # should be the same evaluation but different gains and larger cover expect_equal(bst2$evaluation_log, bst2u$evaluation_log) expect_equal(tr2[Feature == 'Leaf']$Quality, tr2u[Feature == 'Leaf']$Quality) expect_gt(sum(abs(tr2[Feature != 'Leaf']$Quality - tr2u[Feature != 'Leaf']$Quality)), 100) expect_gt(sum(tr2u$Cover) / sum(tr2$Cover), 1.5) # the results should be the same as for the model with an extra 'refresh' updater expect_equal(bst2r$evaluation_log, bst2u$evaluation_log) if (!win32_flag) { expect_equal(tr2r, tr2u, tolerance = 0.00001, check.attributes = FALSE) } # process type 'update' for no-subsampling model, refreshing only the tree stats from TEST data: p1ut <- modifyList(p1, list(process_type = 'update', updater = 'refresh', refresh_leaf = FALSE)) bst1ut <- xgb.train(p1ut, dtest, nrounds = 10, watchlist, verbose = 0, xgb_model = bst1) tr1ut <- xgb.model.dt.tree(model = bst1ut) # should be the same evaluations but different gains and smaller cover (test data is smaller) expect_equal(bst1$evaluation_log, bst1ut$evaluation_log) expect_equal(tr1[Feature == 'Leaf']$Quality, tr1ut[Feature == 'Leaf']$Quality) expect_gt(sum(abs(tr1[Feature != 'Leaf']$Quality - tr1ut[Feature != 'Leaf']$Quality)), 100) expect_lt(sum(tr1ut$Cover) / sum(tr1$Cover), 0.5) }) test_that("updating works for multiclass & multitree", { dtr <- xgb.DMatrix(as.matrix(iris[, -5]), label = as.numeric(iris$Species) - 1) watchlist <- list(train = dtr) p0 <- list(max_depth = 2, eta = 0.5, nthread = 2, subsample = 0.6, objective = "multi:softprob", num_class = 3, num_parallel_tree = 2, base_score = 0) set.seed(121) bst0 <- xgb.train(p0, dtr, 5, watchlist, verbose = 0) tr0 <- xgb.model.dt.tree(model = bst0) # run update process for an original model with subsampling p0u <- modifyList(p0, list(process_type = 'update', updater = 'refresh', refresh_leaf = FALSE)) bst0u <- xgb.train(p0u, dtr, nrounds = bst0$niter, watchlist, xgb_model = bst0, verbose = 0) tr0u <- xgb.model.dt.tree(model = bst0u) # should be the same evaluation but different gains and larger cover expect_equal(bst0$evaluation_log, bst0u$evaluation_log) expect_equal(tr0[Feature == 'Leaf']$Quality, tr0u[Feature == 'Leaf']$Quality) expect_gt(sum(abs(tr0[Feature != 'Leaf']$Quality - tr0u[Feature != 'Leaf']$Quality)), 100) expect_gt(sum(tr0u$Cover) / sum(tr0$Cover), 1.5) }) xgboost-1.5.2/R-package/vignettes/000077500000000000000000000000001417122711700170115ustar00rootroot00000000000000xgboost-1.5.2/R-package/vignettes/discoverYourData.Rmd000066400000000000000000000411511417122711700227460ustar00rootroot00000000000000--- title: "Understand your dataset with XGBoost" output: rmarkdown::html_vignette: css: vignette.css number_sections: yes toc: yes author: Tianqi Chen, Tong He, Michaël Benesty, Yuan Tang vignette: > %\VignetteIndexEntry{Discover your data} %\VignetteEngine{knitr::rmarkdown} \usepackage[utf8]{inputenc} --- Understand your dataset with XGBoost ==================================== Introduction ------------ The purpose of this vignette is to show you how to use **XGBoost** to discover and understand your own dataset better. This vignette is not about predicting anything (see [XGBoost presentation](https://github.com/dmlc/xgboost/blob/master/R-package/vignettes/xgboostPresentation.Rmd)). We will explain how to use **XGBoost** to highlight the *link* between the *features* of your data and the *outcome*. Package loading: ```{r libLoading, results='hold', message=F, warning=F} require(xgboost) require(Matrix) require(data.table) if (!require('vcd')) install.packages('vcd') ``` > **VCD** package is used for one of its embedded dataset only. Preparation of the dataset -------------------------- ### Numeric v.s. categorical variables **XGBoost** manages only `numeric` vectors. What to do when you have *categorical* data? A *categorical* variable has a fixed number of different values. For instance, if a variable called *Colour* can have only one of these three values, *red*, *blue* or *green*, then *Colour* is a *categorical* variable. > In **R**, a *categorical* variable is called `factor`. > > Type `?factor` in the console for more information. To answer the question above we will convert *categorical* variables to `numeric` one. ### Conversion from categorical to numeric variables #### Looking at the raw data In this Vignette we will see how to transform a *dense* `data.frame` (*dense* = few zeroes in the matrix) with *categorical* variables to a very *sparse* matrix (*sparse* = lots of zero in the matrix) of `numeric` features. The method we are going to see is usually called [one-hot encoding](https://en.wikipedia.org/wiki/One-hot). The first step is to load `Arthritis` dataset in memory and wrap it with `data.table` package. ```{r, results='hide'} data(Arthritis) df <- data.table(Arthritis, keep.rownames = FALSE) ``` > `data.table` is 100% compliant with **R** `data.frame` but its syntax is more consistent and its performance for large dataset is [best in class](https://stackoverflow.com/questions/21435339/data-table-vs-dplyr-can-one-do-something-well-the-other-cant-or-does-poorly) (`dplyr` from **R** and `Pandas` from **Python** [included](https://github.com/Rdatatable/data.table/wiki/Benchmarks-%3A-Grouping)). Some parts of **XGBoost** **R** package use `data.table`. The first thing we want to do is to have a look to the first few lines of the `data.table`: ```{r} head(df) ``` Now we will check the format of each column. ```{r} str(df) ``` 2 columns have `factor` type, one has `ordinal` type. > `ordinal` variable : > > * can take a limited number of values (like `factor`) ; > * these values are ordered (unlike `factor`). Here these ordered values are: `Marked > Some > None` #### Creation of new features based on old ones We will add some new *categorical* features to see if it helps. ##### Grouping per 10 years For the first feature we create groups of age by rounding the real age. Note that we transform it to `factor` so the algorithm treat these age groups as independent values. Therefore, 20 is not closer to 30 than 60. To make it short, the distance between ages is lost in this transformation. ```{r} head(df[,AgeDiscret := as.factor(round(Age/10,0))]) ``` ##### Random split into two groups Following is an even stronger simplification of the real age with an arbitrary split at 30 years old. We choose this value **based on nothing**. We will see later if simplifying the information based on arbitrary values is a good strategy (you may already have an idea of how well it will work...). ```{r} head(df[,AgeCat:= as.factor(ifelse(Age > 30, "Old", "Young"))]) ``` ##### Risks in adding correlated features These new features are highly correlated to the `Age` feature because they are simple transformations of this feature. For many machine learning algorithms, using correlated features is not a good idea. It may sometimes make prediction less accurate, and most of the time make interpretation of the model almost impossible. GLM, for instance, assumes that the features are uncorrelated. Fortunately, decision tree algorithms (including boosted trees) are very robust to these features. Therefore we have nothing to do to manage this situation. ##### Cleaning data We remove ID as there is nothing to learn from this feature (it would just add some noise). ```{r, results='hide'} df[,ID:=NULL] ``` We will list the different values for the column `Treatment`: ```{r} levels(df[,Treatment]) ``` #### Encoding categorical features Next step, we will transform the categorical data to dummy variables. Several encoding methods exist, e.g., [one-hot encoding](https://en.wikipedia.org/wiki/One-hot) is a common approach. We will use the [dummy contrast coding](https://stats.idre.ucla.edu/r/library/r-library-contrast-coding-systems-for-categorical-variables/) which is popular because it produces "full rank" encoding (also see [this blog post by Max Kuhn](http://appliedpredictivemodeling.com/blog/2013/10/23/the-basics-of-encoding-categorical-data-for-predictive-models)). The purpose is to transform each value of each *categorical* feature into a *binary* feature `{0, 1}`. For example, the column `Treatment` will be replaced by two columns, `TreatmentPlacebo`, and `TreatmentTreated`. Each of them will be *binary*. Therefore, an observation which has the value `Placebo` in column `Treatment` before the transformation will have after the transformation the value `1` in the new column `TreatmentPlacebo` and the value `0` in the new column `TreatmentTreated`. The column `TreatmentPlacebo` will disappear during the contrast encoding, as it would be absorbed into a common constant intercept column. Column `Improved` is excluded because it will be our `label` column, the one we want to predict. ```{r, warning=FALSE,message=FALSE} sparse_matrix <- sparse.model.matrix(Improved ~ ., data = df)[,-1] head(sparse_matrix) ``` > Formula `Improved ~ .` used above means transform all *categorical* features but column `Improved` to binary values. The `-1` column selection removes the intercept column which is full of `1` (this column is generated by the conversion). For more information, you can type `?sparse.model.matrix` in the console. Create the output `numeric` vector (not as a sparse `Matrix`): ```{r} output_vector = df[,Improved] == "Marked" ``` 1. set `Y` vector to `0`; 2. set `Y` to `1` for rows where `Improved == Marked` is `TRUE` ; 3. return `Y` vector. Build the model --------------- The code below is very usual. For more information, you can look at the documentation of `xgboost` function (or at the vignette [XGBoost presentation](https://github.com/dmlc/xgboost/blob/master/R-package/vignettes/xgboostPresentation.Rmd)). ```{r} bst <- xgboost(data = sparse_matrix, label = output_vector, max_depth = 4, eta = 1, nthread = 2, nrounds = 10,objective = "binary:logistic") ``` You can see some `train-error: 0.XXXXX` lines followed by a number. It decreases. Each line shows how well the model explains your data. Lower is better. A small value for training error may be a symptom of [overfitting](https://en.wikipedia.org/wiki/Overfitting), meaning the model will not accurately predict the future values. > Here you can see the numbers decrease until line 7 and then increase. > > It probably means we are overfitting. To fix that I should reduce the number of rounds to `nrounds = 4`. I will let things like that because I don't really care for the purpose of this example :-) Feature importance ------------------ ## Measure feature importance ### Build the feature importance data.table Remember, each binary column corresponds to a single value of one of *categorical* features. ```{r} importance <- xgb.importance(feature_names = colnames(sparse_matrix), model = bst) head(importance) ``` > The column `Gain` provide the information we are looking for. > > As you can see, features are classified by `Gain`. `Gain` is the improvement in accuracy brought by a feature to the branches it is on. The idea is that before adding a new split on a feature X to the branch there was some wrongly classified elements, after adding the split on this feature, there are two new branches, and each of these branch is more accurate (one branch saying if your observation is on this branch then it should be classified as `1`, and the other branch saying the exact opposite). `Cover` measures the relative quantity of observations concerned by a feature. `Frequency` is a simpler way to measure the `Gain`. It just counts the number of times a feature is used in all generated trees. You should not use it (unless you know why you want to use it). #### Improvement in the interpretability of feature importance data.table We can go deeper in the analysis of the model. In the `data.table` above, we have discovered which features counts to predict if the illness will go or not. But we don't yet know the role of these features. For instance, one of the question we may want to answer would be: does receiving a placebo treatment helps to recover from the illness? One simple solution is to count the co-occurrences of a feature and a class of the classification. For that purpose we will execute the same function as above but using two more parameters, `data` and `label`. ```{r} importanceRaw <- xgb.importance(feature_names = colnames(sparse_matrix), model = bst, data = sparse_matrix, label = output_vector) # Cleaning for better display importanceClean <- importanceRaw[,`:=`(Cover=NULL, Frequency=NULL)] head(importanceClean) ``` > In the table above we have removed two not needed columns and select only the first lines. First thing you notice is the new column `Split`. It is the split applied to the feature on a branch of one of the tree. Each split is present, therefore a feature can appear several times in this table. Here we can see the feature `Age` is used several times with different splits. How the split is applied to count the co-occurrences? It is always `<`. For instance, in the second line, we measure the number of persons under 61.5 years with the illness gone after the treatment. The two other new columns are `RealCover` and `RealCover %`. In the first column it measures the number of observations in the dataset where the split is respected and the label marked as `1`. The second column is the percentage of the whole population that `RealCover` represents. Therefore, according to our findings, getting a placebo doesn't seem to help but being younger than 61 years may help (seems logic). > You may wonder how to interpret the `< 1.00001` on the first line. Basically, in a sparse `Matrix`, there is no `0`, therefore, looking for one hot-encoded categorical observations validating the rule `< 1.00001` is like just looking for `1` for this feature. ### Plotting the feature importance All these things are nice, but it would be even better to plot the results. ```{r, fig.width=8, fig.height=5, fig.align='center'} xgb.plot.importance(importance_matrix = importance) ``` Feature have automatically been divided in 2 clusters: the interesting features... and the others. > Depending of the dataset and the learning parameters you may have more than two clusters. Default value is to limit them to `10`, but you can increase this limit. Look at the function documentation for more information. According to the plot above, the most important features in this dataset to predict if the treatment will work are : * the Age ; * having received a placebo or not ; * the sex is third but already included in the not interesting features group ; * then we see our generated features (AgeDiscret). We can see that their contribution is very low. ### Do these results make sense? Let's check some **Chi2** between each of these features and the label. Higher **Chi2** means better correlation. ```{r, warning=FALSE, message=FALSE} c2 <- chisq.test(df$Age, output_vector) print(c2) ``` Pearson correlation between Age and illness disappearing is **`r round(c2$statistic, 2 )`**. ```{r, warning=FALSE, message=FALSE} c2 <- chisq.test(df$AgeDiscret, output_vector) print(c2) ``` Our first simplification of Age gives a Pearson correlation is **`r round(c2$statistic, 2)`**. ```{r, warning=FALSE, message=FALSE} c2 <- chisq.test(df$AgeCat, output_vector) print(c2) ``` The perfectly random split I did between young and old at 30 years old have a low correlation of **`r round(c2$statistic, 2)`**. It's a result we may expect as may be in my mind > 30 years is being old (I am 32 and starting feeling old, this may explain that), but for the illness we are studying, the age to be vulnerable is not the same. Morality: don't let your *gut* lower the quality of your model. In *data science* expression, there is the word *science* :-) Conclusion ---------- As you can see, in general *destroying information by simplifying it won't improve your model*. **Chi2** just demonstrates that. But in more complex cases, creating a new feature based on existing one which makes link with the outcome more obvious may help the algorithm and improve the model. The case studied here is not enough complex to show that. Check [Kaggle website](http://www.kaggle.com/) for some challenging datasets. However it's almost always worse when you add some arbitrary rules. Moreover, you can notice that even if we have added some not useful new features highly correlated with other features, the boosting tree algorithm have been able to choose the best one, which in this case is the Age. Linear model may not be that smart in this scenario. Special Note: What about Random Forests™? ----------------------------------------- As you may know, [Random Forests](https://en.wikipedia.org/wiki/Random_forest) algorithm is cousin with boosting and both are part of the [ensemble learning](https://en.wikipedia.org/wiki/Ensemble_learning) family. Both trains several decision trees for one dataset. The *main* difference is that in Random Forests, trees are independent and in boosting, the tree `N+1` focus its learning on the loss (<=> what has not been well modeled by the tree `N`). This difference have an impact on a corner case in feature importance analysis: the *correlated features*. Imagine two features perfectly correlated, feature `A` and feature `B`. For one specific tree, if the algorithm needs one of them, it will choose randomly (true in both boosting and Random Forests). However, in Random Forests this random choice will be done for each tree, because each tree is independent from the others. Therefore, approximatively, depending of your parameters, 50% of the trees will choose feature `A` and the other 50% will choose feature `B`. So the *importance* of the information contained in `A` and `B` (which is the same, because they are perfectly correlated) is diluted in `A` and `B`. So you won't easily know this information is important to predict what you want to predict! It is even worse when you have 10 correlated features... In boosting, when a specific link between feature and outcome have been learned by the algorithm, it will try to not refocus on it (in theory it is what happens, reality is not always that simple). Therefore, all the importance will be on feature `A` or on feature `B` (but not both). You will know that one feature have an important role in the link between the observations and the label. It is still up to you to search for the correlated features to the one detected as important if you need to know all of them. If you want to try Random Forests algorithm, you can tweak XGBoost parameters! For instance, to compute a model with 1000 trees, with a 0.5 factor on sampling rows and columns: ```{r, warning=FALSE, message=FALSE} data(agaricus.train, package='xgboost') data(agaricus.test, package='xgboost') train <- agaricus.train test <- agaricus.test #Random Forest - 1000 trees bst <- xgboost(data = train$data, label = train$label, max_depth = 4, num_parallel_tree = 1000, subsample = 0.5, colsample_bytree =0.5, nrounds = 1, objective = "binary:logistic") #Boosting - 3 rounds bst <- xgboost(data = train$data, label = train$label, max_depth = 4, nrounds = 3, objective = "binary:logistic") ``` > Note that the parameter `round` is set to `1`. > [**Random Forests**](https://www.stat.berkeley.edu/~breiman/RandomForests/cc_papers.htm) is a trademark of Leo Breiman and Adele Cutler and is licensed exclusively to Salford Systems for the commercial release of the software. xgboost-1.5.2/R-package/vignettes/vignette.css000066400000000000000000000073441417122711700213600ustar00rootroot00000000000000body { margin: 0 auto; background-color: white; /* --------- FONT FAMILY -------- following are some optional font families. 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It is an efficient and scalable implementation of gradient boosting framework by \citep{friedman2001greedy} \citep{friedman2000additive}. The package includes efficient linear model solver and tree learning algorithm. It supports various objective functions, including regression, classification and ranking. The package is made to be extendible, so that users are also allowed to define their own objectives easily. It has several features: \begin{enumerate} \item{Speed: }{\verb@xgboost@ can automatically do parallel computation on Windows and Linux, with openmp. It is generally over 10 times faster than \verb@gbm@.} \item{Input Type: }{\verb@xgboost@ takes several types of input data:} \begin{itemize} \item{Dense Matrix: }{R's dense matrix, i.e. \verb@matrix@} \item{Sparse Matrix: }{R's sparse matrix \verb@Matrix::dgCMatrix@} \item{Data File: }{Local data files} \item{xgb.DMatrix: }{\verb@xgboost@'s own class. Recommended.} \end{itemize} \item{Sparsity: }{\verb@xgboost@ accepts sparse input for both tree booster and linear booster, and is optimized for sparse input.} \item{Customization: }{\verb@xgboost@ supports customized objective function and evaluation function} \item{Performance: }{\verb@xgboost@ has better performance on several different datasets.} \end{enumerate} \section{Example with Mushroom data} In this section, we will illustrate some common usage of \verb@xgboost@. The Mushroom data is cited from UCI Machine Learning Repository. \citep{Bache+Lichman:2013} <>= library(xgboost) data(agaricus.train, package='xgboost') data(agaricus.test, package='xgboost') train <- agaricus.train test <- agaricus.test bst <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 1, nrounds = 2, objective = "binary:logistic") xgb.save(bst, 'model.save') bst = xgb.load('model.save') pred <- predict(bst, test$data) @ \verb@xgboost@ is the main function to train a \verb@Booster@, i.e. a model. \verb@predict@ does prediction on the model. Here we can save the model to a binary local file, and load it when needed. We can't inspect the trees inside. However we have another function to save the model in plain text. <>= xgb.dump(bst, 'model.dump') @ The output looks like \begin{verbatim} booster[0]: 0:[f28<1.00001] yes=1,no=2,missing=2 1:[f108<1.00001] yes=3,no=4,missing=4 3:leaf=1.85965 4:leaf=-1.94071 2:[f55<1.00001] yes=5,no=6,missing=6 5:leaf=-1.70044 6:leaf=1.71218 booster[1]: 0:[f59<1.00001] yes=1,no=2,missing=2 1:leaf=-6.23624 2:[f28<1.00001] yes=3,no=4,missing=4 3:leaf=-0.96853 4:leaf=0.784718 \end{verbatim} It is important to know \verb@xgboost@'s own data type: \verb@xgb.DMatrix@. It speeds up \verb@xgboost@, and is needed for advanced features such as training from initial prediction value, weighted training instance. We can use \verb@xgb.DMatrix@ to construct an \verb@xgb.DMatrix@ object: <>= dtrain <- xgb.DMatrix(train$data, label = train$label) class(dtrain) head(getinfo(dtrain,'label')) @ We can also save the matrix to a binary file. Then load it simply with \verb@xgb.DMatrix@ <>= xgb.DMatrix.save(dtrain, 'xgb.DMatrix') dtrain = xgb.DMatrix('xgb.DMatrix') @ \section{Advanced Examples} The function \verb@xgboost@ is a simple function with less parameter, in order to be R-friendly. The core training function is wrapped in \verb@xgb.train@. It is more flexible than \verb@xgboost@, but it requires users to read the document a bit more carefully. \verb@xgb.train@ only accept a \verb@xgb.DMatrix@ object as its input, while it supports advanced features as custom objective and evaluation functions. <>= logregobj <- function(preds, dtrain) { labels <- getinfo(dtrain, "label") preds <- 1/(1 + exp(-preds)) grad <- preds - labels hess <- preds * (1 - preds) return(list(grad = grad, hess = hess)) } evalerror <- function(preds, dtrain) { labels <- getinfo(dtrain, "label") err <- sqrt(mean((preds-labels)^2)) return(list(metric = "MSE", value = err)) } dtest <- xgb.DMatrix(test$data, label = test$label) watchlist <- list(eval = dtest, train = dtrain) param <- list(max_depth = 2, eta = 1) bst <- xgb.train(param, dtrain, nrounds = 2, watchlist, logregobj, evalerror, maximize = FALSE) @ The gradient and second order gradient is required for the output of customized objective function. We also have \verb@slice@ for row extraction. It is useful in cross-validation. For a walkthrough demo, please see \verb@R-package/demo/@ for further details. \section{The Higgs Boson competition} We have made a demo for \href{http://www.kaggle.com/c/higgs-boson}{the Higgs Boson Machine Learning Challenge}. Here are the instructions to make a submission \begin{enumerate} \item Download the \href{http://www.kaggle.com/c/higgs-boson/data}{datasets} and extract them to \verb@data/@. \item Run scripts under \verb@xgboost/demo/kaggle-higgs/@: \href{https://github.com/tqchen/xgboost/blob/master/demo/kaggle-higgs/higgs-train.R}{higgs-train.R} and \href{https://github.com/tqchen/xgboost/blob/master/demo/kaggle-higgs/higgs-pred.R}{higgs-pred.R}. The computation will take less than a minute on Intel i7. \item Go to the \href{http://www.kaggle.com/c/higgs-boson/submissions/attach}{submission page} and submit your result. \end{enumerate} We provide \href{https://github.com/tqchen/xgboost/blob/master/demo/kaggle-higgs/speedtest.R}{a script} to compare the time cost on the higgs dataset with \verb@gbm@ and \verb@xgboost@. The training set contains 350000 records and 30 features. \verb@xgboost@ can automatically do parallel computation. On a machine with Intel i7-4700MQ and 24GB memories, we found that \verb@xgboost@ costs about 35 seconds, which is about 20 times faster than \verb@gbm@. When we limited \verb@xgboost@ to use only one thread, it was still about two times faster than \verb@gbm@. Meanwhile, the result from \verb@xgboost@ reaches \href{http://www.kaggle.com/c/higgs-boson/details/evaluation}{3.60@AMS} with a single model. This results stands in the \href{http://www.kaggle.com/c/higgs-boson/leaderboard}{top 30\%} of the competition. \bibliographystyle{jss} \nocite{*} % list uncited references \bibliography{xgboost} \end{document} <>= file.remove("xgb.DMatrix") file.remove("model.dump") file.remove("model.save") @ xgboost-1.5.2/R-package/vignettes/xgboost.bib000066400000000000000000000016211417122711700211540ustar00rootroot00000000000000@article{friedman2001greedy, title={Greedy function approximation: a gradient boosting machine}, author={Friedman, Jerome H}, journal={Annals of Statistics}, pages={1189--1232}, year={2001}, publisher={JSTOR} } @article{friedman2000additive, title={Additive logistic regression: a statistical view of boosting (with discussion and a rejoinder by the authors)}, author={Friedman, Jerome and Hastie, Trevor and Tibshirani, Robert and others}, journal={The annals of statistics}, volume={28}, number={2}, pages={337--407}, year={2000}, publisher={Institute of Mathematical Statistics} } @misc{ Bache+Lichman:2013 , author = "K. Bache and M. Lichman", year = "2013", title = "{UCI} Machine Learning Repository", url = "http://archive.ics.uci.edu/ml/", institution = "University of California, Irvine, School of Information and Computer Sciences" } xgboost-1.5.2/R-package/vignettes/xgboostPresentation.Rmd000066400000000000000000000405431417122711700235440ustar00rootroot00000000000000--- title: "XGBoost presentation" output: rmarkdown::html_vignette: css: vignette.css number_sections: yes toc: yes bibliography: xgboost.bib author: Tianqi Chen, Tong He, Michaël Benesty vignette: > %\VignetteIndexEntry{XGBoost presentation} %\VignetteEngine{knitr::rmarkdown} \usepackage[utf8]{inputenc} --- XGBoost R Tutorial ================== ## Introduction **XGBoost** is short for e**X**treme **G**radient **Boost**ing package. The purpose of this Vignette is to show you how to use **XGBoost** to build a model and make predictions. It is an efficient and scalable implementation of gradient boosting framework by @friedman2000additive and @friedman2001greedy. Two solvers are included: - *linear* model ; - *tree learning* algorithm. It supports various objective functions, including *regression*, *classification* and *ranking*. The package is made to be extendible, so that users are also allowed to define their own objective functions easily. It has been [used](https://github.com/dmlc/xgboost) to win several [Kaggle](http://www.kaggle.com) competitions. It has several features: * Speed: it can automatically do parallel computation on *Windows* and *Linux*, with *OpenMP*. It is generally over 10 times faster than the classical `gbm`. * Input Type: it takes several types of input data: * *Dense* Matrix: *R*'s *dense* matrix, i.e. `matrix` ; * *Sparse* Matrix: *R*'s *sparse* matrix, i.e. `Matrix::dgCMatrix` ; * Data File: local data files ; * `xgb.DMatrix`: its own class (recommended). * Sparsity: it accepts *sparse* input for both *tree booster* and *linear booster*, and is optimized for *sparse* input ; * Customization: it supports customized objective functions and evaluation functions. ## Installation ### GitHub version For weekly updated version (highly recommended), install from *GitHub*: ```{r installGithub, eval=FALSE} install.packages("drat", repos="https://cran.rstudio.com") drat:::addRepo("dmlc") install.packages("xgboost", repos="http://dmlc.ml/drat/", type = "source") ``` > *Windows* user will need to install [Rtools](https://cran.r-project.org/bin/windows/Rtools/) first. ### CRAN version The version 0.4-2 is on CRAN, and you can install it by: ```{r, eval=FALSE} install.packages("xgboost") ``` Formerly available versions can be obtained from the CRAN [archive](https://cran.r-project.org/src/contrib/Archive/xgboost/) ## Learning For the purpose of this tutorial we will load **XGBoost** package. ```{r libLoading, results='hold', message=F, warning=F} require(xgboost) ``` ### Dataset presentation In this example, we are aiming to predict whether a mushroom can be eaten or not (like in many tutorials, example data are the same as you will use on in your every day life :-). Mushroom data is cited from UCI Machine Learning Repository. @Bache+Lichman:2013. ### Dataset loading We will load the `agaricus` datasets embedded with the package and will link them to variables. The datasets are already split in: * `train`: will be used to build the model ; * `test`: will be used to assess the quality of our model. Why *split* the dataset in two parts? In the first part we will build our model. In the second part we will want to test it and assess its quality. Without dividing the dataset we would test the model on the data which the algorithm have already seen. ```{r datasetLoading, results='hold', message=F, warning=F} data(agaricus.train, package='xgboost') data(agaricus.test, package='xgboost') train <- agaricus.train test <- agaricus.test ``` > In the real world, it would be up to you to make this division between `train` and `test` data. The way to do it is out of the purpose of this article, however `caret` package may [help](http://topepo.github.io/caret/data-splitting.html). Each variable is a `list` containing two things, `label` and `data`: ```{r dataList, message=F, warning=F} str(train) ``` `label` is the outcome of our dataset meaning it is the binary *classification* we will try to predict. Let's discover the dimensionality of our datasets. ```{r dataSize, message=F, warning=F} dim(train$data) dim(test$data) ``` This dataset is very small to not make the **R** package too heavy, however **XGBoost** is built to manage huge dataset very efficiently. As seen below, the `data` are stored in a `dgCMatrix` which is a *sparse* matrix and `label` vector is a `numeric` vector (`{0,1}`): ```{r dataClass, message=F, warning=F} class(train$data)[1] class(train$label) ``` ### Basic Training using XGBoost This step is the most critical part of the process for the quality of our model. #### Basic training We are using the `train` data. As explained above, both `data` and `label` are stored in a `list`. In a *sparse* matrix, cells containing `0` are not stored in memory. Therefore, in a dataset mainly made of `0`, memory size is reduced. It is very usual to have such dataset. We will train decision tree model using the following parameters: * `objective = "binary:logistic"`: we will train a binary classification model ; * `max_depth = 2`: the trees won't be deep, because our case is very simple ; * `nthread = 2`: the number of CPU threads we are going to use; * `nrounds = 2`: there will be two passes on the data, the second one will enhance the model by further reducing the difference between ground truth and prediction. ```{r trainingSparse, message=F, warning=F} bstSparse <- xgboost(data = train$data, label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") ``` > More complex the relationship between your features and your `label` is, more passes you need. #### Parameter variations ##### Dense matrix Alternatively, you can put your dataset in a *dense* matrix, i.e. a basic **R** matrix. ```{r trainingDense, message=F, warning=F} bstDense <- xgboost(data = as.matrix(train$data), label = train$label, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") ``` ##### xgb.DMatrix **XGBoost** offers a way to group them in a `xgb.DMatrix`. You can even add other meta data in it. It will be useful for the most advanced features we will discover later. ```{r trainingDmatrix, message=F, warning=F} dtrain <- xgb.DMatrix(data = train$data, label = train$label) bstDMatrix <- xgboost(data = dtrain, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic") ``` ##### Verbose option **XGBoost** has several features to help you to view how the learning progress internally. The purpose is to help you to set the best parameters, which is the key of your model quality. One of the simplest way to see the training progress is to set the `verbose` option (see below for more advanced techniques). ```{r trainingVerbose0, message=T, warning=F} # verbose = 0, no message bst <- xgboost(data = dtrain, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic", verbose = 0) ``` ```{r trainingVerbose1, message=T, warning=F} # verbose = 1, print evaluation metric bst <- xgboost(data = dtrain, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic", verbose = 1) ``` ```{r trainingVerbose2, message=T, warning=F} # verbose = 2, also print information about tree bst <- xgboost(data = dtrain, max_depth = 2, eta = 1, nthread = 2, nrounds = 2, objective = "binary:logistic", verbose = 2) ``` ## Basic prediction using XGBoost ## Perform the prediction The purpose of the model we have built is to classify new data. As explained before, we will use the `test` dataset for this step. ```{r predicting, message=F, warning=F} pred <- predict(bst, test$data) # size of the prediction vector print(length(pred)) # limit display of predictions to the first 10 print(head(pred)) ``` These numbers doesn't look like *binary classification* `{0,1}`. We need to perform a simple transformation before being able to use these results. ## Transform the regression in a binary classification The only thing that **XGBoost** does is a *regression*. **XGBoost** is using `label` vector to build its *regression* model. How can we use a *regression* model to perform a binary classification? If we think about the meaning of a regression applied to our data, the numbers we get are probabilities that a datum will be classified as `1`. Therefore, we will set the rule that if this probability for a specific datum is `> 0.5` then the observation is classified as `1` (or `0` otherwise). ```{r predictingTest, message=F, warning=F} prediction <- as.numeric(pred > 0.5) print(head(prediction)) ``` ## Measuring model performance To measure the model performance, we will compute a simple metric, the *average error*. ```{r predictingAverageError, message=F, warning=F} err <- mean(as.numeric(pred > 0.5) != test$label) print(paste("test-error=", err)) ``` > Note that the algorithm has not seen the `test` data during the model construction. Steps explanation: 1. `as.numeric(pred > 0.5)` applies our rule that when the probability (<=> regression <=> prediction) is `> 0.5` the observation is classified as `1` and `0` otherwise ; 2. `probabilityVectorPreviouslyComputed != test$label` computes the vector of error between true data and computed probabilities ; 3. `mean(vectorOfErrors)` computes the *average error* itself. The most important thing to remember is that **to do a classification, you just do a regression to the** `label` **and then apply a threshold**. *Multiclass* classification works in a similar way. This metric is **`r round(err, 2)`** and is pretty low: our yummy mushroom model works well! ## Advanced features Most of the features below have been implemented to help you to improve your model by offering a better understanding of its content. ### Dataset preparation For the following advanced features, we need to put data in `xgb.DMatrix` as explained above. ```{r DMatrix, message=F, warning=F} dtrain <- xgb.DMatrix(data = train$data, label=train$label) dtest <- xgb.DMatrix(data = test$data, label=test$label) ``` ### Measure learning progress with xgb.train Both `xgboost` (simple) and `xgb.train` (advanced) functions train models. One of the special feature of `xgb.train` is the capacity to follow the progress of the learning after each round. Because of the way boosting works, there is a time when having too many rounds lead to an overfitting. You can see this feature as a cousin of cross-validation method. The following techniques will help you to avoid overfitting or optimizing the learning time in stopping it as soon as possible. One way to measure progress in learning of a model is to provide to **XGBoost** a second dataset already classified. Therefore it can learn on the first dataset and test its model on the second one. Some metrics are measured after each round during the learning. > in some way it is similar to what we have done above with the average error. The main difference is that below it was after building the model, and now it is during the construction that we measure errors. For the purpose of this example, we use `watchlist` parameter. It is a list of `xgb.DMatrix`, each of them tagged with a name. ```{r watchlist, message=F, warning=F} watchlist <- list(train=dtrain, test=dtest) bst <- xgb.train(data=dtrain, max_depth=2, eta=1, nthread = 2, nrounds=2, watchlist=watchlist, objective = "binary:logistic") ``` **XGBoost** has computed at each round the same average error metric than seen above (we set `nrounds` to 2, that is why we have two lines). Obviously, the `train-error` number is related to the training dataset (the one the algorithm learns from) and the `test-error` number to the test dataset. Both training and test error related metrics are very similar, and in some way, it makes sense: what we have learned from the training dataset matches the observations from the test dataset. If with your own dataset you have not such results, you should think about how you divided your dataset in training and test. May be there is something to fix. Again, `caret` package may [help](http://topepo.github.io/caret/data-splitting.html). For a better understanding of the learning progression, you may want to have some specific metric or even use multiple evaluation metrics. ```{r watchlist2, message=F, warning=F} bst <- xgb.train(data=dtrain, max_depth=2, eta=1, nthread = 2, nrounds=2, watchlist=watchlist, eval_metric = "error", eval_metric = "logloss", objective = "binary:logistic") ``` > `eval_metric` allows us to monitor two new metrics for each round, `logloss` and `error`. ### Linear boosting Until now, all the learnings we have performed were based on boosting trees. **XGBoost** implements a second algorithm, based on linear boosting. The only difference with previous command is `booster = "gblinear"` parameter (and removing `eta` parameter). ```{r linearBoosting, message=F, warning=F} bst <- xgb.train(data=dtrain, booster = "gblinear", max_depth=2, nthread = 2, nrounds=2, watchlist=watchlist, eval_metric = "error", eval_metric = "logloss", objective = "binary:logistic") ``` In this specific case, *linear boosting* gets slightly better performance metrics than decision trees based algorithm. In simple cases, it will happen because there is nothing better than a linear algorithm to catch a linear link. However, decision trees are much better to catch a non linear link between predictors and outcome. Because there is no silver bullet, we advise you to check both algorithms with your own datasets to have an idea of what to use. ### Manipulating xgb.DMatrix #### Save / Load Like saving models, `xgb.DMatrix` object (which groups both dataset and outcome) can also be saved using `xgb.DMatrix.save` function. ```{r DMatrixSave, message=F, warning=F} xgb.DMatrix.save(dtrain, "dtrain.buffer") # to load it in, simply call xgb.DMatrix dtrain2 <- xgb.DMatrix("dtrain.buffer") bst <- xgb.train(data=dtrain2, max_depth=2, eta=1, nthread = 2, nrounds=2, watchlist=watchlist, objective = "binary:logistic") ``` ```{r DMatrixDel, include=FALSE} file.remove("dtrain.buffer") ``` #### Information extraction Information can be extracted from `xgb.DMatrix` using `getinfo` function. Hereafter we will extract `label` data. ```{r getinfo, message=F, warning=F} label = getinfo(dtest, "label") pred <- predict(bst, dtest) err <- as.numeric(sum(as.integer(pred > 0.5) != label))/length(label) print(paste("test-error=", err)) ``` ### View feature importance/influence from the learnt model Feature importance is similar to R gbm package's relative influence (rel.inf). ``` importance_matrix <- xgb.importance(model = bst) print(importance_matrix) xgb.plot.importance(importance_matrix = importance_matrix) ``` #### View the trees from a model You can dump the tree you learned using `xgb.dump` into a text file. ```{r dump, message=T, warning=F} xgb.dump(bst, with_stats = TRUE) ``` You can plot the trees from your model using ```xgb.plot.tree`` ``` xgb.plot.tree(model = bst) ``` > if you provide a path to `fname` parameter you can save the trees to your hard drive. #### Save and load models Maybe your dataset is big, and it takes time to train a model on it? May be you are not a big fan of losing time in redoing the same task again and again? In these very rare cases, you will want to save your model and load it when required. Hopefully for you, **XGBoost** implements such functions. ```{r saveModel, message=F, warning=F} # save model to binary local file xgb.save(bst, "xgboost.model") ``` > `xgb.save` function should return `r TRUE` if everything goes well and crashes otherwise. An interesting test to see how identical our saved model is to the original one would be to compare the two predictions. ```{r loadModel, message=F, warning=F} # load binary model to R bst2 <- xgb.load("xgboost.model") pred2 <- predict(bst2, test$data) # And now the test print(paste("sum(abs(pred2-pred))=", sum(abs(pred2-pred)))) ``` ```{r clean, include=FALSE} # delete the created model file.remove("./xgboost.model") ``` > result is `0`? We are good! In some very specific cases, like when you want to pilot **XGBoost** from `caret` package, you will want to save the model as a *R* binary vector. See below how to do it. ```{r saveLoadRBinVectorModel, message=F, warning=F} # save model to R's raw vector rawVec <- xgb.serialize(bst) # print class print(class(rawVec)) # load binary model to R bst3 <- xgb.load(rawVec) pred3 <- predict(bst3, test$data) # pred2 should be identical to pred print(paste("sum(abs(pred3-pred))=", sum(abs(pred2-pred)))) ``` > Again `0`? It seems that `XGBoost` works pretty well! ## References xgboost-1.5.2/R-package/vignettes/xgboostfromJSON.Rmd000066400000000000000000000163771417122711700225360ustar00rootroot00000000000000--- title: "XGBoost from JSON" output: rmarkdown::html_vignette: number_sections: yes toc: yes author: Roland Stevenson vignette: > %\VignetteIndexEntry{XGBoost from JSON} %\VignetteEngine{knitr::rmarkdown} \usepackage[utf8]{inputenc} --- XGBoost from JSON ================= ## Introduction The purpose of this Vignette is to show you how to correctly load and work with an **XGBoost** model that has been dumped to JSON. **XGBoost** internally converts all data to [32-bit floats](https://en.wikipedia.org/wiki/Single-precision_floating-point_format), and the values dumped to JSON are decimal representations of these values. When working with a model that has been parsed from a JSON file, care must be taken to correctly treat: - the input data, which should be converted to 32-bit floats - any 32-bit floats that were stored in JSON as decimal representations - any calculations must be done with 32-bit mathematical operators ## Setup For the purpose of this tutorial we will load the xgboost, jsonlite, and float packages. We'll also set `digits=22` in our options in case we want to inspect many digits of our results. ```{r} require(xgboost) require(jsonlite) require(float) options(digits=22) ``` We will create a toy binary logistic model based on the example first provided [here](https://github.com/dmlc/xgboost/issues/3960), so that we can easily understand the structure of the dumped JSON model object. This will allow us to understand where discrepancies can occur and how they should be handled. ```{r} dates <- c(20180130, 20180130, 20180130, 20180130, 20180130, 20180130, 20180131, 20180131, 20180131, 20180131, 20180131, 20180131, 20180131, 20180131, 20180131, 20180134, 20180134, 20180134) labels <- c(1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) data <- data.frame(dates = dates, labels=labels) bst <- xgboost( data = as.matrix(data$dates), label = labels, nthread = 2, nrounds = 1, objective = "binary:logistic", missing = NA, max_depth = 1 ) ``` ## Comparing results We will now dump the model to JSON and attempt to illustrate a variety of issues that can arise, and how to properly deal with them. First let's dump the model to JSON: ```{r} bst_json <- xgb.dump(bst, with_stats = FALSE, dump_format='json') bst_from_json <- fromJSON(bst_json, simplifyDataFrame = FALSE) node <- bst_from_json[[1]] cat(bst_json) ``` The tree JSON shown by the above code-chunk tells us that if the data is less than 20180132, the tree will output the value in the first leaf. Otherwise it will output the value in the second leaf. Let's try to reproduce this manually with the data we have and confirm that it matches the model predictions we've already calculated. ```{r} bst_preds_logodds <- predict(bst,as.matrix(data$dates), outputmargin = TRUE) # calculate the logodds values using the JSON representation bst_from_json_logodds <- ifelse(data$dates When working with imported JSON, all data must be converted to 32-bit floats To explain this, let's repeat the comparison and round to two decimals: ```{r} round(bst_preds_logodds,2) == round(bst_from_json_logodds,2) ``` If we round to two decimals, we see that only the elements related to data values of `20180131` don't agree. If we convert the data to floats, they agree: ```{r} # now convert the dates to floats first bst_from_json_logodds <- ifelse(fl(data$dates) All JSON parameters stored as floats must be converted to floats. Let's now say we do care about numbers past the first two decimals. ```{r} # test that values are equal bst_preds_logodds == bst_from_json_logodds ``` None are exactly equal. What happened? Although we've converted the data to 32-bit floats, we also need to convert the JSON parameters to 32-bit floats. Let's do this: ```{r} # now convert the dates to floats first bst_from_json_logodds <- ifelse(fl(data$dates) Always use 32-bit numbers and operators We were able to get the log-odds to agree, so now let's manually calculate the sigmoid of the log-odds. This should agree with the xgboost predictions. ```{r} bst_preds <- predict(bst,as.matrix(data$dates)) # calculate the predictions casting doubles to floats bst_from_json_preds <- ifelse(fl(data$dates) eXtreme Gradient Boosting =========== [![Build Status](https://xgboost-ci.net/job/xgboost/job/master/badge/icon)](https://xgboost-ci.net/blue/organizations/jenkins/xgboost/activity) [![Build Status](https://img.shields.io/travis/dmlc/xgboost.svg?label=build&logo=travis&branch=master)](https://travis-ci.org/dmlc/xgboost) [![XGBoost-CI](https://github.com/dmlc/xgboost/workflows/XGBoost-CI/badge.svg?branch=master)](https://github.com/dmlc/xgboost/actions) [![Documentation Status](https://readthedocs.org/projects/xgboost/badge/?version=latest)](https://xgboost.readthedocs.org) [![GitHub license](http://dmlc.github.io/img/apache2.svg)](./LICENSE) [![CRAN Status Badge](http://www.r-pkg.org/badges/version/xgboost)](http://cran.r-project.org/web/packages/xgboost) [![PyPI version](https://badge.fury.io/py/xgboost.svg)](https://pypi.python.org/pypi/xgboost/) [![Conda version](https://img.shields.io/conda/vn/conda-forge/py-xgboost.svg)](https://anaconda.org/conda-forge/py-xgboost) [![Optuna](https://img.shields.io/badge/Optuna-integrated-blue)](https://optuna.org) [![Twitter](https://img.shields.io/badge/@XGBoostProject--_.svg?style=social&logo=twitter)](https://twitter.com/XGBoostProject) [Community](https://xgboost.ai/community) | [Documentation](https://xgboost.readthedocs.org) | [Resources](demo/README.md) | [Contributors](CONTRIBUTORS.md) | [Release Notes](NEWS.md) XGBoost is an optimized distributed gradient boosting library designed to be highly ***efficient***, ***flexible*** and ***portable***. It implements machine learning algorithms under the [Gradient Boosting](https://en.wikipedia.org/wiki/Gradient_boosting) framework. XGBoost provides a parallel tree boosting (also known as GBDT, GBM) that solve many data science problems in a fast and accurate way. The same code runs on major distributed environment (Kubernetes, Hadoop, SGE, MPI, Dask) and can solve problems beyond billions of examples. License ------- © Contributors, 2021. Licensed under an [Apache-2](https://github.com/dmlc/xgboost/blob/master/LICENSE) license. Contribute to XGBoost --------------------- XGBoost has been developed and used by a group of active community members. Your help is very valuable to make the package better for everyone. Checkout the [Community Page](https://xgboost.ai/community). Reference --------- - Tianqi Chen and Carlos Guestrin. [XGBoost: A Scalable Tree Boosting System](http://arxiv.org/abs/1603.02754). In 22nd SIGKDD Conference on Knowledge Discovery and Data Mining, 2016 - XGBoost originates from research project at University of Washington. Sponsors -------- Become a sponsor and get a logo here. See details at [Sponsoring the XGBoost Project](https://xgboost.ai/sponsors). The funds are used to defray the cost of continuous integration and testing infrastructure (https://xgboost-ci.net). ## Open Source Collective sponsors [![Backers on Open Collective](https://opencollective.com/xgboost/backers/badge.svg)](#backers) [![Sponsors on Open Collective](https://opencollective.com/xgboost/sponsors/badge.svg)](#sponsors) ### Sponsors [[Become a sponsor](https://opencollective.com/xgboost#sponsor)] NVIDIA ### Backers [[Become a backer](https://opencollective.com/xgboost#backer)] ## Other sponsors The sponsors in this list are donating cloud hours in lieu of cash donation. Amazon Web Services xgboost-1.5.2/amalgamation/000077500000000000000000000000001417122711700156415ustar00rootroot00000000000000xgboost-1.5.2/amalgamation/dmlc-minimum0.cc000066400000000000000000000010551417122711700206210ustar00rootroot00000000000000/*! * Copyright 2015 by Contributors. * \brief Mininum DMLC library Amalgamation, used for easy plugin of dmlc lib. * Normally this is not needed. */ #include "../dmlc-core/src/io/line_split.cc" #include "../dmlc-core/src/io/recordio_split.cc" #include "../dmlc-core/src/io/input_split_base.cc" #include "../dmlc-core/src/io/local_filesys.cc" #include "../dmlc-core/src/io/filesys.cc" #include "../dmlc-core/src/io/indexed_recordio_split.cc" #include "../dmlc-core/src/data.cc" #include "../dmlc-core/src/io.cc" #include "../dmlc-core/src/recordio.cc" xgboost-1.5.2/amalgamation/xgboost-all0.cc000066400000000000000000000051461417122711700204710ustar00rootroot00000000000000/*! * Copyright 2015-2019 by Contributors. * \brief XGBoost Amalgamation. * This offers an alternative way to compile the entire library from this single file. * * Example usage command. * - $(CXX) -std=c++0x -fopenmp -o -shared libxgboost.so xgboost-all0.cc -ldmlc -lrabit * * \author Tianqi Chen. */ // metrics #include "../src/metric/metric.cc" #include "../src/metric/elementwise_metric.cc" #include "../src/metric/multiclass_metric.cc" #include "../src/metric/rank_metric.cc" #include "../src/metric/auc.cc" #include "../src/metric/survival_metric.cc" // objectives #include "../src/objective/objective.cc" #include "../src/objective/regression_obj.cc" #include "../src/objective/multiclass_obj.cc" #include "../src/objective/rank_obj.cc" #include "../src/objective/hinge.cc" #include "../src/objective/aft_obj.cc" // gbms #include "../src/gbm/gbm.cc" #include "../src/gbm/gbtree.cc" #include "../src/gbm/gbtree_model.cc" #include "../src/gbm/gblinear.cc" #include "../src/gbm/gblinear_model.cc" // data #include "../src/data/data.cc" #include "../src/data/simple_dmatrix.cc" #include "../src/data/sparse_page_raw_format.cc" #include "../src/data/ellpack_page.cc" #include "../src/data/gradient_index.cc" #include "../src/data/gradient_index_page_source.cc" #include "../src/data/gradient_index_format.cc" #include "../src/data/sparse_page_dmatrix.cc" #include "../src/data/proxy_dmatrix.cc" // prediction #include "../src/predictor/predictor.cc" #include "../src/predictor/cpu_predictor.cc" // trees #include "../src/tree/param.cc" #include "../src/tree/tree_model.cc" #include "../src/tree/tree_updater.cc" #include "../src/tree/updater_colmaker.cc" #include "../src/tree/updater_quantile_hist.cc" #include "../src/tree/updater_prune.cc" #include "../src/tree/updater_refresh.cc" #include "../src/tree/updater_sync.cc" #include "../src/tree/updater_histmaker.cc" #include "../src/tree/constraints.cc" // linear #include "../src/linear/linear_updater.cc" #include "../src/linear/updater_coordinate.cc" #include "../src/linear/updater_shotgun.cc" // global #include "../src/learner.cc" #include "../src/logging.cc" #include "../src/global_config.cc" #include "../src/common/common.cc" #include "../src/common/random.cc" #include "../src/common/charconv.cc" #include "../src/common/timer.cc" #include "../src/common/quantile.cc" #include "../src/common/host_device_vector.cc" #include "../src/common/hist_util.cc" #include "../src/common/json.cc" #include "../src/common/io.cc" #include "../src/common/survival_util.cc" #include "../src/common/version.cc" // c_api #include "../src/c_api/c_api.cc" #include "../src/c_api/c_api_error.cc" xgboost-1.5.2/cmake/000077500000000000000000000000001417122711700142675ustar00rootroot00000000000000xgboost-1.5.2/cmake/Doc.cmake000066400000000000000000000010441417122711700157750ustar00rootroot00000000000000function (run_doxygen) find_package(Doxygen REQUIRED) if (NOT DOXYGEN_DOT_FOUND) message(FATAL_ERROR "Command `dot` not found. Please install graphviz.") endif (NOT DOXYGEN_DOT_FOUND) configure_file( ${xgboost_SOURCE_DIR}/doc/Doxyfile.in ${CMAKE_CURRENT_BINARY_DIR}/Doxyfile @ONLY) add_custom_target( doc_doxygen ALL COMMAND ${DOXYGEN_EXECUTABLE} ${CMAKE_CURRENT_BINARY_DIR}/Doxyfile WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR} COMMENT "Generate C APIs documentation." VERBATIM) endfunction (run_doxygen) xgboost-1.5.2/cmake/FindPrefetchIntrinsics.cmake000066400000000000000000000012531417122711700217010ustar00rootroot00000000000000function (find_prefetch_intrinsics) include(CheckCXXSourceCompiles) check_cxx_source_compiles(" #include int main() { char data = 0; const char* address = &data; _mm_prefetch(address, _MM_HINT_NTA); return 0; } " XGBOOST_MM_PREFETCH_PRESENT) check_cxx_source_compiles(" int main() { char data = 0; const char* address = &data; __builtin_prefetch(address, 0, 0); return 0; } " XGBOOST_BUILTIN_PREFETCH_PRESENT) set(XGBOOST_MM_PREFETCH_PRESENT ${XGBOOST_MM_PREFETCH_PRESENT} PARENT_SCOPE) set(XGBOOST_BUILTIN_PREFETCH_PRESENT ${XGBOOST_BUILTIN_PREFETCH_PRESENT} PARENT_SCOPE) endfunction (find_prefetch_intrinsics) xgboost-1.5.2/cmake/Python_version.in000066400000000000000000000001071417122711700176430ustar00rootroot00000000000000@xgboost_VERSION_MAJOR@.@xgboost_VERSION_MINOR@.@xgboost_VERSION_PATCH@xgboost-1.5.2/cmake/RPackageInstall.cmake.in000066400000000000000000000022431417122711700207030ustar00rootroot00000000000000# Commands to install the R package as a CMake install target function(check_call) set(cmd COMMAND) cmake_parse_arguments( PARSE_ARGV 0 CALL_ARG "" "" "${cmd}" ) string(REPLACE ";" " " commands "${CALL_ARG_COMMAND}") message("Command: ${commands}") execute_process(COMMAND ${CALL_ARG_COMMAND} OUTPUT_VARIABLE _out ERROR_VARIABLE _err RESULT_VARIABLE _res) if(NOT "${_res}" EQUAL "0") message(FATAL_ERROR "out: ${_out}, err: ${_err}, res: ${_res}") endif() endfunction() # Important paths set(build_dir "@build_dir@") set(LIBR_EXECUTABLE "@LIBR_EXECUTABLE@") # Back up cmake_install.cmake file(WRITE "${build_dir}/R-package/src/Makevars" "all:") file(WRITE "${build_dir}/R-package/src/Makevars.win" "all:") # Install dependencies set(XGB_DEPS_SCRIPT "deps = setdiff(c('data.table', 'jsonlite', 'Matrix'), rownames(installed.packages())); if(length(deps)>0) install.packages(deps, repo = 'https://cloud.r-project.org/')") check_call(COMMAND "${LIBR_EXECUTABLE}" -q -e "${XGB_DEPS_SCRIPT}") # Install the XGBoost R package check_call(COMMAND "${LIBR_EXECUTABLE}" CMD INSTALL --no-multiarch --build "${build_dir}/R-package")xgboost-1.5.2/cmake/RPackageInstallTargetSetup.cmake000066400000000000000000000012631417122711700224670ustar00rootroot00000000000000# Assembles the R-package files in build_dir; # if necessary, installs the main R package dependencies; # runs R CMD INSTALL. function(setup_rpackage_install_target rlib_target build_dir) configure_file(${PROJECT_SOURCE_DIR}/cmake/RPackageInstall.cmake.in ${PROJECT_BINARY_DIR}/RPackageInstall.cmake @ONLY) install( DIRECTORY "${xgboost_SOURCE_DIR}/R-package" DESTINATION "${build_dir}" PATTERN "src/*" EXCLUDE PATTERN "R-package/configure" EXCLUDE ) install(TARGETS ${rlib_target} LIBRARY DESTINATION "${build_dir}/R-package/src/" RUNTIME DESTINATION "${build_dir}/R-package/src/") install(SCRIPT ${PROJECT_BINARY_DIR}/RPackageInstall.cmake) endfunction() xgboost-1.5.2/cmake/Sanitizer.cmake000066400000000000000000000042221417122711700172410ustar00rootroot00000000000000# Set appropriate compiler and linker flags for sanitizers. # # Usage of this module: # enable_sanitizers("address;leak") # Add flags macro(enable_sanitizer sanitizer) if(${sanitizer} MATCHES "address") find_package(ASan) set(SAN_COMPILE_FLAGS "${SAN_COMPILE_FLAGS} -fsanitize=address") if (ASan_FOUND) link_libraries(${ASan_LIBRARY}) endif (ASan_FOUND) elseif(${sanitizer} MATCHES "thread") find_package(TSan) set(SAN_COMPILE_FLAGS "${SAN_COMPILE_FLAGS} -fsanitize=thread") if (TSan_FOUND) link_libraries(${TSan_LIBRARY}) endif (TSan_FOUND) elseif(${sanitizer} MATCHES "leak") find_package(LSan) set(SAN_COMPILE_FLAGS "${SAN_COMPILE_FLAGS} -fsanitize=leak") if (LSan_FOUND) link_libraries(${LSan_LIBRARY}) endif (LSan_FOUND) elseif(${sanitizer} MATCHES "undefined") find_package(UBSan) set(SAN_COMPILE_FLAGS "${SAN_COMPILE_FLAGS} -fsanitize=undefined -fno-sanitize-recover=undefined") if (UBSan_FOUND) link_libraries(${UBSan_LIBRARY}) endif (UBSan_FOUND) else() message(FATAL_ERROR "Santizer ${sanitizer} not supported.") endif() endmacro() macro(enable_sanitizers SANITIZERS) # Check sanitizers compatibility. # Idealy, we should use if(san IN_LIST SANITIZERS) ... endif() # But I haven't figure out how to make it work. foreach ( _san ${SANITIZERS} ) string(TOLOWER ${_san} _san) if (_san MATCHES "thread") if (${_use_other_sanitizers}) message(FATAL_ERROR "thread sanitizer is not compatible with ${_san} sanitizer.") endif() set(_use_thread_sanitizer 1) else () if (${_use_thread_sanitizer}) message(FATAL_ERROR "${_san} sanitizer is not compatible with thread sanitizer.") endif() set(_use_other_sanitizers 1) endif() endforeach() message("Sanitizers: ${SANITIZERS}") foreach( _san ${SANITIZERS} ) string(TOLOWER ${_san} _san) enable_sanitizer(${_san}) endforeach() message("Sanitizers compile flags: ${SAN_COMPILE_FLAGS}") set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${SAN_COMPILE_FLAGS}") set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} ${SAN_COMPILE_FLAGS}") endmacro() xgboost-1.5.2/cmake/Utils.cmake000066400000000000000000000237631417122711700164040ustar00rootroot00000000000000# Automatically set source group based on folder function(auto_source_group SOURCES) foreach(FILE ${SOURCES}) get_filename_component(PARENT_DIR "${FILE}" PATH) # skip src or include and changes /'s to \\'s string(REPLACE "${CMAKE_CURRENT_LIST_DIR}" "" GROUP "${PARENT_DIR}") string(REPLACE "/" "\\\\" GROUP "${GROUP}") string(REGEX REPLACE "^\\\\" "" GROUP "${GROUP}") source_group("${GROUP}" FILES "${FILE}") endforeach() endfunction(auto_source_group) # Force static runtime for MSVC function(msvc_use_static_runtime) if(MSVC) set(variables CMAKE_C_FLAGS_DEBUG CMAKE_C_FLAGS_MINSIZEREL CMAKE_C_FLAGS_RELEASE CMAKE_C_FLAGS_RELWITHDEBINFO CMAKE_CXX_FLAGS_DEBUG CMAKE_CXX_FLAGS_MINSIZEREL CMAKE_CXX_FLAGS_RELEASE CMAKE_CXX_FLAGS_RELWITHDEBINFO ) foreach(variable ${variables}) if(${variable} MATCHES "/MD") string(REGEX REPLACE "/MD" "/MT" ${variable} "${${variable}}") set(${variable} "${${variable}}" PARENT_SCOPE) endif() endforeach() set(variables CMAKE_CUDA_FLAGS CMAKE_CUDA_FLAGS_DEBUG CMAKE_CUDA_FLAGS_MINSIZEREL CMAKE_CUDA_FLAGS_RELEASE CMAKE_CUDA_FLAGS_RELWITHDEBINFO ) foreach(variable ${variables}) if(${variable} MATCHES "-MD") string(REGEX REPLACE "-MD" "-MT" ${variable} "${${variable}}") set(${variable} "${${variable}}" PARENT_SCOPE) endif() if(${variable} MATCHES "/MD") string(REGEX REPLACE "/MD" "/MT" ${variable} "${${variable}}") set(${variable} "${${variable}}" PARENT_SCOPE) endif() endforeach() endif() endfunction(msvc_use_static_runtime) # Set output directory of target, ignoring debug or release function(set_output_directory target dir) set_target_properties(${target} PROPERTIES RUNTIME_OUTPUT_DIRECTORY ${dir} RUNTIME_OUTPUT_DIRECTORY_DEBUG ${dir} RUNTIME_OUTPUT_DIRECTORY_RELEASE ${dir} RUNTIME_OUTPUT_DIRECTORY_RELWITHDEBINFO ${dir} RUNTIME_OUTPUT_DIRECTORY_MINSIZEREL ${dir} LIBRARY_OUTPUT_DIRECTORY ${dir} LIBRARY_OUTPUT_DIRECTORY_DEBUG ${dir} LIBRARY_OUTPUT_DIRECTORY_RELEASE ${dir} LIBRARY_OUTPUT_DIRECTORY_RELWITHDEBINFO ${dir} LIBRARY_OUTPUT_DIRECTORY_MINSIZEREL ${dir} ARCHIVE_OUTPUT_DIRECTORY ${dir} ARCHIVE_OUTPUT_DIRECTORY_DEBUG ${dir} ARCHIVE_OUTPUT_DIRECTORY_RELEASE ${dir} ARCHIVE_OUTPUT_DIRECTORY_RELWITHDEBINFO ${dir} ARCHIVE_OUTPUT_DIRECTORY_MINSIZEREL ${dir}) endfunction(set_output_directory) # Set a default build type to release if none was specified function(set_default_configuration_release) if(CMAKE_CONFIGURATION_TYPES STREQUAL "Debug;Release;MinSizeRel;RelWithDebInfo") # multiconfig generator? set(CMAKE_CONFIGURATION_TYPES Release CACHE STRING "" FORCE) elseif(NOT CMAKE_BUILD_TYPE AND NOT CMAKE_CONFIGURATION_TYPES) message(STATUS "Setting build type to 'Release' as none was specified.") set(CMAKE_BUILD_TYPE Release CACHE STRING "Choose the type of build." FORCE ) endif() endfunction(set_default_configuration_release) # Generate nvcc compiler flags given a list of architectures # Also generates PTX for the most recent architecture for forwards compatibility function(format_gencode_flags flags out) if(CMAKE_CUDA_COMPILER_VERSION MATCHES "^([0-9]+\\.[0-9]+)") set(CUDA_VERSION "${CMAKE_MATCH_1}") endif() # Set up architecture flags if(NOT flags) if (CUDA_VERSION VERSION_GREATER_EQUAL "11.1") set(flags "50;52;60;61;70;75;80;86") elseif (CUDA_VERSION VERSION_GREATER_EQUAL "11.0") set(flags "35;50;52;60;61;70;75;80") elseif(CUDA_VERSION VERSION_GREATER_EQUAL "10.0") set(flags "35;50;52;60;61;70;75") elseif(CUDA_VERSION VERSION_GREATER_EQUAL "9.0") set(flags "35;50;52;60;61;70") else() set(flags "35;50;52;60;61") endif() endif() if (CMAKE_VERSION VERSION_GREATER_EQUAL "3.18") cmake_policy(SET CMP0104 NEW) foreach(ver ${flags}) set(CMAKE_CUDA_ARCHITECTURES "${ver}-real;${ver}-virtual;${CMAKE_CUDA_ARCHITECTURES}") endforeach() set(CMAKE_CUDA_ARCHITECTURES "${CMAKE_CUDA_ARCHITECTURES}" PARENT_SCOPE) message(STATUS "CMAKE_CUDA_ARCHITECTURES: ${CMAKE_CUDA_ARCHITECTURES}") else() # Generate SASS foreach(ver ${flags}) set(${out} "${${out}}--generate-code=arch=compute_${ver},code=sm_${ver};") endforeach() # Generate PTX for last architecture list(GET flags -1 ver) set(${out} "${${out}}--generate-code=arch=compute_${ver},code=compute_${ver};") set(${out} "${${out}}" PARENT_SCOPE) message(STATUS "CUDA GEN_CODE: ${GEN_CODE}") endif (CMAKE_VERSION VERSION_GREATER_EQUAL "3.18") endfunction(format_gencode_flags flags) macro(enable_nvtx target) find_package(NVTX REQUIRED) target_include_directories(${target} PRIVATE "${NVTX_INCLUDE_DIR}") target_link_libraries(${target} PRIVATE "${NVTX_LIBRARY}") target_compile_definitions(${target} PRIVATE -DXGBOOST_USE_NVTX=1) endmacro() # Set CUDA related flags to target. Must be used after code `format_gencode_flags`. function(xgboost_set_cuda_flags target) target_compile_options(${target} PRIVATE $<$:--expt-extended-lambda> $<$:--expt-relaxed-constexpr> $<$:${GEN_CODE}> $<$:-Xcompiler=${OpenMP_CXX_FLAGS}>) if (CMAKE_VERSION VERSION_GREATER_EQUAL "3.18") set_property(TARGET ${target} PROPERTY CUDA_ARCHITECTURES ${CMAKE_CUDA_ARCHITECTURES}) endif (CMAKE_VERSION VERSION_GREATER_EQUAL "3.18") if (USE_DEVICE_DEBUG) target_compile_options(${target} PRIVATE $<$,$>:-G;-src-in-ptx>) else (USE_DEVICE_DEBUG) target_compile_options(${target} PRIVATE $<$:-lineinfo>) endif (USE_DEVICE_DEBUG) if (USE_NVTX) enable_nvtx(${target}) endif (USE_NVTX) if (NOT BUILD_WITH_CUDA_CUB) target_compile_definitions(${target} PRIVATE -DXGBOOST_USE_CUDA=1 -DTHRUST_IGNORE_CUB_VERSION_CHECK=1) target_include_directories(${target} PRIVATE ${xgboost_SOURCE_DIR}/cub/ ${xgboost_SOURCE_DIR}/gputreeshap) else () target_compile_definitions(${target} PRIVATE -DXGBOOST_USE_CUDA=1) target_include_directories(${target} PRIVATE ${xgboost_SOURCE_DIR}/gputreeshap) endif (NOT BUILD_WITH_CUDA_CUB) if (MSVC) target_compile_options(${target} PRIVATE $<$:-Xcompiler=/utf-8>) endif (MSVC) set_target_properties(${target} PROPERTIES CUDA_STANDARD 14 CUDA_STANDARD_REQUIRED ON CUDA_SEPARABLE_COMPILATION OFF) endfunction(xgboost_set_cuda_flags) macro(xgboost_link_nccl target) if (BUILD_STATIC_LIB) target_include_directories(${target} PUBLIC ${NCCL_INCLUDE_DIR}) target_compile_definitions(${target} PUBLIC -DXGBOOST_USE_NCCL=1) target_link_libraries(${target} PUBLIC ${NCCL_LIBRARY}) else () target_include_directories(${target} PRIVATE ${NCCL_INCLUDE_DIR}) target_compile_definitions(${target} PRIVATE -DXGBOOST_USE_NCCL=1) target_link_libraries(${target} PRIVATE ${NCCL_LIBRARY}) endif (BUILD_STATIC_LIB) endmacro(xgboost_link_nccl) # compile options macro(xgboost_target_properties target) set_target_properties(${target} PROPERTIES CXX_STANDARD 14 CXX_STANDARD_REQUIRED ON POSITION_INDEPENDENT_CODE ON) if (HIDE_CXX_SYMBOLS) #-- Hide all C++ symbols set_target_properties(${target} PROPERTIES C_VISIBILITY_PRESET hidden CXX_VISIBILITY_PRESET hidden CUDA_VISIBILITY_PRESET hidden ) endif (HIDE_CXX_SYMBOLS) if (ENABLE_ALL_WARNINGS) target_compile_options(${target} PUBLIC $,-Xcompiler=-Wall -Xcompiler=-Wextra,-Wall -Wextra> ) endif(ENABLE_ALL_WARNINGS) target_compile_options(${target} PRIVATE $<$,$>:/MP> $<$>,$>:-funroll-loops>) if (MSVC) target_compile_options(${target} PRIVATE $<$>:/utf-8> -D_CRT_SECURE_NO_WARNINGS -D_CRT_SECURE_NO_DEPRECATE ) endif (MSVC) if (WIN32 AND MINGW) target_compile_options(${target} PUBLIC -static-libstdc++) endif (WIN32 AND MINGW) endmacro(xgboost_target_properties) # Custom definitions used in xgboost. macro(xgboost_target_defs target) if (NOT ${target} STREQUAL "dmlc") # skip dmlc core for custom logging. target_compile_definitions(${target} PRIVATE -DDMLC_LOG_CUSTOMIZE=1 $<$>:_MWAITXINTRIN_H_INCLUDED>) endif () if (USE_DEBUG_OUTPUT) target_compile_definitions(${target} PRIVATE -DXGBOOST_USE_DEBUG_OUTPUT=1) endif (USE_DEBUG_OUTPUT) if (XGBOOST_MM_PREFETCH_PRESENT) target_compile_definitions(${target} PRIVATE -DXGBOOST_MM_PREFETCH_PRESENT=1) endif(XGBOOST_MM_PREFETCH_PRESENT) if (XGBOOST_BUILTIN_PREFETCH_PRESENT) target_compile_definitions(${target} PRIVATE -DXGBOOST_BUILTIN_PREFETCH_PRESENT=1) endif (XGBOOST_BUILTIN_PREFETCH_PRESENT) endmacro(xgboost_target_defs) # handles dependencies macro(xgboost_target_link_libraries target) if (BUILD_STATIC_LIB) target_link_libraries(${target} PUBLIC Threads::Threads ${CMAKE_THREAD_LIBS_INIT}) else() target_link_libraries(${target} PRIVATE Threads::Threads ${CMAKE_THREAD_LIBS_INIT}) endif (BUILD_STATIC_LIB) if (USE_OPENMP) if (BUILD_STATIC_LIB) target_link_libraries(${target} PUBLIC OpenMP::OpenMP_CXX) else() target_link_libraries(${target} PRIVATE OpenMP::OpenMP_CXX) endif (BUILD_STATIC_LIB) endif (USE_OPENMP) if (USE_CUDA) xgboost_set_cuda_flags(${target}) endif (USE_CUDA) if (USE_NCCL) xgboost_link_nccl(${target}) endif (USE_NCCL) if (USE_NVTX) enable_nvtx(${target}) endif (USE_NVTX) if (RABIT_BUILD_MPI) target_link_libraries(${target} PRIVATE MPI::MPI_CXX) endif (RABIT_BUILD_MPI) endmacro(xgboost_target_link_libraries) xgboost-1.5.2/cmake/Version.cmake000066400000000000000000000005711417122711700167210ustar00rootroot00000000000000function (write_version) message(STATUS "xgboost VERSION: ${xgboost_VERSION}") configure_file( ${xgboost_SOURCE_DIR}/cmake/version_config.h.in ${xgboost_SOURCE_DIR}/include/xgboost/version_config.h @ONLY) configure_file( ${xgboost_SOURCE_DIR}/cmake/Python_version.in ${xgboost_SOURCE_DIR}/python-package/xgboost/VERSION @ONLY) endfunction (write_version) xgboost-1.5.2/cmake/modules/000077500000000000000000000000001417122711700157375ustar00rootroot00000000000000xgboost-1.5.2/cmake/modules/FindASan.cmake000066400000000000000000000006321417122711700203650ustar00rootroot00000000000000set(ASan_LIB_NAME ASan) find_library(ASan_LIBRARY NAMES libasan.so libasan.so.5 libasan.so.4 libasan.so.3 libasan.so.2 libasan.so.1 libasan.so.0 PATHS ${SANITIZER_PATH} /usr/lib64 /usr/lib /usr/local/lib64 /usr/local/lib ${CMAKE_PREFIX_PATH}/lib) include(FindPackageHandleStandardArgs) find_package_handle_standard_args(ASan DEFAULT_MSG ASan_LIBRARY) mark_as_advanced( ASan_LIBRARY ASan_LIB_NAME) xgboost-1.5.2/cmake/modules/FindLSan.cmake000066400000000000000000000005521417122711700204010ustar00rootroot00000000000000set(LSan_LIB_NAME lsan) find_library(LSan_LIBRARY NAMES liblsan.so liblsan.so.0 liblsan.so.0.0.0 PATHS ${SANITIZER_PATH} /usr/lib64 /usr/lib /usr/local/lib64 /usr/local/lib ${CMAKE_PREFIX_PATH}/lib) include(FindPackageHandleStandardArgs) find_package_handle_standard_args(LSan DEFAULT_MSG LSan_LIBRARY) mark_as_advanced( LSan_LIBRARY LSan_LIB_NAME) xgboost-1.5.2/cmake/modules/FindLibR.cmake000066400000000000000000000142411417122711700203740ustar00rootroot00000000000000# CMake module for R # Borrows ideas from RStudio's FindLibR.cmake # # Defines the following: # LIBR_FOUND # LIBR_HOME # LIBR_EXECUTABLE # LIBR_INCLUDE_DIRS # LIBR_LIB_DIR # LIBR_CORE_LIBRARY # and a cmake function to create R.lib for MSVC # # The following could be provided by user through cmake's -D options: # LIBR_EXECUTABLE (for unix and win) # R_VERSION (for win) # R_ARCH (for win 64 when want 32 bit build) # # TODO: # - someone to verify OSX detection, # - possibly, add OSX detection based on current R in PATH or LIBR_EXECUTABLE # - improve registry-based R_HOME detection in Windows (from a set of R_VERSION's) # Windows users might want to change this to their R version: if(NOT R_VERSION) set(R_VERSION "4.0.0") endif() if(NOT R_ARCH) if("${CMAKE_SIZEOF_VOID_P}" STREQUAL "4") set(R_ARCH "i386") else() set(R_ARCH "x64") endif() endif() # Creates R.lib and R.def in the build directory for linking with MSVC function(create_rlib_for_msvc) # various checks and warnings if(NOT WIN32 OR (NOT MSVC AND NOT MINGW)) message(FATAL_ERROR "create_rlib_for_msvc() can only be used with MSVC or MINGW") endif() if(NOT EXISTS "${LIBR_LIB_DIR}") message(FATAL_ERROR "LIBR_LIB_DIR was not set!") endif() find_program(DLLTOOL_EXE dlltool) if(NOT DLLTOOL_EXE) message(FATAL_ERROR "\ndlltool.exe not found!\ \nDo you have Rtools installed with its MinGW's bin/ in PATH?") endif() # extract symbols from R.dll into R.def and R.lib import library get_filename_component( LIBR_RSCRIPT_EXECUTABLE_DIR ${LIBR_EXECUTABLE} DIRECTORY ) set(LIBR_RSCRIPT_EXECUTABLE "${LIBR_RSCRIPT_EXECUTABLE_DIR}/Rscript") execute_process( COMMAND ${LIBR_RSCRIPT_EXECUTABLE} "${CMAKE_CURRENT_BINARY_DIR}/../../R-package/inst/make-r-def.R" "${LIBR_LIB_DIR}/R.dll" "${CMAKE_CURRENT_BINARY_DIR}/R.def" ) execute_process(COMMAND ${DLLTOOL_EXE} "--input-def" "${CMAKE_CURRENT_BINARY_DIR}/R.def" "--output-lib" "${CMAKE_CURRENT_BINARY_DIR}/R.lib") endfunction(create_rlib_for_msvc) # detection for OSX if(APPLE) find_library(LIBR_LIBRARIES R) if(LIBR_LIBRARIES MATCHES ".*\\.framework") set(LIBR_HOME "${LIBR_LIBRARIES}/Resources" CACHE PATH "R home directory") set(LIBR_INCLUDE_DIRS "${LIBR_HOME}/include" CACHE PATH "R include directory") set(LIBR_EXECUTABLE "${LIBR_HOME}/R" CACHE PATH "R executable") set(LIBR_LIB_DIR "${LIBR_HOME}/lib" CACHE PATH "R lib directory") else() get_filename_component(_LIBR_LIBRARIES "${LIBR_LIBRARIES}" REALPATH) get_filename_component(_LIBR_LIBRARIES_DIR "${_LIBR_LIBRARIES}" DIRECTORY) set(LIBR_EXECUTABLE "${_LIBR_LIBRARIES_DIR}/../bin/R") execute_process( COMMAND ${LIBR_EXECUTABLE} "--slave" "--vanilla" "-e" "cat(R.home())" OUTPUT_VARIABLE LIBR_HOME) set(LIBR_HOME ${LIBR_HOME} CACHE PATH "R home directory") set(LIBR_INCLUDE_DIRS "${LIBR_HOME}/include" CACHE PATH "R include directory") set(LIBR_LIB_DIR "${LIBR_HOME}/lib" CACHE PATH "R lib directory") endif() # detection for UNIX & Win32 else() # attempt to find R executable if(NOT LIBR_EXECUTABLE) find_program(LIBR_EXECUTABLE NAMES R R.exe) endif() if(UNIX) if(NOT LIBR_EXECUTABLE) message(FATAL_ERROR "Unable to locate R executable.\ \nEither add its location to PATH or provide it through the LIBR_EXECUTABLE cmake variable") endif() # ask R for the home path execute_process( COMMAND ${LIBR_EXECUTABLE} "--slave" "--vanilla" "-e" "cat(R.home())" OUTPUT_VARIABLE LIBR_HOME ) # ask R for the include dir execute_process( COMMAND ${LIBR_EXECUTABLE} "--slave" "--vanilla" "-e" "cat(R.home('include'))" OUTPUT_VARIABLE LIBR_INCLUDE_DIRS ) # ask R for the lib dir execute_process( COMMAND ${LIBR_EXECUTABLE} "--slave" "--vanilla" "-e" "cat(R.home('lib'))" OUTPUT_VARIABLE LIBR_LIB_DIR ) # Windows else() # ask R for R_HOME if(LIBR_EXECUTABLE) execute_process( COMMAND ${LIBR_EXECUTABLE} "--slave" "--no-save" "-e" "cat(normalizePath(R.home(),winslash='/'))" OUTPUT_VARIABLE LIBR_HOME) endif() # if R executable not available, query R_HOME path from registry if(NOT LIBR_HOME) get_filename_component(LIBR_HOME "[HKEY_LOCAL_MACHINE\\SOFTWARE\\R-core\\R\\${R_VERSION};InstallPath]" ABSOLUTE) if(NOT LIBR_HOME) message(FATAL_ERROR "\nUnable to locate R executable.\ \nEither add its location to PATH or provide it through the LIBR_EXECUTABLE cmake variable") endif() endif() # set exe location based on R_ARCH if(NOT LIBR_EXECUTABLE) set(LIBR_EXECUTABLE "${LIBR_HOME}/bin/${R_ARCH}/R.exe") endif() # set other R paths based on home path set(LIBR_INCLUDE_DIRS "${LIBR_HOME}/include") set(LIBR_LIB_DIR "${LIBR_HOME}/bin/${R_ARCH}") message(STATUS "LIBR_HOME [${LIBR_HOME}]") message(STATUS "LIBR_EXECUTABLE [${LIBR_EXECUTABLE}]") message(STATUS "LIBR_INCLUDE_DIRS [${LIBR_INCLUDE_DIRS}]") message(STATUS "LIBR_LIB_DIR [${LIBR_LIB_DIR}]") message(STATUS "LIBR_CORE_LIBRARY [${LIBR_CORE_LIBRARY}]") endif() endif() if((WIN32 AND MSVC) OR (WIN32 AND MINGW)) # create a local R.lib import library for R.dll if it doesn't exist if(NOT EXISTS "${CMAKE_CURRENT_BINARY_DIR}/R.lib") create_rlib_for_msvc() endif() endif() # look for the core R library find_library(LIBR_CORE_LIBRARY NAMES R HINTS "${CMAKE_CURRENT_BINARY_DIR}" "${LIBR_LIB_DIR}" "${LIBR_HOME}/bin" "${LIBR_LIBRARIES}") if(LIBR_CORE_LIBRARY-NOTFOUND) message(STATUS "Could not find R core shared library.") endif() set(LIBR_HOME ${LIBR_HOME} CACHE PATH "R home directory") set(LIBR_EXECUTABLE ${LIBR_EXECUTABLE} CACHE PATH "R executable") set(LIBR_INCLUDE_DIRS ${LIBR_INCLUDE_DIRS} CACHE PATH "R include directory") set(LIBR_LIB_DIR ${LIBR_LIB_DIR} CACHE PATH "R shared libraries directory") set(LIBR_CORE_LIBRARY ${LIBR_CORE_LIBRARY} CACHE PATH "R core shared library") # define find requirements include(FindPackageHandleStandardArgs) find_package_handle_standard_args(LibR DEFAULT_MSG LIBR_HOME LIBR_EXECUTABLE LIBR_INCLUDE_DIRS LIBR_LIB_DIR LIBR_CORE_LIBRARY ) if(LIBR_FOUND) message(STATUS "Found R: ${LIBR_EXECUTABLE}") endif() xgboost-1.5.2/cmake/modules/FindNVML.cmake000066400000000000000000000010041417122711700203110ustar00rootroot00000000000000if (NVML_LIBRARY) unset(NVML_LIBRARY CACHE) endif(NVML_LIBRARY) set(NVML_LIB_NAME nvml) find_path(NVML_INCLUDE_DIR NAMES nvml.h PATHS ${CUDA_HOME}/include ${CUDA_INCLUDE} /usr/local/cuda/include) find_library(NVML_LIBRARY NAMES nvidia-ml) message(STATUS "Using nvml library: ${NVML_LIBRARY}") include(FindPackageHandleStandardArgs) find_package_handle_standard_args(NVML DEFAULT_MSG NVML_INCLUDE_DIR NVML_LIBRARY) mark_as_advanced( NVML_INCLUDE_DIR NVML_LIBRARY ) xgboost-1.5.2/cmake/modules/FindNVTX.cmake000066400000000000000000000011051417122711700203360ustar00rootroot00000000000000if (NVTX_LIBRARY) unset(NVTX_LIBRARY CACHE) endif (NVTX_LIBRARY) set(NVTX_LIB_NAME nvToolsExt) find_path(NVTX_INCLUDE_DIR NAMES nvToolsExt.h PATHS ${CUDA_HOME}/include ${CUDA_INCLUDE} /usr/local/cuda/include) find_library(NVTX_LIBRARY NAMES nvToolsExt PATHS ${CUDA_HOME}/lib64 /usr/local/cuda/lib64) message(STATUS "Using nvtx library: ${NVTX_LIBRARY}") include(FindPackageHandleStandardArgs) find_package_handle_standard_args(NVTX DEFAULT_MSG NVTX_INCLUDE_DIR NVTX_LIBRARY) mark_as_advanced( NVTX_INCLUDE_DIR NVTX_LIBRARY ) xgboost-1.5.2/cmake/modules/FindNccl.cmake000066400000000000000000000043641417122711700204300ustar00rootroot00000000000000# # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # # Tries to find NCCL headers and libraries. # # Usage of this module as follows: # # find_package(NCCL) # # Variables used by this module, they can change the default behaviour and need # to be set before calling find_package: # # NCCL_ROOT - When set, this path is inspected instead of standard library # locations as the root of the NCCL installation. # The environment variable NCCL_ROOT overrides this variable. # # This module defines # Nccl_FOUND, whether nccl has been found # NCCL_INCLUDE_DIR, directory containing header # NCCL_LIBRARY, directory containing nccl library # NCCL_LIB_NAME, nccl library name # USE_NCCL_LIB_PATH, when set, NCCL_LIBRARY path is also inspected for the # location of the nccl library. This would disable # switching between static and shared. # # This module assumes that the user has already called find_package(CUDA) if (NCCL_LIBRARY) if(NOT USE_NCCL_LIB_PATH) # Don't cache NCCL_LIBRARY to enable switching between static and shared. unset(NCCL_LIBRARY CACHE) endif(NOT USE_NCCL_LIB_PATH) endif() if (BUILD_WITH_SHARED_NCCL) # libnccl.so set(NCCL_LIB_NAME nccl) else () # libnccl_static.a set(NCCL_LIB_NAME nccl_static) endif (BUILD_WITH_SHARED_NCCL) find_path(NCCL_INCLUDE_DIR NAMES nccl.h PATHS $ENV{NCCL_ROOT}/include ${NCCL_ROOT}/include) find_library(NCCL_LIBRARY NAMES ${NCCL_LIB_NAME} PATHS $ENV{NCCL_ROOT}/lib/ ${NCCL_ROOT}/lib) message(STATUS "Using nccl library: ${NCCL_LIBRARY}") include(FindPackageHandleStandardArgs) find_package_handle_standard_args(Nccl DEFAULT_MSG NCCL_INCLUDE_DIR NCCL_LIBRARY) mark_as_advanced( NCCL_INCLUDE_DIR NCCL_LIBRARY ) xgboost-1.5.2/cmake/modules/FindTSan.cmake000066400000000000000000000005521417122711700204110ustar00rootroot00000000000000set(TSan_LIB_NAME tsan) find_library(TSan_LIBRARY NAMES libtsan.so libtsan.so.0 libtsan.so.0.0.0 PATHS ${SANITIZER_PATH} /usr/lib64 /usr/lib /usr/local/lib64 /usr/local/lib ${CMAKE_PREFIX_PATH}/lib) include(FindPackageHandleStandardArgs) find_package_handle_standard_args(TSan DEFAULT_MSG TSan_LIBRARY) mark_as_advanced( TSan_LIBRARY TSan_LIB_NAME) xgboost-1.5.2/cmake/modules/FindUBSan.cmake000066400000000000000000000006501417122711700205130ustar00rootroot00000000000000set(UBSan_LIB_NAME UBSan) find_library(UBSan_LIBRARY NAMES libubsan.so libubsan.so.5 libubsan.so.4 libubsan.so.3 libubsan.so.2 libubsan.so.1 libubsan.so.0 PATHS ${SANITIZER_PATH} /usr/lib64 /usr/lib /usr/local/lib64 /usr/local/lib ${CMAKE_PREFIX_PATH}/lib) include(FindPackageHandleStandardArgs) find_package_handle_standard_args(UBSan DEFAULT_MSG UBSan_LIBRARY) mark_as_advanced( UBSan_LIBRARY UBSan_LIB_NAME) xgboost-1.5.2/cmake/version_config.h.in000066400000000000000000000004601417122711700200570ustar00rootroot00000000000000/*! * Copyright 2019 XGBoost contributors */ #ifndef XGBOOST_VERSION_CONFIG_H_ #define XGBOOST_VERSION_CONFIG_H_ #define XGBOOST_VER_MAJOR @xgboost_VERSION_MAJOR@ #define XGBOOST_VER_MINOR @xgboost_VERSION_MINOR@ #define XGBOOST_VER_PATCH @xgboost_VERSION_PATCH@ #endif // XGBOOST_VERSION_CONFIG_H_ xgboost-1.5.2/cmake/xgboost-config.cmake.in000066400000000000000000000011571417122711700206320ustar00rootroot00000000000000@PACKAGE_INIT@ set(USE_OPENMP @USE_OPENMP@) set(USE_CUDA @USE_CUDA@) set(USE_NCCL @USE_NCCL@) set(XGBOOST_BUILD_STATIC_LIB @BUILD_STATIC_LIB@) include(CMakeFindDependencyMacro) if (XGBOOST_BUILD_STATIC_LIB) find_dependency(Threads) if(USE_OPENMP) find_dependency(OpenMP) endif() if(USE_CUDA) find_dependency(CUDA) endif() # nccl should be linked statically if xgboost is built as static library. endif (XGBOOST_BUILD_STATIC_LIB) if(NOT TARGET xgboost::xgboost) include(${CMAKE_CURRENT_LIST_DIR}/XGBoostTargets.cmake) endif() message(STATUS "Found XGBoost (found version \"${xgboost_VERSION}\")") xgboost-1.5.2/cmake/xgboost.pc.in000066400000000000000000000004341417122711700167060ustar00rootroot00000000000000prefix=@CMAKE_INSTALL_PREFIX@ version=@xgboost_VERSION@ exec_prefix=${prefix}/bin libdir=${prefix}/lib includedir=${prefix}/include Name: xgboost Description: XGBoost - Scalable and Flexible Gradient Boosting. Version: ${version} Cflags: -I${includedir} Libs: -L${libdir} -lxgboost xgboost-1.5.2/cub/000077500000000000000000000000001417122711700137605ustar00rootroot00000000000000xgboost-1.5.2/demo/000077500000000000000000000000001417122711700141335ustar00rootroot00000000000000xgboost-1.5.2/demo/.gitignore000066400000000000000000000000171417122711700161210ustar00rootroot00000000000000*.libsvm *.pkl xgboost-1.5.2/demo/CLI/000077500000000000000000000000001417122711700145425ustar00rootroot00000000000000xgboost-1.5.2/demo/CLI/binary_classification/000077500000000000000000000000001417122711700211015ustar00rootroot00000000000000xgboost-1.5.2/demo/CLI/binary_classification/README.md000066400000000000000000000175671417122711700224000ustar00rootroot00000000000000Binary Classification ===================== This is the quick start tutorial for xgboost CLI version. Here we demonstrate how to use XGBoost for a binary classification task. Before getting started, make sure you compile xgboost in the root directory of the project by typing ```make```. The script 'runexp.sh' can be used to run the demo. Here we use [mushroom dataset](https://archive.ics.uci.edu/ml/datasets/Mushroom) from UCI machine learning repository. ### Tutorial #### Generate Input Data XGBoost takes LIBSVM format. An example of faked input data is below: ``` 1 101:1.2 102:0.03 0 1:2.1 10001:300 10002:400 ... ``` Each line represent a single instance, and in the first line '1' is the instance label,'101' and '102' are feature indices, '1.2' and '0.03' are feature values. In the binary classification case, '1' is used to indicate positive samples, and '0' is used to indicate negative samples. We also support probability values in [0,1] as label, to indicate the probability of the instance being positive. First we will transform the dataset into classic LIBSVM format and split the data into training set and test set by running: ``` python mapfeat.py python mknfold.py agaricus.txt 1 ``` The two files, 'agaricus.txt.train' and 'agaricus.txt.test' will be used as training set and test set. #### Training Then we can run the training process: ``` ../../xgboost mushroom.conf ``` mushroom.conf is the configuration for both training and testing. Each line containing the [attribute]=[value] configuration: ```conf # General Parameters, see comment for each definition # can be gbtree or gblinear booster = gbtree # choose logistic regression loss function for binary classification objective = binary:logistic # Tree Booster Parameters # step size shrinkage eta = 1.0 # minimum loss reduction required to make a further partition gamma = 1.0 # minimum sum of instance weight(hessian) needed in a child min_child_weight = 1 # maximum depth of a tree max_depth = 3 # Task Parameters # the number of round to do boosting num_round = 2 # 0 means do not save any model except the final round model save_period = 0 # The path of training data data = "agaricus.txt.train" # The path of validation data, used to monitor training process, here [test] sets name of the validation set eval[test] = "agaricus.txt.test" # The path of test data test:data = "agaricus.txt.test" ``` We use the tree booster and logistic regression objective in our setting. This indicates that we accomplish our task using classic gradient boosting regression tree(GBRT), which is a promising method for binary classification. The parameters shown in the example gives the most common ones that are needed to use xgboost. If you are interested in more parameter settings, the complete parameter settings and detailed descriptions are [here](https://xgboost.readthedocs.io/en/stable/parameter.html). Besides putting the parameters in the configuration file, we can set them by passing them as arguments as below: ``` ../../xgboost mushroom.conf max_depth=6 ``` This means that the parameter max_depth will be set as 6 rather than 3 in the conf file. When you use command line, make sure max_depth=6 is passed in as single argument, i.e. do not contain space in the argument. When a parameter setting is provided in both command line input and the config file, the command line setting will override the setting in config file. In this example, we use tree booster for gradient boosting. If you would like to use linear booster for regression, you can keep all the parameters except booster and the tree booster parameters as below: ```conf # General Parameters # choose the linear booster booster = gblinear ... # Change Tree Booster Parameters into Linear Booster Parameters # L2 regularization term on weights, default 0 lambda = 0.01 # L1 regularization term on weights, default 0 alpha = 0.01 # L2 regularization term on bias, default 0 lambda_bias = 0.01 # Regression Parameters ... ``` #### Get Predictions After training, we can use the output model to get the prediction of the test data: ``` ../../xgboost mushroom.conf task=pred model_in=0002.model ``` For binary classification, the output predictions are probability confidence scores in [0,1], corresponds to the probability of the label to be positive. #### Dump Model This is a preliminary feature, so only tree models support text dump. XGBoost can display the tree models in text or JSON files, and we can scan the model in an easy way: ``` ../../xgboost mushroom.conf task=dump model_in=0002.model name_dump=dump.raw.txt ../../xgboost mushroom.conf task=dump model_in=0002.model fmap=featmap.txt name_dump=dump.nice.txt ``` In this demo, the tree boosters obtained will be printed in dump.raw.txt and dump.nice.txt, and the latter one is easier to understand because of usage of feature mapping featmap.txt Format of ```featmap.txt: \n ```: - Feature id must be from 0 to number of features, in sorted order. - i means this feature is binary indicator feature - q means this feature is a quantitative value, such as age, time, can be missing - int means this feature is integer value (when int is hinted, the decision boundary will be integer) #### Monitoring Progress When you run training we can find there are messages displayed on screen ``` tree train end, 1 roots, 12 extra nodes, 0 pruned nodes ,max_depth=3 [0] test-error:0.016139 boosting round 1, 0 sec elapsed tree train end, 1 roots, 10 extra nodes, 0 pruned nodes ,max_depth=3 [1] test-error:0.000000 ``` The messages for evaluation are printed into stderr, so if you want only to log the evaluation progress, simply type ``` ../../xgboost mushroom.conf 2>log.txt ``` Then you can find the following content in log.txt ``` [0] test-error:0.016139 [1] test-error:0.000000 ``` We can also monitor both training and test statistics, by adding following lines to configure ```conf eval[test] = "agaricus.txt.test" eval[trainname] = "agaricus.txt.train" ``` Run the command again, we can find the log file becomes ``` [0] test-error:0.016139 trainname-error:0.014433 [1] test-error:0.000000 trainname-error:0.001228 ``` The rule is eval[name-printed-in-log] = filename, then the file will be added to monitoring process, and evaluated each round. xgboost also supports monitoring multiple metrics, suppose we also want to monitor average log-likelihood of each prediction during training, simply add ```eval_metric=logloss``` to configure. Run again, we can find the log file becomes ``` [0] test-error:0.016139 test-negllik:0.029795 trainname-error:0.014433 trainname-negllik:0.027023 [1] test-error:0.000000 test-negllik:0.000000 trainname-error:0.001228 trainname-negllik:0.002457 ``` ### Saving Progress Models If you want to save model every two round, simply set save_period=2. You will find 0002.model in the current folder. If you want to change the output folder of models, add model_dir=foldername. By default xgboost saves the model of last round. #### Continue from Existing Model If you want to continue boosting from existing model, say 0002.model, use ``` ../../xgboost mushroom.conf model_in=0002.model num_round=2 model_out=continue.model ``` xgboost will load from 0002.model continue boosting for 2 rounds, and save output to continue.model. However, beware that the training and evaluation data specified in mushroom.conf should not change when you use this function. #### Use Multi-Threading When you are working with a large dataset, you may want to take advantage of parallelism. If your compiler supports OpenMP, xgboost is naturally multi-threaded, to set number of parallel running add ```nthread``` parameter to your configuration. Eg. ```nthread=10``` Set nthread to be the number of your real cpu (On Unix, this can be found using ```lscpu```) Some systems will have ```Thread(s) per core = 2```, for example, a 4 core cpu with 8 threads, in such case set ```nthread=4``` and not 8. xgboost-1.5.2/demo/CLI/binary_classification/agaricus-lepiota.data000066400000000000000000013317101417122711700251730ustar00rootroot00000000000000p,x,s,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,s,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,b,s,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,m p,x,y,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,s,g,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,y,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,g e,b,s,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,m e,b,y,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,m p,x,y,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,g e,b,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,y,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,y,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,s,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,g 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e,b,s,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,y,n,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,y,p e,b,y,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,m e,s,f,n,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,y,n,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,y,p e,x,y,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,f,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,f,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,m e,b,s,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,g e,b,y,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,y,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,s,n,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,y,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,g e,s,f,n,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,s,w,t,a,f,w,n,w,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,y,n,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,s,g e,b,y,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,b,y,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,g e,b,s,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,y,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,f,n,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,y,u e,f,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,y,g e,x,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g e,f,y,y,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,y,p e,b,s,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,g e,b,s,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,y,n,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,y,g e,b,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,f,g,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,n,y,u e,b,s,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,f,y,t,l,f,w,n,n,t,b,s,s,w,w,p,w,o,p,u,v,d e,b,y,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,y,y,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,s,g e,b,y,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,m e,b,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,m e,b,y,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,y,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,m e,b,s,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,g p,x,y,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,u e,s,f,n,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,n,y,u e,f,f,n,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,m e,f,y,n,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,s,p p,x,y,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,g e,b,s,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,m e,f,f,g,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,u e,b,y,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,y,n,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,y,p e,x,f,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,s,w,t,l,f,w,n,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,b,s,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,m e,f,s,y,t,a,f,w,n,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,s,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,f,g,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,n,y,u e,b,s,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,s,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,y,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,m e,f,s,w,t,a,f,w,n,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,g e,b,s,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,s,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,f,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,s,g e,f,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,y,p p,x,s,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,u e,b,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,g e,b,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,y,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,g e,b,y,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,s,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,g e,b,s,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,f,y,t,a,f,w,n,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,f,g,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,y,u e,f,y,y,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,s,g e,b,s,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,y,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,y,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,g e,s,f,g,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,m p,x,s,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,g e,x,y,y,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,s,g e,f,f,w,t,a,f,w,n,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,m e,b,y,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,s,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,g p,x,y,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,u e,b,s,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,f,g,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,y,u p,x,y,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,y,y,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,y,p e,f,f,n,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,u e,b,s,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,f,w,t,l,f,w,n,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,g e,b,y,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,y,y,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,g e,f,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,s,p e,f,y,y,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,y,p e,x,s,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,s,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,m p,x,s,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,f,w,t,a,f,w,n,p,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,s,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,s,w,t,l,f,w,n,p,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,y,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,m e,f,y,y,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,y,p e,x,s,n,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,s,g e,f,y,y,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,y,g p,x,s,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,g e,s,f,n,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,n,v,u e,b,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,m e,b,s,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,g e,b,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,f,n,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,s,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,m e,b,y,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g e,b,y,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,y,n,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,s,g p,x,y,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,g e,x,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,y,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,m e,f,f,w,t,l,f,w,n,w,t,b,s,s,w,w,p,w,o,p,u,v,d e,f,f,g,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,s,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,y,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,m e,b,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,m p,f,y,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,s,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,m p,f,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,y,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,y,y,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,s,p e,x,y,n,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,s,p e,f,y,n,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,y,g e,x,y,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,f,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,s,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,m p,x,y,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,s,g e,b,y,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,m e,s,f,n,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,s,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,y,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,m e,f,y,n,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,g e,b,y,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,y,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,y,p e,f,f,g,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,y,u e,x,f,g,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,k,y,u e,b,y,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,s,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,s,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,s,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,f,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,s,y,t,a,f,w,n,p,t,b,s,s,w,w,p,w,o,p,n,v,d p,x,y,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,g e,x,f,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,a,g e,b,y,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,s,y,t,l,f,w,n,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,b,y,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,y,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,y,d e,b,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,s,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,y,n,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,y,g e,x,f,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,s,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,g p,x,y,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,y,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,f,w,t,a,f,w,n,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,b,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,g p,x,y,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,s,y,t,a,f,w,n,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,f,w,t,l,f,w,n,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,s,w,t,l,f,w,n,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,m e,f,f,y,t,a,f,w,n,w,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,s,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,g e,b,y,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,y,n,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,s,p e,b,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,s,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,m p,x,y,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,u e,b,s,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,g e,b,y,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g p,x,y,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,u e,b,s,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,m e,b,y,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,y,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,y,n,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,y,g e,b,s,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,f,g,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,y,g e,x,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g e,b,y,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,m e,f,f,y,t,a,f,w,n,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,b,y,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,f,n,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,f,y,t,l,f,w,n,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,s,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,s,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,f,n,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,n,y,u e,f,s,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,y,n,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,s,p e,b,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g e,b,s,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,y,y,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,s,p e,s,f,g,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,y,n,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,y,p p,x,y,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,y,p e,x,y,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,f,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,f,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,a,g e,f,s,n,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,a,g e,f,y,n,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,s,p e,x,s,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,g e,f,f,n,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,y,y,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,s,p e,x,f,y,t,a,f,w,n,p,t,b,s,s,w,w,p,w,o,p,u,v,d e,b,y,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,f,g,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,y,y,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,s,g e,f,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,y,g e,x,s,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,m e,s,f,n,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,y,u e,x,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,s,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,g e,s,f,n,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,y,u e,b,y,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,y,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,b,y,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g p,x,y,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,s,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,y,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,s,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,y,d p,x,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,s,u e,x,y,n,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,y,p e,x,s,n,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,a,g e,b,y,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,s,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,m e,b,s,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,s,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,m e,b,y,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,f,g,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,y,n,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,s,g e,x,f,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,s,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,f,g,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,u p,x,s,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,u e,b,y,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,g e,b,y,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,m p,x,y,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,u e,b,s,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,s,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,y,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,y,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,s,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,s,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,y,n,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,y,p e,x,s,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,s,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,s,p e,x,y,y,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,y,g p,x,y,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,g e,b,y,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,f,w,t,l,f,w,n,p,t,b,s,s,w,w,p,w,o,p,u,v,d p,x,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,y,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,g e,f,f,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,y,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,g e,b,y,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,m p,x,y,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,u e,f,y,n,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,s,g e,x,s,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,s,w,t,a,f,w,n,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,n,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,y,p e,b,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,s,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,a,g e,f,f,g,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,y,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,y,y,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,y,g e,b,s,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,g e,b,s,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,s,w,t,l,f,w,n,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,b,s,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,f,y,t,a,f,w,n,n,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,y,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,m e,b,y,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,y,n,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,y,p e,x,y,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,y,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,y,p e,x,y,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,s,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,y,n,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,s,g e,x,s,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,g e,f,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,g e,b,s,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,f,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,m e,b,s,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g e,b,s,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,f,y,t,l,f,w,n,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,b,s,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,s,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,a,g e,b,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,b,s,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,m e,f,y,y,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,y,p e,f,y,n,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,y,p e,x,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,m e,f,y,y,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,s,g e,b,s,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,y,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,f,n,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,y,n,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,y,g e,x,s,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,s,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g e,b,y,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g e,f,y,y,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,s,p e,x,y,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,y,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,m e,f,f,w,t,a,f,w,n,n,t,b,s,s,w,w,p,w,o,p,u,v,d e,s,f,g,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,y,u e,f,s,y,t,l,f,w,n,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,g,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,y,u e,x,f,n,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,y,u e,b,y,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,s,w,t,a,f,w,n,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,b,y,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,y,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,y,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,s,w,t,l,f,w,n,p,t,b,s,s,w,w,p,w,o,p,u,v,d e,f,f,g,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,k,y,u e,f,s,w,t,a,f,w,n,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,y,g e,x,y,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,m e,s,f,n,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,y,u e,x,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,p e,x,y,n,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,p e,f,f,y,t,a,f,w,n,n,t,b,s,s,w,w,p,w,o,p,u,v,d p,f,s,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,g p,x,s,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,y,n,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,s,p e,x,y,y,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,s,g e,b,s,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,f,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,y,n,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,s,g e,x,y,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,g e,b,s,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,s,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,g e,b,y,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,s,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,m e,b,s,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,y,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,g p,x,s,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,s,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,s,n,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,f,w,t,a,f,w,n,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,g,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,f,n,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,y,u e,b,y,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,f,w,t,a,f,w,n,n,t,b,s,s,w,w,p,w,o,p,u,v,d e,s,f,g,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,f,n,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,f,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,y,p e,b,s,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,y,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,s,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,m e,b,s,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,y,p p,x,s,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,s,u e,f,f,g,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,y,u e,b,s,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,g e,f,y,n,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,s,p e,x,s,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,f,n,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,y,u e,f,y,y,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,y,p e,x,y,n,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,y,p e,x,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,g p,x,y,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,s,g e,f,y,n,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,y,p p,f,s,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,g e,x,f,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,s,g e,b,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,m e,s,f,n,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,y,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,m e,f,s,w,t,a,f,w,n,p,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,s,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,m e,f,f,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,s,g p,x,y,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,s,g e,x,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,s,g e,f,f,n,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,s,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,y,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,m e,f,f,g,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,f,y,t,l,f,w,n,p,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,f,n,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,y,u e,x,f,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,y,y,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,s,p e,f,s,w,t,l,f,w,n,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,s,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,y,p p,x,y,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,f,w,t,l,f,w,n,w,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,s,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,y,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,m e,b,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,s,y,t,a,f,w,n,w,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,s,y,t,a,f,w,n,n,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,f,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,s,g e,b,s,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,m p,x,y,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,g e,x,y,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,g e,f,s,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,s,g p,x,s,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,s,g e,b,y,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,m e,f,f,y,t,l,f,w,n,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,s,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,g e,b,y,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,y,n,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,y,g e,x,s,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,f,n,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,s,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,y,y,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,y,g p,x,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,s,g e,x,s,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,s,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,y,y,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,y,g e,f,y,y,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,s,g e,x,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,m e,s,f,g,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,f,n,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,y,u e,s,f,g,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,y,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,m p,x,s,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,s,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,y,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,g p,x,y,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,s,g e,x,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,m p,x,s,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,u e,b,s,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,m e,b,y,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,m p,x,y,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,g p,x,s,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,s,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,y,n,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,y,g e,f,f,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,s,p e,b,y,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,s,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,s,g e,f,y,n,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,y,g e,x,s,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,m e,f,f,g,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,s,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,f,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,s,g e,f,s,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,a,g p,x,s,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,s,u e,x,y,y,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,s,g e,b,s,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,f,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,a,g e,b,y,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,g e,b,s,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,m e,s,f,g,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,y,u e,f,y,y,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,s,g e,b,s,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,f,w,t,l,f,w,n,n,t,b,s,s,w,w,p,w,o,p,u,v,d e,f,y,y,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,p e,f,f,g,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,y,u e,x,s,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,m e,f,f,y,t,l,f,w,n,w,t,b,s,s,w,w,p,w,o,p,u,v,d e,s,f,g,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,y,u e,b,y,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,g e,b,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,g e,f,f,n,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,s,g e,b,y,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,f,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,g e,x,y,n,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,s,g e,b,y,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,m e,f,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,s,g e,x,y,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,s,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,y,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,y,n,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,y,g e,f,y,n,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,s,p e,f,y,n,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,y,g e,f,y,y,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,p e,x,s,y,t,l,f,w,n,n,t,b,s,s,w,w,p,w,o,p,u,v,d e,b,y,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,m e,b,s,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,y,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,f,w,t,l,f,w,n,p,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,s,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,g e,b,s,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,y,y,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,y,g p,x,y,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,s,g p,x,y,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,s,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,g e,f,f,w,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,s,g e,b,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,y,y,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,y,p e,f,f,g,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,y,u e,b,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,s,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,m p,x,y,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,s,g p,x,s,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,s,g e,b,s,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,g e,b,s,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,y,n,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,s,g e,x,y,y,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,y,g e,f,y,y,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,y,p e,x,y,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,s,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,f,n,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,f,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,f,y,t,l,f,w,n,w,t,b,s,s,w,w,p,w,o,p,u,v,d e,f,y,y,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,s,p e,f,f,n,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,k,y,u e,f,f,g,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,y,g e,x,y,y,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,y,p e,b,s,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,s,w,t,l,f,w,n,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,f,y,t,a,f,w,n,w,t,b,s,s,w,w,p,w,o,p,u,v,d e,b,s,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,y,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,m e,f,f,g,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,u e,b,y,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,g e,b,s,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,g e,b,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,y,n,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,s,p e,f,s,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,a,g p,x,y,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,g e,b,y,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,g e,b,s,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,m p,x,y,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,g p,x,s,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,s,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,a,g p,x,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,s,g e,f,f,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,y,y,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,p e,b,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,m e,f,y,y,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,s,p e,f,y,y,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,y,p e,b,y,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,m e,s,f,n,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,y,u e,x,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,m e,b,y,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,m e,f,y,y,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,s,p e,f,s,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,s,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,m e,b,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,g e,b,y,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,g e,b,y,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,m e,b,s,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,y,y,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,p e,x,y,n,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,s,g e,s,f,n,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,y,n,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,s,g e,x,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,g e,f,s,y,t,l,f,w,n,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,s,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,a,g e,f,y,y,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,g p,x,y,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,s,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,f,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,s,g e,b,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,y,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,m e,f,y,y,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,y,g e,x,f,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,s,g p,x,s,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,s,g p,x,y,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,y,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g e,b,y,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,f,w,t,a,f,w,n,w,t,b,s,s,w,w,p,w,o,p,n,v,d p,x,y,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,s,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,f,g,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,f,n,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,u e,b,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,y,n,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,s,g e,b,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,y,y,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,s,p e,x,y,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,g e,b,y,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,g e,b,y,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,m p,x,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,s,y,t,a,f,w,n,n,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,y,n,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,s,p e,b,s,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,f,s,w,t,a,f,w,n,n,t,b,s,s,w,w,p,w,o,p,u,v,d e,b,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,g e,b,y,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,m e,b,s,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,g e,f,y,y,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,y,g e,x,s,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,a,g e,b,y,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,y,n,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,y,p e,b,s,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,g e,f,y,n,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,y,g e,x,s,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,f,n,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,y,n,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,s,p e,f,f,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,s,w,t,l,f,w,n,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,n,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,n,y,u e,b,y,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,m e,b,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,s,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,g e,b,s,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,y,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,s,y,t,a,f,w,n,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,s,g p,x,y,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,s,u e,x,y,n,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,y,g e,x,s,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,g e,b,y,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,y,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,m e,s,f,n,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,k,y,u e,b,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,s,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,s,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,g p,x,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,g e,x,f,n,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,g p,x,y,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,s,g e,x,y,y,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,y,p e,b,y,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g e,f,y,n,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,y,p e,x,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,s,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,g p,x,y,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,g p,x,y,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,s,u e,b,y,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,s,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,s,g p,x,s,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,y,n,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,s,p e,b,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,y,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,g p,x,s,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,u e,b,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,g e,b,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,f,y,y,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,s,g e,b,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,y,g e,b,s,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,s,y,t,l,f,w,n,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,b,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,m e,b,s,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,m p,x,y,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,u p,x,y,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,v,g p,x,s,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,y,n,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,y,g e,x,y,y,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,y,g e,x,s,w,t,a,f,w,n,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,b,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,b,s,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,f,g,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,u e,b,s,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,s,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,y,n,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,s,p e,x,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,m e,f,f,w,t,l,f,w,n,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,w,t,a,f,w,n,w,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,s,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,m e,f,s,y,t,l,f,w,n,p,t,b,s,s,w,w,p,w,o,p,u,v,d e,s,f,g,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,f,y,t,a,f,w,n,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,n,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,y,g e,x,y,y,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,s,g e,x,y,y,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,y,p p,x,s,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,s,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,m p,x,y,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,u e,x,y,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,y,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,s,y,t,a,f,w,n,w,t,b,s,s,w,w,p,w,o,p,u,v,d p,x,y,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,v,g e,b,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,g e,s,f,g,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,y,u e,x,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,f,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,y,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,m e,b,y,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,g e,b,s,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,s,w,t,l,f,w,n,w,t,b,s,s,w,w,p,w,o,p,u,v,d e,b,s,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g e,f,y,n,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,s,g e,s,f,g,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,n,y,u e,x,f,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,a,g e,s,f,n,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,y,n,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,s,p e,f,s,y,t,l,f,w,n,n,t,b,s,s,w,w,p,w,o,p,u,v,d e,b,s,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,g e,b,s,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,m p,x,s,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,g e,f,y,n,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,y,p e,x,s,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,g e,f,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,s,g e,x,y,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,y,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,y,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,f,n,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,y,y,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,y,p e,x,f,g,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,y,u e,x,s,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,f,y,n,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,y,p e,x,s,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,y,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,f,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,y,y,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,s,p e,x,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,s,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,g e,f,y,y,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,y,g e,b,s,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,g e,f,f,w,t,a,f,w,n,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,s,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,y,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,y,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,g e,f,y,y,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,g e,x,s,w,t,a,f,w,n,p,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,s,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,g e,f,y,y,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,y,g e,x,y,y,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,y,p e,x,s,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,f,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,y,y,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,y,g e,x,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,g e,b,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,s,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,y,n,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,s,g e,b,y,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,s,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,s,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,y,y,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,y,p e,x,f,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,s,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,s,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,s,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,f,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,s,g p,f,s,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,s,g e,x,f,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,s,g p,f,y,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,u p,x,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,v,g e,b,s,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,f,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,s,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g e,f,f,g,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,s,g,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,s,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,y,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,f,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,s,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,f,n,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,s,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,y,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,s,y,t,l,f,w,n,w,t,b,s,s,w,w,p,w,o,p,u,v,d e,f,f,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,s,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,s,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,a,g p,x,y,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,f,g,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,y,u e,b,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,s,g,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,a,g e,f,f,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,s,g p,f,s,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,s,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,f,n,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,y,u e,f,s,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,y,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,f,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,s,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,y,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,y,d e,b,y,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,f,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,s,g p,x,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,s,g e,x,f,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,f,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,f,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,f,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,s,g e,b,y,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,f,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,a,g p,f,y,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,v,u p,x,y,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,s,u e,b,s,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,s,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,f,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,s,g e,b,s,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,m p,x,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,y,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,f,w,t,l,f,w,n,n,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,y,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,f,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,a,g e,f,f,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,s,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,s,g,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,s,g p,f,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,s,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,s,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,f,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,f,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,f,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,f,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,s,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,s,g e,b,y,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,y,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g e,f,f,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,a,g e,f,f,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,s,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,m e,f,f,g,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,f,n,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,s,g p,x,s,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,f,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,f,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,s,w,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,s,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,y,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,s,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,s,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,s,n,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,s,g e,f,f,n,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,s,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,s,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,y,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,m e,f,s,w,t,a,f,w,n,w,t,b,s,s,w,w,p,w,o,p,u,v,d e,b,s,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,m p,f,y,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,f,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,y,n,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,y,g e,f,s,n,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,s,g p,x,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,g e,x,y,n,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,y,g e,x,s,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,s,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,f,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,f,n,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,s,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,y,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,s,w,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,s,p e,f,s,n,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,f,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,f,y,t,a,f,w,n,p,t,b,s,s,w,w,p,w,o,p,u,v,d e,f,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,s,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,y,d p,f,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,s,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,f,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,a,g e,b,s,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,m e,b,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,y,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,m p,f,y,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,u p,f,y,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,g e,x,f,n,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,s,y,t,l,f,w,n,w,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,y,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,s,w,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,f,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,y,d p,x,y,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,g e,x,f,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,s,g e,f,f,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,s,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,f,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,y,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,m e,f,f,y,t,a,f,w,n,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,f,g,f,n,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,y,u p,x,s,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,y,y,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,y,p e,f,y,n,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,p e,x,f,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,y,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,s,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,s,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,f,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,s,g p,f,y,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,s,u e,x,f,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,f,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,f,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,f,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,y,y,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,s,p e,x,f,n,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,s,g e,b,s,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,f,w,t,l,f,w,n,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,s,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,f,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,s,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,s,y,t,l,f,w,n,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,s,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,f,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,s,g p,f,y,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,u e,f,f,y,t,l,f,w,n,p,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,f,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,f,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,s,g e,x,s,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,a,g p,f,y,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,s,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,f,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,y,y,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,s,p e,f,s,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,a,g e,f,f,n,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,y,u p,f,y,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,g e,f,f,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,y,n,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,s,p e,f,f,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,a,g p,f,y,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,u e,b,s,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,m e,f,f,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,s,g e,b,s,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,g e,f,f,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,s,g e,b,y,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,y,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,m p,f,y,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,g e,x,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,g e,s,f,n,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,y,u e,x,y,n,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,y,g e,f,f,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,f,y,t,l,f,w,n,n,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,s,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,a,g p,f,y,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,f,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,s,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,f,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,s,g p,x,y,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,s,g e,x,f,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,s,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,f,g,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,s,g p,x,y,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,s,g e,f,f,n,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,s,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,a,g p,x,y,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,f,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,a,g e,b,y,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,s,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,a,g p,f,s,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,s,g e,x,y,n,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,s,g e,f,f,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,a,g e,f,y,n,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,s,g e,f,f,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,f,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,s,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,f,n,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,s,g,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,f,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,s,g e,f,f,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,s,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,s,y,t,a,f,w,n,p,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,f,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,s,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,a,g e,b,s,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,f,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,f,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,a,g p,f,s,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,f,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,a,g p,x,s,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,g e,f,s,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,y,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,f,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,y,d e,b,y,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,g e,f,f,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,s,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,f,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,v,d e,f,f,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,s,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,s,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,f,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,s,g e,f,s,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,f,g,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,f,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,a,g e,f,s,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,a,g e,f,s,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,a,g e,f,y,n,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,y,p p,x,y,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,g e,f,s,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,a,g p,x,y,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,g e,b,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,s,g,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,f,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,f,w,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,s,g e,f,s,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,s,g e,b,y,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,f,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,f,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,s,p e,x,s,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,s,g e,b,s,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,m p,x,s,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,s,n,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,s,g e,b,s,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,s,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,f,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,f,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,f,n,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,f,g,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,f,g,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,y,u e,b,y,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,m e,f,f,n,f,n,f,c,n,g,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,f,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,y,n,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,s,p e,x,y,n,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,y,p e,x,y,y,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,k,y,g e,f,f,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,y,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,y,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,s,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,s,g,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,a,g p,f,s,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,y,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,f,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,f,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,s,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,f,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,y,n,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,s,p e,b,s,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g p,x,s,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,g e,x,f,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,s,g e,b,y,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,s,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,b,y,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,y,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,s,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,g e,b,s,w,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,g e,f,s,n,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,s,g p,f,s,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,s,g e,f,s,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,a,g p,f,y,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,u e,f,s,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,f,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,s,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,s,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,a,g e,f,y,y,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,y,g e,x,f,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,f,n,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,a,g p,f,s,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,s,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,s,g e,f,f,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,f,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,y,y,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,g e,x,s,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,f,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,s,n,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,f,w,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,y,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,f,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,a,g p,x,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,y,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,f,n,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,s,g p,f,y,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,s,g e,f,f,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,f,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,s,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,f,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,s,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,a,g e,f,f,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,s,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,s,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,s,g p,f,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,s,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,a,g p,x,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,g p,f,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,s,u e,f,s,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,f,g,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,a,g e,f,s,g,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,s,g,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,a,g e,f,f,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,a,g e,f,f,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,y,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,f,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,s,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,a,g p,f,y,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,g p,f,y,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,s,g e,x,s,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,a,g p,f,s,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,s,g e,f,f,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,s,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,a,g p,f,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,g p,f,y,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,g p,f,y,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,g p,f,s,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,g e,x,s,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,s,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,f,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,a,g p,f,y,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,s,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,y,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,s,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,s,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,s,g p,f,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,g e,f,f,n,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,f,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,s,g p,f,s,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,f,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,f,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,s,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,s,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,s,g e,b,y,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,s,g,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,f,w,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,s,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,f,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,a,g e,f,f,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,a,g p,x,y,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,s,u e,f,s,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,s,w,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,f,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,f,w,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,a,g p,f,s,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,g p,f,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,g e,x,s,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,f,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,s,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,y,y,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,s,p e,f,s,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,s,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,f,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,a,g e,f,s,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,s,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,s,g,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,f,n,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,s,g e,f,s,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,s,g e,f,s,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,a,g e,f,s,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,f,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,s,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,a,g p,f,s,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,s,g e,x,f,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,a,g e,b,y,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,g e,f,f,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,s,g,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,y,d e,b,s,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,s,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,f,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,y,d p,x,s,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,s,g e,f,f,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,s,g p,f,y,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,s,u e,x,s,n,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,s,n,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,a,g e,b,s,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g e,f,s,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,s,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,f,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,f,g,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,s,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,a,g p,f,s,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,g e,f,f,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,s,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,s,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,f,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,y,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,g e,f,f,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,s,w,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,f,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,a,g p,f,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,s,u e,f,f,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,y,d e,f,s,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,f,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,a,g p,f,y,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,s,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,s,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,s,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,s,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,s,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,a,g e,f,f,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,f,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,f,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,a,g e,f,f,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,s,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,s,g e,f,f,n,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,a,g p,f,y,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,f,w,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,a,g e,f,s,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,f,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,f,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,f,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,s,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,f,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,f,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,s,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,f,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,s,g e,b,s,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,g p,x,y,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,g p,f,s,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,g e,f,f,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,f,n,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,s,g p,f,y,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,g e,f,f,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,s,g p,x,s,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,s,n,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,a,g p,f,y,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,s,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,a,g e,f,s,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,f,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,f,n,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,f,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,f,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,s,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,s,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,s,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,s,g e,f,f,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,s,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,s,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,s,g e,f,s,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,s,g p,f,y,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,s,g e,f,s,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,y,g e,x,f,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,s,g,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,s,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,a,g p,f,y,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,u e,x,s,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,s,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,a,g e,f,s,g,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,a,g e,f,s,n,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,f,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,s,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,s,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,f,w,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,f,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,y,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,s,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,s,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,s,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,a,g p,x,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,s,u e,x,s,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,f,g,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,s,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,f,n,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,a,g e,f,s,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,s,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,p p,f,y,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,s,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,v,d p,f,y,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,s,g p,x,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,u p,f,s,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,u e,x,f,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,y,d e,b,y,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,m p,f,y,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,g e,f,f,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,s,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,s,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,a,g e,f,f,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,f,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,s,g p,f,y,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,u p,f,y,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,g e,x,s,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,f,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,s,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,s,g e,f,f,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,a,g p,f,s,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,f,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,a,g p,f,y,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,s,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,a,g e,f,f,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,s,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,s,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,s,g p,f,s,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,s,u e,x,f,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,s,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,s,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,s,w,t,a,f,w,n,n,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,f,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,y,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,s,y,t,a,f,w,n,p,t,b,s,s,w,w,p,w,o,p,u,v,d e,f,f,g,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,s,n,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,y,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,s,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,a,g p,f,s,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,f,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,f,g,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,s,g e,f,s,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,f,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,a,g p,f,y,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,g e,x,f,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,s,g e,f,s,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,s,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,f,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,s,n,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,a,g e,f,y,y,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,y,g p,x,y,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,f,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,s,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,s,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,s,g p,f,y,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,g e,f,f,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,s,g p,f,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,u e,f,s,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,s,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,f,g,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,a,g e,f,f,n,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,s,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,s,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,f,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,f,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,f,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,a,g e,b,y,y,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,m e,f,f,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,f,g,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,a,g e,f,f,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,y,d p,f,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,f,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,f,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,f,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,s,g,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,s,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,y,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,f,w,t,a,f,w,n,p,t,b,s,s,w,w,p,w,o,p,u,v,d e,f,f,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,s,g e,b,y,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,g e,x,f,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,y,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,g e,f,s,w,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,s,w,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,f,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,s,n,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,s,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,y,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,s,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,y,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,s,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,a,g p,f,y,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,s,u e,f,s,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,s,g p,f,s,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,s,u e,f,s,g,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,f,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,s,g p,x,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,g e,x,s,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,a,g p,x,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,s,u e,x,s,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,s,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,s,g p,f,y,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,f,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,s,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,f,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,f,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,y,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,y,d p,f,s,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,u e,f,f,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,y,y,t,a,f,c,b,w,e,r,s,y,w,w,p,w,o,p,k,y,g e,x,f,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,a,g e,b,s,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,m e,f,s,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,f,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,a,g e,f,f,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,a,g p,f,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,s,u e,x,s,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,a,g e,b,y,y,t,a,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,g e,f,s,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,s,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,f,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,s,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,f,n,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,v,d e,b,y,w,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,m e,x,f,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,v,d p,f,y,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,g e,x,s,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,a,g p,f,s,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,s,n,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,f,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,f,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,s,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,s,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,s,g e,f,s,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,s,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,s,g p,x,y,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,g e,f,f,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,a,g p,f,y,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,s,g e,f,f,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,f,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,s,g p,f,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,s,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,s,g p,x,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,f,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,f,n,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,y,y,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,s,p e,f,f,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,s,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,f,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,s,g e,f,f,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,f,w,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,f,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,f,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,f,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,s,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,a,g e,f,s,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,y,n,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,s,g e,x,y,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,y,d e,f,s,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,a,g e,f,f,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,s,g e,f,s,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,f,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,f,n,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,s,g,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,s,n,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,y,d e,x,s,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,f,n,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,a,g e,f,s,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,f,n,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,y,u p,f,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,u p,f,s,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,f,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,s,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,f,g,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,s,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,f,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,s,g,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,f,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,a,g e,f,s,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,s,g e,f,s,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,f,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,v,d p,f,y,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,f,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,v,d p,f,s,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,s,u p,f,s,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,g p,f,s,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,s,u e,f,f,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,s,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,s,g e,f,f,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,s,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,s,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,a,g p,f,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,g p,f,s,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,g e,f,s,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,s,n,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,s,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,f,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,a,g e,f,f,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,f,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,s,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,s,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,s,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,f,n,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,f,n,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,s,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,s,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,s,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,s,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,s,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,s,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,a,g e,f,f,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,f,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,f,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,a,g e,f,f,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,f,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,y,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,s,y,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,s,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,a,g p,x,y,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,g e,x,f,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,s,g p,x,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,y,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,v,d p,f,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,y,y,t,l,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,y,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,y,n,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,y,p e,x,s,w,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,s,g e,f,s,n,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,s,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,s,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,a,g e,f,s,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,s,n,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,s,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,s,g e,b,s,w,t,l,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,n,g e,x,s,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,s,y,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,s,m p,f,y,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,g e,f,s,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,s,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,s,g,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,f,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,y,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,f,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,y,y,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,y,p e,x,f,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,f,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,s,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,s,g e,f,s,w,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,f,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,s,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,f,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,f,g,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,s,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,f,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,s,w,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,f,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,s,g p,f,y,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,s,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,f,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,f,w,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,s,g p,f,y,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,f,g,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,f,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,f,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,f,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,f,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,s,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,f,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,f,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,y,w,t,l,f,c,b,w,e,c,s,s,w,w,p,w,o,p,k,n,g e,x,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,m e,f,s,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,s,g e,f,s,w,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,a,g e,f,s,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,s,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,f,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,s,n,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,s,g e,b,y,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,n,m p,f,y,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,g e,x,s,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,s,n,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,y,n,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,k,s,g e,x,s,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,s,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,a,g p,x,s,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,s,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,f,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,s,g p,f,s,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,g e,x,f,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,s,n,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,f,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,v,d e,f,s,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,s,g p,f,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,f,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,f,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,s,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,f,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,a,g e,f,y,n,t,l,f,c,b,w,e,r,s,y,w,w,p,w,o,p,n,y,g p,f,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,s,g e,x,f,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,y,u p,f,y,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,s,u e,f,s,w,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,f,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,y,y,t,a,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,y,p e,x,f,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,f,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,a,g p,f,y,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,s,g e,f,f,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,s,g e,f,f,g,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,f,n,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,s,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,s,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,f,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,f,g,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,s,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,s,g p,x,s,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,s,u e,f,s,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,s,n,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,y,g e,x,s,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,f,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,f,w,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,y,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,f,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,f,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,a,g p,f,s,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,s,u p,f,s,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,s,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,f,g,f,n,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,s,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,s,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,a,g p,f,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,s,g e,b,s,y,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,f,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,a,g p,f,y,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,s,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,s,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,s,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,s,g p,f,s,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,s,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,f,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,f,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,a,g p,f,y,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,g e,x,f,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,s,g e,f,s,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,a,g p,f,y,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,s,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,y,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,f,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,f,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,s,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,f,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,f,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,s,g p,f,s,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,s,g e,f,f,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,v,d p,x,s,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,g e,x,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,s,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,y,y,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,g p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,g e,f,s,n,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,s,w,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,s,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,f,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,s,g p,x,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,f,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,n,g e,f,f,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,y,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,f,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,s,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,y,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,s,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,f,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,f,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,y,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,s,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,f,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,a,g e,f,f,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,y,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,v,d p,f,y,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,s,u e,x,y,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,f,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,s,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,y,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,s,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,f,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,f,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,f,y,t,a,f,w,n,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,v,d p,f,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,s,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,f,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,f,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,f,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,s,g,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,y,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,s,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,s,n,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,s,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,s,n,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,f,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,f,w,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,f,g,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,y,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,s,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,s,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,s,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,f,w,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,f,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,v,d e,f,f,w,t,l,f,w,n,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,a,g p,f,y,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,s,g e,f,f,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,s,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,f,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,s,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,f,n,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,s,g,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,y,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,s,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,s,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,s,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,s,g e,f,f,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,s,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,a,g e,f,s,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,f,g,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,f,n,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,a,g e,f,f,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,f,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,v,d e,f,s,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,s,w,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,y,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,g,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,f,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,y,y,t,l,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,y,g p,f,y,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,s,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,a,g e,f,f,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,f,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,f,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,f,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,f,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,y,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,f,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,f,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,s,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,s,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,s,g p,f,y,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,s,u e,b,s,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,n,s,g e,x,f,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,f,g,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,f,n,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,s,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,s,g e,f,s,w,t,l,f,w,n,n,t,b,s,s,w,w,p,w,o,p,u,v,d e,x,f,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,s,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,s,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,y,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,w,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,s,n,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,s,g p,f,s,w,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,f,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,y,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,f,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,f,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,v,d p,x,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,v,g e,x,f,n,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,y,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,y,d p,f,y,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,s,g e,x,f,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,f,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,f,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,f,n,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,s,g e,f,s,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,a,g e,f,s,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,y,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,s,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,s,g e,f,f,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,s,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,f,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,a,g e,f,f,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,s,g p,x,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,u e,x,f,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,s,n,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,s,g p,f,y,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,s,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,f,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,f,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,f,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,f,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,s,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,y,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,s,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,a,g p,f,y,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,s,u e,x,f,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,v,d p,f,s,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,s,u p,f,y,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,f,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,s,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,f,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,f,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,f,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,s,n,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,s,g e,f,f,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,s,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,s,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,f,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,s,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,a,g e,x,f,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,y,d p,f,y,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,y,y,t,l,f,c,b,n,e,r,s,y,w,w,p,w,o,p,n,s,g p,f,s,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,g e,f,f,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,n,s,g e,f,f,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,a,g p,f,s,n,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,s,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,f,n,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,f,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,f,n,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,f,w,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,s,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,a,g e,f,f,w,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,s,g e,f,s,y,t,a,f,w,n,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,w,t,a,f,w,n,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,f,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,f,n,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,f,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,y,d e,x,f,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,f,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,a,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,s,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,a,g e,b,y,w,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,y,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,s,n,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,f,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,s,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,s,n,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,f,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,s,g,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,y,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,f,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,s,n,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,f,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,y,y,t,a,f,c,b,p,e,r,s,y,w,w,p,w,o,p,n,s,p e,x,f,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,f,n,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,s,g e,x,y,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,f,w,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,y,w,t,a,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,s,m e,x,s,n,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,s,w,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,a,g e,f,f,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,f,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,f,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,f,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,s,w,t,a,f,c,b,n,e,c,s,s,w,w,p,w,o,p,k,n,m e,f,s,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,s,g p,f,y,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,g e,f,f,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,f,w,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,y,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,v,d p,f,s,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,u e,f,s,g,f,n,f,w,b,p,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,f,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,y,d p,x,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,s,y,t,l,f,c,b,k,e,c,s,s,w,w,p,w,o,p,k,n,m e,x,f,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,y,d e,x,s,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,y,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,f,g,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,s,g e,f,s,w,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,v,d e,f,f,g,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,f,g,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,s,g e,f,f,n,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,f,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,y,d p,f,y,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,y,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,s,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,a,g e,b,s,w,t,a,f,c,b,g,e,c,s,s,w,w,p,w,o,p,n,s,m e,x,s,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,f,n,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,y,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,f,g,f,n,f,w,b,p,t,e,f,s,w,w,p,w,o,e,k,s,g p,x,s,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,s,g e,x,s,n,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,y,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,v,d p,x,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,f,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,g p,f,s,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,g e,x,f,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,f,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,y,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,v,d p,f,s,n,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,f,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,y,d p,x,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,s,g e,x,f,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,s,g,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,y,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,s,w,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,f,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,v,d p,x,s,p,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,n,s,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,f,w,f,n,f,w,b,k,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,y,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,y,d e,f,f,g,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,s,g p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,p e,x,f,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,y,d p,f,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,k,v,g e,f,y,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,f,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,a,g e,x,f,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,f,g,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,f,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,s,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,f,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,s,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,a,g e,x,y,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,v,d e,f,f,n,f,n,f,w,b,n,t,e,s,f,w,w,p,w,o,e,k,s,g e,f,f,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,y,d p,x,s,p,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,y,d p,f,s,n,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,y,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,s,w,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,y,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,f,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,f,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,n,s,g e,f,y,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,s,g,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,n,s,g e,f,f,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,y,d p,f,y,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,s,u e,x,y,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,s,w,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,y,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,y,d p,f,s,w,t,p,f,c,n,w,e,e,s,s,w,w,p,w,o,p,n,v,u e,x,f,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,s,w,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,s,g e,x,s,g,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,n,s,g e,x,f,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,f,n,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,k,a,g p,x,s,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,n,v,g e,x,y,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,y,d p,x,s,w,t,p,f,c,n,n,e,e,s,s,w,w,p,w,o,p,k,v,g e,f,f,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,f,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,v,d p,x,s,p,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,g e,x,y,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,f,g,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,n,a,g e,x,y,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,y,d p,f,y,n,t,p,f,c,n,k,e,e,s,s,w,w,p,w,o,p,k,s,u e,x,s,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,f,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,y,d p,x,s,p,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,n,s,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,s,w,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,n,s,g e,f,f,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,y,d p,f,y,w,t,p,f,c,n,p,e,e,s,s,w,w,p,w,o,p,n,v,u e,f,f,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,s,w,f,n,f,w,b,h,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,f,n,f,n,f,w,b,k,t,e,f,s,w,w,p,w,o,e,n,a,g e,x,f,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,v,d p,x,s,w,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,s,w,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,y,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,p e,f,f,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,d p,x,f,p,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,n,s,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,y,d p,x,f,w,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,g e,x,y,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,p e,x,f,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,p e,x,f,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,g,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,s,n,f,n,f,w,b,p,t,e,s,f,w,w,p,w,o,e,k,a,g e,f,f,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,f,w,f,n,f,w,b,h,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,y,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,v,d p,x,f,p,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,s,n,f,n,f,w,b,n,t,e,s,s,w,w,p,w,o,e,n,a,g e,x,y,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,g e,x,y,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,y,d e,x,s,g,f,n,f,w,b,h,t,e,f,s,w,w,p,w,o,e,k,s,g e,f,f,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,y,d p,x,f,g,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,s,g,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,y,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,v,d p,x,f,w,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,n,s,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,f,w,f,n,f,w,b,h,t,e,s,s,w,w,p,w,o,e,n,s,g e,x,f,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,f,n,f,n,f,w,b,n,t,e,f,f,w,w,p,w,o,e,k,s,g e,x,f,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,v,d p,x,f,p,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,v,d e,f,s,n,f,n,f,w,b,p,t,e,f,f,w,w,p,w,o,e,n,s,g e,x,y,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,y,d p,x,s,p,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,v,d e,x,s,w,f,n,f,w,b,k,t,e,s,f,w,w,p,w,o,e,k,s,g e,x,y,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,v,d p,x,s,g,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,f,n,f,n,f,w,b,k,t,e,s,s,w,w,p,w,o,e,k,a,g e,x,y,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,y,d p,x,f,w,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,p e,x,y,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,p e,x,f,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,f,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,p e,x,f,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,y,d e,x,f,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,f,g,f,n,f,w,b,n,t,e,f,s,w,w,p,w,o,e,n,s,g e,x,y,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,v,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,p e,f,y,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,d p,x,f,g,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,p e,f,f,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,y,d p,x,f,w,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,n,s,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,g p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,p e,f,y,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,v,d p,x,f,p,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,k,s,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,v,d p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,p e,f,y,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,v,d p,x,f,g,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,v,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,v,d p,x,s,p,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,v,d p,x,s,w,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,v,d p,x,s,g,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,f,p,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,d p,x,s,w,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,p e,f,y,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,v,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,p e,f,y,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,y,d p,x,s,w,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,p e,f,y,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,p e,f,y,n,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,y,d p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,p e,f,f,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,v,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,p e,f,y,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,p e,f,f,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,g e,f,y,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,g p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,p p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,g e,f,y,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,g e,f,f,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,v,d p,x,s,g,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,v,d p,x,s,p,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,p p,x,s,g,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,g p,x,f,g,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,v,d p,x,s,g,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,f,w,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,v,d p,x,s,w,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,p e,f,y,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,v,d p,x,s,w,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,f,w,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,f,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,y,d p,x,s,w,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,n,s,d e,x,y,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,p p,x,f,p,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,p p,x,f,w,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,p e,f,y,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,v,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,p p,x,s,g,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,p p,x,f,p,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,v,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,g e,f,y,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,p,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,f,w,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,p e,f,f,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,y,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,g p,x,s,p,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,y,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,g e,f,y,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,y,d p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,p e,f,y,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,g e,f,y,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,g p,x,f,w,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,v,d p,x,s,g,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,p p,x,s,w,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,p p,x,s,w,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,p e,x,y,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,g e,f,y,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,v,d p,x,s,w,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,k,s,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,g e,f,f,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,g e,f,y,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,y,d p,x,s,g,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,v,d p,x,f,p,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,g e,f,y,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,y,d p,x,s,p,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,p p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,p e,f,y,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,v,d p,x,s,g,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,n,v,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,d p,x,f,p,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,y,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,g e,f,f,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,y,d p,x,f,w,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,p p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,p p,x,s,p,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,y,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,y,d p,x,f,p,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,v,d p,x,s,w,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,g e,f,f,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,g e,f,f,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,g e,f,y,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,v,d p,x,f,w,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,y,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,v,d p,x,f,p,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,v,d p,x,s,w,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,k,s,d p,x,f,p,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,p e,x,f,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,v,d p,x,s,p,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,g e,f,y,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,y,d p,x,f,w,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,y,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,p e,f,f,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,v,d p,x,f,g,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,p e,f,y,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,v,d p,x,s,g,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,g e,f,f,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,y,d p,x,f,w,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,g p,x,f,g,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,v,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,g e,f,y,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,y,d p,x,f,p,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,s,g,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,v,d p,x,s,p,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,v,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,p e,x,f,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,y,d p,x,s,p,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,n,s,d e,x,y,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,y,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,v,d p,x,s,w,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,d p,x,f,p,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,v,d p,x,f,g,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,y,d p,x,f,p,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,y,d p,x,s,w,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,k,s,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,g p,x,s,g,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,g p,x,s,p,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,y,d p,x,s,g,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,n,s,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,y,d p,x,s,g,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,g p,x,s,g,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,y,d p,x,f,g,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,v,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,p p,x,s,g,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,p e,f,y,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,v,d p,x,f,g,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,v,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,p e,f,f,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,p e,f,y,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,v,d p,x,f,p,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,v,d p,x,f,p,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,s,w,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,v,d p,x,s,p,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,g p,x,f,g,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,p p,x,f,w,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,y,d p,x,f,w,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,k,s,d e,x,y,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,y,d p,x,f,w,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,y,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,v,d p,x,f,g,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,s,p,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,p e,x,y,n,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,y,d p,x,f,g,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,p e,f,y,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,y,d p,x,s,w,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,w,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,g e,f,y,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,p e,f,f,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,g e,f,y,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,v,d p,x,f,w,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,g e,x,f,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,y,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,y,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,y,d p,x,s,g,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,v,d p,x,s,p,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,k,s,d p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,y,d p,x,f,p,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,y,d p,x,s,w,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,y,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,v,d p,x,s,g,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,v,d p,x,s,p,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,v,d p,x,s,p,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,y,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,y,d p,x,f,p,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,v,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,d p,x,s,g,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,v,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,d p,x,f,g,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,y,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,g e,f,f,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,p e,f,y,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,y,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,p e,f,f,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,g e,f,y,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,y,d p,x,f,g,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,v,d p,x,f,p,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,k,s,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,y,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,g e,f,y,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,g e,f,y,n,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,g e,f,f,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,y,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,v,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,d p,x,s,g,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,g p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,p e,f,f,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,y,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,y,d p,x,f,p,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,y,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,g p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,p e,f,f,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,f,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,y,d p,x,f,p,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,p e,x,f,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,y,d p,x,s,g,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,k,s,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,g e,f,y,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,y,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,g e,f,f,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,g p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,p e,f,y,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,v,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,p e,f,y,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,v,d p,x,f,g,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,v,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,y,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,p e,x,y,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,y,d p,x,s,w,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,y,d p,x,s,p,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,p e,f,y,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,y,d p,x,s,p,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,y,d p,x,s,w,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,k,s,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,p e,f,y,n,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,g p,x,f,w,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,v,d p,x,f,w,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,g e,f,y,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,n,v,d p,x,s,p,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,y,d p,x,s,p,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,y,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,g e,f,y,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,y,d p,x,f,p,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,p e,f,f,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,y,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,y,d p,x,f,g,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,g e,f,y,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,v,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,y,d e,x,f,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,v,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,y,d e,x,y,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,d p,x,s,w,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,n,v,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,p e,f,y,n,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,p,g,p,w,o,p,k,y,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,y,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,v,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,g e,f,y,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,d p,x,f,w,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,k,s,d p,x,f,g,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,k,v,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,y,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,p p,x,s,g,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,v,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,v,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,p p,x,f,g,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,v,d p,x,s,g,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,f,w,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,g e,f,y,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,v,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,p e,f,f,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,y,d e,x,f,g,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,f,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,p e,f,y,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,y,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,v,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,y,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,p e,x,y,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,y,d p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,v,d p,x,f,g,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,y,d p,x,s,w,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,v,d p,x,s,w,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,y,d p,x,s,g,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,v,d p,x,f,p,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,y,d p,x,s,p,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,y,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,g e,f,y,g,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,g e,f,y,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,v,d p,x,s,p,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,k,s,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,p e,f,f,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,k,v,d e,x,f,g,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,d e,x,y,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,k,y,d p,x,f,w,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,y,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,g e,f,y,g,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,y,d p,x,s,w,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,k,v,d p,x,s,w,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,k,s,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,v,d e,f,y,g,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,p e,f,f,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,y,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,g e,f,f,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,y,d p,x,f,g,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,y,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,y,d p,x,s,p,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,g e,f,y,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,n,v,d p,x,s,w,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,w,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,n,v,d e,x,y,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,v,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,d p,x,f,w,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,v,d p,x,f,w,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,s,g,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,k,s,d e,x,y,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,d p,x,f,g,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,d p,x,s,g,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,n,v,d e,x,f,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,v,d p,x,f,p,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,v,d p,x,s,p,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,f,g,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,y,d p,x,f,g,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,k,s,d p,x,s,g,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,y,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,y,d p,x,f,g,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,k,v,d p,x,s,w,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,n,s,d e,f,y,n,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,g e,f,y,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,g e,f,y,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,g p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,p e,f,f,e,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,v,d p,x,f,w,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,g p,x,f,w,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,d e,f,y,g,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,k,y,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,g e,x,f,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,y,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,v,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,y,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,g e,f,f,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,g e,f,y,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,n,v,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,p p,x,s,p,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,g e,f,f,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,v,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,k,y,d p,x,f,p,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,g e,x,y,g,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,y,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,w,g,p,w,o,p,n,y,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,g e,f,f,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,v,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,g p,x,s,p,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,f,g,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,k,s,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,v,d p,x,s,g,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,v,u p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,v,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,p p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,g p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,p p,x,s,w,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,p p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,p e,f,y,n,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,v,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,p p,x,s,p,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,n,s,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,g p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,g p,x,s,w,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,n,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,g p,x,f,p,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,k,v,d p,f,s,w,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,v,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,p e,x,y,b,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,g p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,g e,f,f,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,y,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,g p,x,f,g,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,f,g,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,g p,x,s,g,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,s,g p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,g e,f,y,g,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,y,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,p e,f,y,n,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,y,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,v,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,p e,f,f,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,n,v,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,p e,x,f,e,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,p p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,d e,x,f,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,y,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,v,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,p p,x,y,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,g p,x,s,g,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,n,v,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,g p,f,s,b,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,s,g p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,d p,x,s,w,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,k,s,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,d e,f,f,e,t,n,f,c,b,w,t,b,s,s,w,p,p,w,o,p,k,v,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,g p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,k,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,y,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,d p,x,s,w,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,g,w,p,w,o,p,k,v,d p,x,f,w,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,k,s,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,d p,x,f,p,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,n,v,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,d p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,p e,f,y,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,v,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,p p,x,f,g,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,n,s,d p,x,s,p,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,k,v,d e,x,f,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,v,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,g e,f,f,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,k,y,d p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,p e,f,y,g,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,n,y,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,p e,f,f,e,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,y,n,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,v,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,g e,f,y,u,f,n,f,c,n,h,e,?,s,f,w,w,p,w,o,f,h,y,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,y,d p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,p p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,p e,x,f,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,v,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,d e,f,y,n,t,n,f,c,b,n,t,b,s,s,w,w,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,y,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,g e,x,f,e,t,n,f,c,b,w,t,b,s,s,p,p,p,w,o,p,k,v,d e,f,f,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,y,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,p p,x,f,w,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,d p,x,y,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,n,y,d p,x,y,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l e,f,y,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,v,d p,b,s,b,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,m e,f,f,g,t,n,f,c,b,w,t,b,s,s,g,g,p,w,o,p,k,y,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,g e,f,y,g,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,k,y,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,g p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,g e,f,f,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,v,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,g p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,p e,f,y,e,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,k,v,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,g e,f,f,n,t,n,f,c,b,u,t,b,s,s,w,p,p,w,o,p,k,v,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,p e,f,y,n,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,k,y,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,p e,f,f,e,t,n,f,c,b,p,t,b,s,s,g,g,p,w,o,p,k,y,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,d p,x,s,g,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,k,s,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,v,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,g p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,p e,f,y,n,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,v,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,w,t,b,s,s,p,g,p,w,o,p,k,v,d p,f,s,g,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,v,u p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,p p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,p p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,p e,f,y,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,n,y,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,p e,f,f,e,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,v,d e,f,y,e,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,y,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,p e,f,y,n,t,n,f,c,b,u,t,b,s,s,g,p,p,w,o,p,k,y,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,g e,f,f,g,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,v,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,d e,f,f,c,f,n,f,w,n,w,e,b,f,f,w,n,p,w,o,e,w,v,l p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,g p,x,s,b,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,s,u p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,k,y,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,p e,f,y,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,k,y,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,d e,f,f,g,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,g p,x,f,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,p e,f,y,n,t,n,f,c,b,p,t,b,s,s,p,w,p,w,o,p,n,y,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,n,v,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,p p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,g p,f,s,b,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,s,u e,f,f,e,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,y,d p,x,y,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d e,x,y,g,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,v,d p,x,f,g,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,f,p,f,c,f,w,n,n,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,y,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,g p,x,s,g,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,s,u p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,g p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,g p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,g p,f,s,g,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,v,u p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,p p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,p e,f,y,e,t,n,f,c,b,p,t,b,s,s,w,w,p,w,o,p,n,v,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,g p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,p p,x,f,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,p p,f,s,w,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,s,u p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,p p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,g p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,d p,x,s,w,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,s,g p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,g p,x,s,b,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,s,g p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,g e,f,y,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,y,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,g p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,p p,x,f,p,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,k,s,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,p p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,p p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,p e,k,y,n,f,n,f,w,n,w,e,b,f,f,w,n,p,w,o,e,w,v,l p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,d p,x,f,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,g e,f,s,p,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,g e,k,s,p,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,g p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,g e,f,y,g,t,n,f,c,b,w,t,b,s,s,p,w,p,w,o,p,n,y,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,g p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,d p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,g p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,p p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,p e,x,y,r,f,n,f,c,n,p,e,?,s,f,w,w,p,w,o,f,h,v,d p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,d p,x,y,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,d p,k,y,n,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,g e,f,y,e,t,n,f,c,b,w,t,b,s,s,g,p,p,w,o,p,k,y,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,g p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,g p,f,s,b,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,s,u p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,g e,x,s,e,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,p p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,g p,b,y,w,t,n,f,w,n,w,e,b,s,s,w,w,p,w,o,p,w,c,l p,f,s,b,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,v,u p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,p p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,p p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,g p,x,s,w,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,s,u e,f,y,g,t,n,f,c,b,n,t,b,s,s,g,p,p,w,o,p,n,v,d p,x,y,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,g e,f,y,e,t,n,f,c,b,n,t,b,s,s,p,g,p,w,o,p,k,v,d e,x,y,b,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,g p,x,f,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,g p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,p p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,p e,x,y,u,f,n,f,c,n,h,e,?,s,f,w,w,p,w,o,f,h,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,d p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,d e,f,f,e,t,n,f,c,b,u,t,b,s,s,g,w,p,w,o,p,n,y,d p,f,s,b,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,v,u p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,p p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,d e,f,y,n,t,n,f,c,b,u,t,b,s,s,w,g,p,w,o,p,k,v,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,g e,x,s,b,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,p e,f,f,e,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,k,y,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,g p,x,y,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,g p,x,s,g,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,g p,f,s,g,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,s,u p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,d e,f,y,g,t,n,f,c,b,u,t,b,s,s,p,g,p,w,o,p,k,y,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,p e,f,y,n,t,n,f,c,b,n,t,b,s,s,g,g,p,w,o,p,n,v,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,g p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,g e,k,y,b,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,p p,x,y,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,p p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,g p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,d p,x,s,w,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,v,u p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,p p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,p e,f,y,n,t,n,f,c,b,p,t,b,s,s,w,p,p,w,o,p,k,y,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,p p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,d e,f,f,c,f,n,f,w,n,w,e,b,s,f,w,n,p,w,o,e,w,v,l p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,p p,f,f,y,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,p p,x,s,g,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,v,g e,f,s,n,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,y,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,x,s,g,f,c,f,w,n,u,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,p p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,d e,x,s,b,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,d p,x,y,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,g e,x,y,u,f,n,f,c,n,h,e,?,s,f,w,w,p,w,o,f,h,v,d e,f,y,b,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,g p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,g p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,g p,f,s,b,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,v,g p,f,s,w,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,m p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,g,g,p,w,o,p,n,v,d e,x,y,u,f,n,f,c,n,u,e,?,s,f,w,w,p,w,o,f,h,v,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,p p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,p e,f,f,e,t,n,f,c,b,w,t,b,s,s,w,g,p,w,o,p,n,v,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,p p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,p p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,p p,x,f,w,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,n,v,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,g p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,g p,x,y,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d e,f,y,b,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,g p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,p p,x,f,g,f,c,f,c,n,u,e,b,s,s,w,w,p,w,o,p,k,s,d p,f,s,b,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,v,g e,f,f,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,k,v,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,p p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,g e,f,f,g,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,k,v,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,g p,f,s,w,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,s,u p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,d e,f,y,u,f,n,f,c,n,h,e,?,s,f,w,w,p,w,o,f,h,v,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,g p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,g e,f,y,n,t,n,f,c,b,n,t,b,s,s,p,p,p,w,o,p,n,y,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,g p,x,s,w,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,s,u e,f,y,e,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w e,x,y,u,f,n,f,c,n,w,e,?,s,f,w,w,p,w,o,f,h,y,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,p p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,p e,f,s,p,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,p p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,g p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,d p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,g p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,p e,f,y,n,t,n,f,c,b,n,t,b,s,s,w,g,p,w,o,p,n,y,d p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,p p,x,s,g,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,s,g p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,p p,x,f,w,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,k,s,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,d p,f,s,b,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,s,u p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,g p,f,s,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,g p,f,s,b,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,v,u p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,p e,f,y,u,f,n,f,c,n,u,e,?,s,f,w,w,p,w,o,f,h,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,g e,f,f,e,t,n,f,c,b,w,t,b,s,s,g,w,p,w,o,p,n,v,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,g p,x,y,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,p p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,g e,f,y,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,y,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,g e,f,f,e,t,n,f,c,b,w,t,b,s,s,w,w,p,w,o,p,k,y,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,p p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,p p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,p p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,d p,x,f,p,f,c,f,w,n,p,e,b,s,s,w,w,p,w,o,p,k,s,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,p p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,p e,x,s,p,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,d p,x,s,p,f,c,f,w,n,g,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,g p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,g e,f,f,e,t,n,f,c,b,p,t,b,s,s,p,p,p,w,o,p,n,y,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,g e,f,y,n,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,v,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,p p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,g e,f,f,g,t,n,f,c,b,u,t,b,s,s,w,w,p,w,o,p,n,y,d p,x,s,g,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,s,g p,x,y,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,f,s,g,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,v,g p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,g p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,d e,f,y,e,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,g e,f,y,n,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,g p,k,f,n,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,p p,x,y,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,p p,f,s,w,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,v,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,g e,x,y,e,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,d p,b,f,y,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,d p,x,s,g,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,s,u p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,g e,k,y,e,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,p e,k,y,n,f,n,f,w,n,w,e,b,f,s,w,n,p,w,o,e,w,v,l p,x,s,w,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,n,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,d p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,p p,b,s,b,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,g p,x,s,w,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,v,g e,f,y,e,t,n,f,c,b,n,t,b,s,s,w,p,p,w,o,p,n,y,d p,b,s,w,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,m e,f,y,p,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,x,s,w,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,v,g e,k,y,n,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,p p,f,s,b,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,v,u p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,p e,k,s,e,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w e,f,y,n,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w e,f,s,b,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,d e,f,f,g,t,n,f,c,b,u,t,b,s,s,p,p,p,w,o,p,n,v,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,p p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,g p,x,s,g,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,v,g p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,g p,x,y,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,p e,f,y,n,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w e,f,y,e,t,n,f,c,b,p,t,b,s,s,g,p,p,w,o,p,k,v,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,p,w,p,w,o,p,n,v,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,p p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,d p,b,y,w,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,m p,f,f,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,p p,x,y,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,p e,f,y,p,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,x,s,w,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,s,g p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,g p,f,s,b,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,s,u p,x,f,g,f,c,f,c,n,g,e,b,s,s,w,w,p,w,o,p,k,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,p p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,g p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,p e,x,y,r,f,n,f,c,n,p,e,?,s,f,w,w,p,w,o,f,h,y,d e,f,y,w,f,n,f,c,n,h,e,?,s,f,w,w,p,w,o,f,h,v,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,p p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,g p,x,y,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,x,y,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,p e,f,s,e,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,p p,f,s,g,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,s,g p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,p p,x,s,g,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,v,u p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,g p,x,s,w,f,c,f,c,n,n,e,b,s,s,w,w,p,w,o,p,k,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,p e,f,y,e,t,n,f,c,b,u,t,b,s,s,p,w,p,w,o,p,n,y,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,p e,k,s,b,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,g e,x,f,n,f,n,f,w,n,w,e,b,s,f,w,n,p,w,o,e,w,v,l e,x,y,e,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,g p,f,s,g,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,v,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,p p,x,y,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,g p,x,y,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p e,k,s,b,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,d p,x,f,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,g e,k,s,p,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,y,n,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,p p,f,s,b,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,v,u e,f,s,b,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,s,w,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,s,u p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,p p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,d p,x,s,b,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,v,u p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,g p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,d p,f,s,g,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,s,u e,f,s,b,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w e,x,s,p,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w e,k,s,n,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,y,p,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,g p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,g p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,p p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,p e,f,y,u,f,n,f,c,n,w,e,?,s,f,w,w,p,w,o,f,h,y,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,g p,x,y,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,p e,f,s,b,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,p p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,d e,x,s,n,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,d p,x,y,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,d p,x,y,n,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d p,b,s,b,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,g p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,d e,f,y,u,f,n,f,c,n,u,e,?,s,f,w,w,p,w,o,f,h,y,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,g p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,d e,x,y,e,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,f,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,g p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,p e,k,s,b,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,p p,f,s,w,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,v,u p,x,s,g,f,c,f,c,n,p,e,b,s,s,w,w,p,w,o,p,n,v,d p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,d e,f,y,u,f,n,f,c,n,p,e,?,s,f,w,w,p,w,o,f,h,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,g p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,p p,x,s,g,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,s,u p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,g p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,d p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,g p,f,f,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,p p,x,y,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,p p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,p p,f,s,b,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,v,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,d p,x,y,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l e,k,y,b,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w e,f,y,b,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,g p,f,y,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,g p,x,s,b,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,s,u p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,p p,x,s,w,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,s,u p,x,f,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,p p,x,y,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,p p,x,s,w,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,s,u p,f,s,b,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,s,g p,x,s,w,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,s,u p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,p e,x,y,w,f,n,f,c,n,u,e,?,s,f,w,w,p,w,o,f,h,y,d e,x,s,e,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,g p,x,y,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,d e,f,f,e,t,n,f,c,b,n,t,b,s,s,g,w,p,w,o,p,n,y,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,g p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,p p,k,f,y,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,g e,k,f,c,f,n,f,w,n,w,e,b,f,s,w,n,p,w,o,e,w,v,l p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,p p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,p p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,g p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,d p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,d p,b,y,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,g e,k,y,p,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,y,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,p p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,g e,k,y,b,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,d p,x,s,w,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,s,u p,x,y,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,x,y,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,x,y,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,f,g,w,t,n,f,w,n,w,e,b,s,s,w,w,p,w,o,p,w,c,l p,x,s,g,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,v,u e,f,y,c,f,n,f,w,n,w,e,b,f,s,w,n,p,w,o,e,w,v,l p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,d p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,p e,f,y,p,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,x,s,b,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,v,g p,x,s,g,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,s,g p,x,y,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p e,k,y,c,f,n,f,w,n,w,e,b,s,f,w,n,p,w,o,e,w,v,l p,x,s,w,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,s,u p,x,s,w,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,v,g p,f,s,b,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,v,u p,f,s,b,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,v,g e,k,y,c,f,n,f,w,n,w,e,b,f,s,w,n,p,w,o,e,w,v,l p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,d p,f,s,w,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,v,g p,f,s,g,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,s,u p,c,g,w,t,n,f,w,n,w,e,b,s,s,w,w,p,w,o,p,w,c,l p,x,s,g,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,s,u p,b,g,w,t,n,f,w,n,w,e,b,s,s,w,w,p,w,o,p,w,c,l p,x,s,b,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,v,g p,f,s,w,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,s,u p,b,f,y,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d p,x,y,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,x,y,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d e,k,s,n,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w e,k,y,b,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,s,w,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,v,g p,f,s,b,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,m p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,p p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,g p,f,s,b,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,g p,x,y,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,x,y,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,d e,x,s,e,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,x,y,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,g p,x,y,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d e,f,f,n,f,n,f,w,n,w,e,b,s,f,w,n,p,w,o,e,w,v,l p,x,y,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p e,x,s,b,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w e,f,y,n,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,p p,f,y,b,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,m p,x,y,n,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d p,x,y,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,x,s,b,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,s,g p,x,s,b,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,v,g p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,p p,f,s,g,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,v,g p,x,y,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,x,s,b,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,v,g p,f,f,n,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d e,x,y,e,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,s,b,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,s,g p,f,s,w,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,s,g e,k,y,e,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,p p,x,f,n,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d e,x,y,n,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,g p,f,s,b,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,v,g p,f,s,b,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,s,g p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,g p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,d e,x,s,p,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w e,f,s,p,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,b,y,w,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,g e,x,y,c,f,n,f,w,n,w,e,b,f,f,w,n,p,w,o,e,w,v,l e,f,s,n,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,x,s,b,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,v,u p,x,s,g,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,v,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,d p,x,s,b,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,v,u p,x,s,w,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,s,g e,f,y,c,f,n,f,w,n,w,e,b,s,f,w,n,p,w,o,e,w,v,l p,x,y,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,d e,x,y,w,f,n,f,c,n,h,e,?,s,f,w,w,p,w,o,f,h,v,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,p p,f,y,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,g p,f,s,g,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,v,u p,x,y,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d e,k,s,p,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,x,y,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,p p,f,s,b,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,s,u e,k,y,p,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,g p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,d p,x,s,b,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,s,g p,x,y,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,d p,f,f,y,f,f,f,c,b,h,e,b,k,k,n,n,p,w,o,l,h,v,d p,f,f,n,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d e,k,s,b,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,g p,x,y,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,x,s,g,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,s,u e,f,s,n,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,p p,x,y,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,x,s,g,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,v,u p,x,s,g,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,v,g p,f,y,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,m e,k,y,b,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,x,s,w,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,v,u p,x,y,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d e,k,y,n,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,d e,x,y,p,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,s,g,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,s,u e,x,s,p,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,b,y,n,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d p,f,s,b,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,v,g p,x,y,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,x,y,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,x,s,b,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,s,u p,x,y,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l e,k,y,p,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w e,k,f,c,f,n,f,w,n,w,e,b,f,f,w,n,p,w,o,e,w,v,l p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,g e,x,s,n,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,p p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,d p,f,s,g,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,v,u p,k,y,w,t,n,f,w,n,w,e,b,s,s,w,w,p,w,o,p,w,c,l e,k,f,n,f,n,f,w,n,w,e,b,f,f,w,n,p,w,o,e,w,v,l p,k,f,y,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d p,f,s,w,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,s,g p,f,y,y,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,d e,k,s,b,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,p p,x,y,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,p p,b,y,w,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,y,g p,x,s,w,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,v,g p,x,s,b,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,v,g e,k,y,b,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,p p,x,s,b,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,s,g p,b,y,b,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,m p,x,s,w,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,v,g e,k,s,n,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,s,g,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,s,u p,x,f,y,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d p,f,s,g,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,v,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,d p,k,y,n,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d p,f,s,b,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,s,u e,f,s,e,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,y,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,x,y,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,x,y,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,x,s,w,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,v,u e,k,s,n,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,g e,x,s,b,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,s,w,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,s,u e,k,f,n,f,n,f,w,n,w,e,b,s,s,w,n,p,w,o,e,w,v,l p,x,y,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,s,w,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,v,g p,x,s,g,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,v,u p,k,y,y,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d p,f,s,w,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,m p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,p e,k,y,p,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,y,w,t,n,f,w,n,w,e,b,s,s,w,w,p,w,o,p,w,c,l p,f,s,b,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,v,u e,f,y,w,f,n,f,c,n,u,e,?,s,f,w,w,p,w,o,f,h,y,d e,x,y,r,f,n,f,c,n,w,e,?,s,f,w,w,p,w,o,f,h,v,d e,x,s,b,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,s,g,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,v,g p,x,y,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,p p,f,s,g,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,s,g p,f,s,b,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,s,g e,f,s,e,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,x,y,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,d e,x,s,n,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,s,g,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,s,g p,x,y,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,f,s,w,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,s,g e,x,f,c,f,n,f,w,n,w,e,b,s,s,w,n,p,w,o,e,w,v,l p,f,s,g,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,v,g p,f,f,g,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,p e,x,y,r,f,n,f,c,n,w,e,?,s,f,w,w,p,w,o,f,h,y,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,p p,x,y,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,x,y,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l e,f,y,e,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,x,s,g,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,v,u e,k,y,n,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w e,f,y,e,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,y,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,b,y,n,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d p,x,y,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p e,f,y,b,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,x,s,w,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,v,g p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,g e,f,y,n,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,b,y,w,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,m e,x,y,n,f,n,f,w,n,w,e,b,s,f,w,n,p,w,o,e,w,v,l p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,p p,x,s,b,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,s,g p,x,y,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,x,s,g,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,s,u p,f,s,g,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,s,u p,x,y,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p e,f,y,w,f,n,f,c,n,p,e,?,s,f,w,w,p,w,o,f,h,v,d p,x,y,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,f,f,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,g p,x,y,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,x,s,w,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,v,g p,f,y,g,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,d p,x,s,w,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,s,u p,k,y,y,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d p,f,s,w,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,v,u p,f,s,g,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,v,u e,x,y,c,f,n,f,w,n,w,e,b,f,s,w,n,p,w,o,e,w,v,l p,x,s,w,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,v,u p,x,y,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,f,y,p,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,g p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,p e,x,s,p,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,y,b,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,g p,x,f,y,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,p e,f,f,n,f,n,f,w,n,w,e,b,f,f,w,n,p,w,o,e,w,v,l e,x,f,n,f,n,f,w,n,w,e,b,f,s,w,n,p,w,o,e,w,v,l p,x,y,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,f,s,g,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,v,u p,x,s,b,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,s,u p,f,s,g,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,v,g p,x,s,b,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,s,g e,x,y,r,f,n,f,c,n,h,e,?,s,f,w,w,p,w,o,f,h,v,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,d p,f,s,g,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,s,u p,x,y,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,g p,f,s,w,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,v,u p,x,s,w,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,s,u p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,p p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,p p,x,y,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,x,y,y,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d e,f,s,n,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,d p,f,s,g,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,s,u p,x,y,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,d p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,d p,f,s,w,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,s,u p,f,s,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,m p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,g e,k,s,p,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,x,s,b,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,s,g p,x,s,w,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,s,g p,x,s,w,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,s,g p,x,y,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,b,y,p,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,m p,x,s,b,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,s,u e,x,y,p,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,y,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,x,y,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,v,p p,x,s,w,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,v,u e,f,y,b,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,s,b,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,v,u e,x,f,c,f,n,f,w,n,w,e,b,f,f,w,n,p,w,o,e,w,v,l e,f,s,p,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w e,x,y,n,f,n,f,w,n,w,e,b,f,f,w,n,p,w,o,e,w,v,l e,f,s,p,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,s,g,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,v,u e,k,s,e,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w e,k,y,e,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,s,w,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,v,g e,k,s,b,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,x,s,b,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,v,g p,b,y,y,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d p,x,s,w,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,s,u p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,g p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,p p,b,f,n,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,p p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,v,p e,f,y,c,f,n,f,w,n,w,e,b,s,s,w,n,p,w,o,e,w,v,l p,x,y,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,f,s,w,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,s,g p,x,y,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,b,y,p,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,d p,x,s,b,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,s,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,p p,f,s,b,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,s,g p,f,s,b,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,s,u p,x,y,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,p e,x,s,n,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,v,g e,f,s,b,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w e,f,s,e,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w e,x,s,n,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,s,w,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,v,u p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,d e,f,s,p,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w e,x,s,e,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,d p,b,y,b,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,m p,f,s,b,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,s,u p,f,s,g,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,s,g p,x,s,b,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,s,g p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,p p,f,s,w,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,s,g p,x,s,g,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,s,u e,f,y,r,f,n,f,c,n,h,e,?,s,f,w,w,p,w,o,f,h,y,d p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,g p,x,y,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,x,s,b,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,s,g e,x,f,c,f,n,f,w,n,w,e,b,f,s,w,n,p,w,o,e,w,v,l p,x,s,g,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,v,u e,x,y,u,f,n,f,c,n,p,e,?,s,f,w,w,p,w,o,f,h,y,d p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,v,p p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,g p,f,y,w,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,m p,x,y,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,x,y,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,x,y,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,p e,x,y,p,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,s,g,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,s,g p,x,s,b,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,v,g p,x,y,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,x,s,g,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,s,u p,x,y,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,f,s,w,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,s,g p,x,s,g,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,v,u p,x,s,g,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,s,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,p p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,p p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,g p,x,s,g,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,s,u p,f,s,b,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,s,u p,f,s,w,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,s,u p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,g p,f,s,b,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,s,g p,x,y,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,x,s,w,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,s,g e,k,s,e,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,y,b,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,m p,x,y,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p e,k,y,n,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,s,w,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,v,u p,f,s,w,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,v,u p,x,y,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,x,s,w,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,s,g p,x,y,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,b,s,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,g p,x,y,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,p p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,d p,x,y,g,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,v,g p,f,y,w,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,m p,f,s,g,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,s,g e,k,y,p,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,x,s,w,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,v,g e,k,s,p,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,s,w,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,s,u p,x,y,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,d p,f,y,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,p p,x,y,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,p e,x,y,e,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,p p,x,y,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,x,s,b,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,v,g p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,d e,k,y,e,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,y,p,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,m p,f,y,w,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,m p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,p p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,g e,f,y,r,f,n,f,c,n,w,e,?,s,f,w,w,p,w,o,f,h,v,d p,x,s,w,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,s,g p,x,s,w,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,s,g p,x,s,b,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,s,u p,x,y,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p e,k,y,e,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w e,k,s,p,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w e,x,y,b,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,x,s,g,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,v,g p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,g p,x,y,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,c,y,w,t,n,f,w,n,w,e,b,s,s,w,w,p,w,o,p,w,c,l p,f,s,w,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,v,g p,f,s,g,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,s,g p,x,y,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,x,s,g,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,s,g p,x,y,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d e,x,y,p,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w e,f,y,w,f,n,f,c,n,h,e,?,s,f,w,w,p,w,o,f,h,y,d p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,g p,x,y,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,x,f,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,d p,x,y,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,x,s,g,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,v,u p,x,y,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d e,k,f,n,f,n,f,w,n,w,e,b,s,f,w,n,p,w,o,e,w,v,l p,x,s,w,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,v,u p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,p e,x,y,p,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,b,y,b,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,m p,f,y,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,p e,f,y,r,f,n,f,c,n,h,e,?,s,f,w,w,p,w,o,f,h,v,d p,x,y,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,x,y,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,f,s,b,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,v,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,d p,x,y,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d e,f,y,n,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,x,y,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l e,f,y,e,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w e,x,y,b,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w e,x,s,n,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,s,w,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,v,g e,x,y,b,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,f,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,d p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,y,g e,k,y,e,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,s,w,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,v,u e,k,y,c,f,n,f,w,n,w,e,b,s,s,w,n,p,w,o,e,w,v,l e,k,y,n,f,n,f,w,n,w,e,b,s,s,w,n,p,w,o,e,w,v,l p,b,s,p,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,m p,x,y,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,x,s,b,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,s,u e,f,y,r,f,n,f,c,n,p,e,?,s,f,w,w,p,w,o,f,h,v,d p,x,s,b,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,s,g e,f,y,u,f,n,f,c,n,p,e,?,s,f,w,w,p,w,o,f,h,y,d p,x,y,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,x,s,w,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,v,u e,x,s,e,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w e,f,y,p,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,x,y,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,x,y,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,x,s,w,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,v,g p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,p e,x,y,n,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w e,x,y,e,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,x,s,w,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,v,u p,x,y,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,g p,f,s,b,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,m p,f,f,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,v,p p,x,s,g,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,v,g e,f,s,p,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w e,x,y,n,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,b,y,w,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,m p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,d p,x,y,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,x,s,b,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,s,g p,x,s,b,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,v,g p,x,y,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,b,y,p,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,g e,x,y,c,f,n,f,w,n,w,e,b,s,s,w,n,p,w,o,e,w,v,l p,x,y,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,x,s,w,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,s,u p,x,y,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d e,f,y,n,f,n,f,w,n,w,e,b,f,s,w,n,p,w,o,e,w,v,l p,x,y,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,f,s,g,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,s,u p,x,y,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d e,x,y,r,f,n,f,c,n,h,e,?,s,f,w,w,p,w,o,f,h,y,d p,b,y,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,m e,x,s,p,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,x,y,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,x,y,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,f,s,g,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,v,g p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,p p,f,y,p,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,m p,x,y,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,x,y,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d e,f,s,b,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,s,b,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,v,u e,x,y,c,f,n,f,w,n,w,e,b,s,f,w,n,p,w,o,e,w,v,l e,x,y,w,f,n,f,c,n,w,e,?,s,f,w,w,p,w,o,f,h,y,d p,x,y,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l e,f,y,n,f,n,f,w,n,w,e,b,s,s,w,n,p,w,o,e,w,v,l p,x,y,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,x,y,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d e,k,y,p,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,s,w,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,m p,x,y,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,g e,k,y,n,f,n,f,w,n,w,e,b,s,f,w,n,p,w,o,e,w,v,l p,f,s,g,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,v,g p,f,s,w,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,g p,f,f,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,g e,f,s,n,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,x,f,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,d p,x,y,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,x,y,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,g p,b,s,w,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,g p,x,s,b,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,v,u e,f,y,b,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w e,x,f,c,f,n,f,w,n,w,e,b,s,f,w,n,p,w,o,e,w,v,l p,f,s,w,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,v,u e,k,s,p,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w e,k,y,n,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w e,x,y,b,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,g p,f,s,g,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,v,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,p e,x,y,e,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,s,b,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,v,g e,x,y,n,f,n,f,w,n,w,e,b,s,s,w,n,p,w,o,e,w,v,l p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,d p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,d p,b,y,b,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,g p,x,y,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,p p,f,f,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,p p,f,y,w,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,g e,k,s,e,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,n,p,w,o,l,h,v,p e,k,s,n,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,y,y,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d p,f,y,g,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,p p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,g p,x,y,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p e,f,s,b,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,s,w,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,v,u p,x,s,w,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,s,g p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,d e,f,y,p,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,g p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,p e,k,s,e,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w e,x,y,n,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,g p,f,s,b,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,v,g p,x,y,g,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,v,d p,f,s,g,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,s,u p,x,s,w,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,v,g p,x,f,n,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d p,f,s,b,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,s,g e,f,y,e,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,g p,x,s,b,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,s,u e,k,f,n,f,n,f,w,n,w,e,b,f,s,w,n,p,w,o,e,w,v,l p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,g e,k,y,c,f,n,f,w,n,w,e,b,f,f,w,n,p,w,o,e,w,v,l p,x,f,g,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,y,p p,x,y,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p e,f,y,p,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,s,b,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,v,g p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,n,p,w,o,l,h,y,d p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,y,g p,x,y,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d e,f,y,r,f,n,f,c,n,w,e,?,s,f,w,w,p,w,o,f,h,y,d p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,p p,x,s,g,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,v,g p,x,s,w,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,v,g p,f,s,b,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,s,g e,x,y,n,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,f,y,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d e,f,y,u,f,n,f,c,n,w,e,?,s,f,w,w,p,w,o,f,h,v,d p,x,y,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l e,x,s,n,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,s,w,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,v,u p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,b,p,w,o,l,h,v,d e,f,s,b,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w e,k,f,c,f,n,f,w,n,w,e,b,s,s,w,n,p,w,o,e,w,v,l p,x,s,g,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,v,u p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,p p,x,y,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l e,f,y,p,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w e,k,y,p,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,g p,x,y,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d e,f,s,n,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,g p,x,y,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d e,f,s,n,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,p,p,w,o,l,h,v,d p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,p p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,y,p e,f,f,c,f,n,f,w,n,w,e,b,f,s,w,n,p,w,o,e,w,v,l p,b,y,b,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,g e,k,y,e,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,x,s,b,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,v,u p,x,s,g,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,v,g p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,g p,x,s,g,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,s,u p,x,y,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,f,s,w,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,v,u e,f,s,p,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,s,b,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,v,g p,x,y,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p e,f,y,w,f,n,f,c,n,u,e,?,s,f,w,w,p,w,o,f,h,v,d e,x,y,p,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,x,s,b,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,v,u p,k,g,w,t,n,f,w,n,w,e,b,s,s,w,w,p,w,o,p,w,c,l p,f,s,g,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,s,g p,x,y,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p e,k,s,e,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,y,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,x,y,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,f,s,w,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,s,g e,f,s,e,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,f,s,b,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,s,g p,b,s,w,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,m e,f,f,n,f,n,f,w,n,w,e,b,f,s,w,n,p,w,o,e,w,v,l p,f,s,g,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,v,u p,x,s,w,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,v,g p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,g e,x,s,b,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w e,f,y,n,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w e,x,y,r,f,n,f,c,n,u,e,?,s,f,w,w,p,w,o,f,h,v,d e,k,s,b,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,x,s,w,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,v,u p,x,y,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d e,x,y,b,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,y,w,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,g p,f,s,b,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,s,u p,x,s,g,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,v,g e,k,s,n,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,s,g,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,s,g e,k,y,p,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,y,b,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,m p,x,y,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,v,p p,x,s,b,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,s,u e,k,f,c,f,n,f,w,n,w,e,b,s,f,w,n,p,w,o,e,w,v,l p,f,s,g,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,v,u p,f,s,w,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,v,g p,b,s,b,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,m p,b,s,p,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,g p,f,s,w,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,s,g e,x,y,n,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,x,y,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,x,y,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,g e,x,s,b,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,y,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,x,s,b,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,s,u p,f,s,p,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,g p,x,y,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,x,s,w,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,v,u p,f,s,w,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,v,u e,f,y,r,f,n,f,c,n,u,e,?,s,f,w,w,p,w,o,f,h,y,d p,f,s,w,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,s,g p,f,s,w,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,s,u e,x,y,w,f,n,f,c,n,u,e,?,s,f,w,w,p,w,o,f,h,v,d p,x,y,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d e,k,y,b,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,y,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,x,y,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,x,s,b,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,s,u e,f,y,r,f,n,f,c,n,p,e,?,s,f,w,w,p,w,o,f,h,y,d p,b,s,p,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,g p,x,s,b,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,v,u e,f,y,c,f,n,f,w,n,w,e,b,f,f,w,n,p,w,o,e,w,v,l e,x,y,u,f,n,f,c,n,p,e,?,s,f,w,w,p,w,o,f,h,v,d p,x,s,b,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,v,u e,x,y,w,f,n,f,c,n,w,e,?,s,f,w,w,p,w,o,f,h,v,d p,x,y,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l e,x,s,p,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,s,p,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,m p,f,y,n,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,p p,f,s,w,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,v,g p,x,y,g,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,v,g e,f,y,e,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,s,b,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,g p,b,s,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,m p,x,y,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,x,s,b,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,v,u p,x,y,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,y,p p,b,y,w,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,g e,f,y,n,f,n,f,w,n,w,e,b,s,f,w,n,p,w,o,e,w,v,l p,f,f,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,g p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,b,p,w,o,l,h,v,p p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,g p,x,s,g,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,s,u p,x,y,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,x,y,y,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d p,x,y,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,f,s,w,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,s,g p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,g e,f,f,n,f,n,f,w,n,w,e,b,s,s,w,n,p,w,o,e,w,v,l p,x,s,g,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,s,g p,f,s,b,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,v,u e,f,s,e,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,x,s,b,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,s,u p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,d p,x,y,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,f,s,w,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,v,g p,f,s,g,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,s,g p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,g e,f,f,c,f,n,f,w,n,w,e,b,s,s,w,n,p,w,o,e,w,v,l p,x,y,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l e,k,y,e,t,n,f,c,b,e,e,?,s,s,w,e,p,w,t,e,w,c,w p,x,y,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,s,w,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,s,g p,x,y,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l e,x,s,n,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,p p,x,s,w,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,v,u e,f,s,e,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,d p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,v,d e,f,y,e,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,s,g,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,v,g e,k,s,n,t,n,f,c,b,e,e,?,s,s,e,w,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,b,p,w,o,l,h,y,d p,x,s,w,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,s,g p,x,y,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,g p,f,y,w,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,g p,x,y,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d e,f,y,w,f,n,f,c,n,w,e,?,s,f,w,w,p,w,o,f,h,v,d e,x,y,w,f,n,f,c,n,h,e,?,s,f,w,w,p,w,o,f,h,y,d p,x,y,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,f,s,g,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,s,u e,x,y,u,f,n,f,c,n,w,e,?,s,f,w,w,p,w,o,f,h,v,d p,f,s,w,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,g p,x,y,y,f,f,f,c,b,g,e,b,k,k,p,b,p,w,o,l,h,v,d p,f,s,g,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,v,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,n,p,w,o,l,h,y,p p,x,f,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,v,g p,f,y,y,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,y,d p,x,s,g,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,s,g e,f,y,r,f,n,f,c,n,u,e,?,s,f,w,w,p,w,o,f,h,v,d p,f,s,w,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,s,g e,k,s,n,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,x,y,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,x,s,g,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,s,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,p,p,p,w,o,l,h,y,g p,b,s,w,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,m p,x,y,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,b,s,b,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,m p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,g p,x,y,g,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,d e,x,y,e,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w e,k,s,b,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,x,y,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l e,x,s,e,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,s,b,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,m e,f,s,n,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,y,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p e,f,y,b,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,x,s,g,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,s,u p,f,s,b,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,g p,x,y,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,x,y,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,y,y,f,f,f,c,b,h,e,b,k,k,b,b,p,w,o,l,h,y,g p,x,y,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,x,y,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,f,s,g,t,f,f,c,b,w,t,b,f,s,w,w,p,w,o,p,h,v,u e,x,y,p,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w e,x,y,u,f,n,f,c,n,u,e,?,s,f,w,w,p,w,o,f,h,y,d p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,y,p p,x,s,g,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,v,g p,x,y,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,f,s,g,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,v,u p,x,s,b,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,v,g p,x,f,y,f,f,f,c,b,h,e,b,k,k,b,p,p,w,o,l,h,y,g p,b,s,w,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,g e,k,y,n,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,x,y,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,v,p e,x,y,b,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w p,x,s,b,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,v,g p,f,s,g,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,v,u p,f,s,b,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,s,u p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,b,p,w,o,l,h,y,d p,x,y,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,f,s,w,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,v,u e,k,y,n,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w e,x,s,e,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w e,x,y,w,f,n,f,c,n,p,e,?,s,f,w,w,p,w,o,f,h,v,d p,f,s,b,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,s,u p,f,s,g,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,s,u e,f,s,e,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,y,g p,x,y,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,f,s,w,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,g p,f,y,g,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,d e,x,f,n,f,n,f,w,n,w,e,b,s,s,w,n,p,w,o,e,w,v,l p,f,y,y,f,f,f,c,b,p,e,b,k,k,b,n,p,w,o,l,h,y,d p,x,s,w,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,s,u e,x,s,b,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w e,x,s,p,t,n,f,c,b,w,e,?,s,s,w,e,p,w,t,e,w,c,w p,x,s,g,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,v,g p,f,f,g,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,p p,x,s,w,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,s,g p,x,f,y,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,v,p p,f,s,w,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,s,u e,k,y,n,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w e,x,y,p,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,y,g e,f,y,b,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w e,x,s,e,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,s,g,t,f,f,c,b,p,t,b,f,f,w,w,p,w,o,p,h,v,u p,f,s,b,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,v,u p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,p p,x,s,b,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,v,u p,f,s,w,t,f,f,c,b,h,t,b,s,s,w,w,p,w,o,p,h,v,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,g p,f,y,y,f,f,f,c,b,p,e,b,k,k,n,p,p,w,o,l,h,y,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,n,p,p,w,o,l,h,y,p p,f,f,g,f,f,f,c,b,g,e,b,k,k,b,n,p,w,o,l,h,v,p p,b,s,p,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,m p,x,y,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,b,s,w,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,g e,x,y,n,t,n,f,c,b,w,e,?,s,s,w,w,p,w,t,e,w,c,w p,x,y,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,x,y,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,x,y,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,f,s,b,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,s,g p,b,y,y,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d p,x,s,g,t,f,f,c,b,w,t,b,f,f,w,w,p,w,o,p,h,v,u e,f,y,p,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w e,k,s,p,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w e,f,y,n,t,n,f,c,b,w,e,?,s,s,e,e,p,w,t,e,w,c,w p,b,y,p,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,m p,x,s,g,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,v,g p,x,s,g,t,f,f,c,b,p,t,b,s,s,w,w,p,w,o,p,h,s,g p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,g p,x,y,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,f,y,b,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,r,v,g p,x,s,b,t,f,f,c,b,h,t,b,f,f,w,w,p,w,o,p,h,v,u p,b,s,b,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,g e,f,y,w,f,n,f,c,n,p,e,?,s,f,w,w,p,w,o,f,h,y,d e,x,y,n,f,n,f,w,n,w,e,b,f,s,w,n,p,w,o,e,w,v,l p,x,f,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,v,p p,f,s,b,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,v,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,v,g e,k,s,e,t,n,f,c,b,e,e,?,s,s,e,e,p,w,t,e,w,c,w p,f,f,y,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,p p,b,f,n,f,n,f,c,n,w,e,?,k,y,w,n,p,w,o,e,w,v,d p,x,y,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,f,y,y,f,f,f,c,b,h,e,b,k,k,n,b,p,w,o,l,h,y,d p,x,y,y,f,f,f,c,b,g,e,b,k,k,n,b,p,w,o,l,h,y,g p,x,s,g,t,f,f,c,b,p,t,b,f,s,w,w,p,w,o,p,h,s,g p,x,y,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d e,x,y,n,t,n,f,c,b,w,e,?,s,s,e,w,p,w,t,e,w,c,w e,f,y,n,f,n,f,w,n,w,e,b,f,f,w,n,p,w,o,e,w,v,l p,f,y,b,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,g p,k,f,n,f,n,f,c,n,w,e,?,k,y,w,y,p,w,o,e,w,v,d p,f,y,g,f,f,f,c,b,h,e,b,k,k,p,n,p,w,o,l,h,v,g p,x,y,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,f,f,g,f,f,f,c,b,h,e,b,k,k,p,p,p,w,o,l,h,y,d p,f,f,g,f,f,f,c,b,p,e,b,k,k,b,p,p,w,o,l,h,v,d p,x,s,g,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,s,g e,x,y,r,f,n,f,c,n,u,e,?,s,f,w,w,p,w,o,f,h,y,d p,x,y,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,f,s,p,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,m p,x,y,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,f,s,b,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,v,g p,x,s,b,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,v,u e,k,s,e,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w p,f,s,b,t,f,f,c,b,w,t,b,s,f,w,w,p,w,o,p,h,s,g e,x,f,n,f,n,f,w,n,w,e,b,f,f,w,n,p,w,o,e,w,v,l p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,v,d e,f,y,w,f,n,f,c,n,w,e,?,s,f,w,w,p,w,o,f,h,y,d p,f,s,w,t,f,f,c,b,w,t,b,s,s,w,w,p,w,o,p,h,s,u p,f,s,p,t,n,f,c,b,r,e,b,s,s,w,w,p,w,t,p,r,v,g p,f,y,y,f,f,f,c,b,p,e,b,k,k,p,n,p,w,o,l,h,y,d p,f,s,g,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,s,g p,x,y,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,b,p,w,o,l,h,v,g p,f,s,g,t,f,f,c,b,h,t,b,f,s,w,w,p,w,o,p,h,s,g p,f,s,w,t,f,f,c,b,h,t,b,s,f,w,w,p,w,o,p,h,s,u p,x,y,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,f,f,y,f,f,f,c,b,p,e,b,k,k,n,n,p,w,o,l,h,y,d p,x,y,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,b,y,b,t,n,f,c,b,g,e,b,s,s,w,w,p,w,t,p,r,v,g p,f,y,y,f,f,f,c,b,g,e,b,k,k,b,p,p,w,o,l,h,v,g p,x,y,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,x,y,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d e,k,y,b,t,n,f,c,b,e,e,?,s,s,w,w,p,w,t,e,w,c,w e,x,y,w,f,n,f,c,n,p,e,?,s,f,w,w,p,w,o,f,h,y,d p,f,s,b,t,f,f,c,b,p,t,b,s,f,w,w,p,w,o,p,h,v,u p,f,y,y,f,f,f,c,b,g,e,b,k,k,n,p,p,w,o,l,h,y,g p,x,y,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,f,s,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,x,y,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,x,s,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,f,y,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,k,y,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,y,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,f,y,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,f,y,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,x,s,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,f,s,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,f,y,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,k,s,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,f,y,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,k,s,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,f,y,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,f,s,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,f,s,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,f,s,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,f,y,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,x,s,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,f,y,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,x,y,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,n,c,l p,f,s,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,n,v,l p,f,y,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,f,y,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,f,y,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,f,s,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,x,y,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,x,s,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,f,s,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,f,s,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,f,s,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,f,s,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,x,y,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,x,s,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,f,y,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,x,y,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,k,s,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,k,s,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,f,y,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,x,y,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,f,y,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,x,s,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p e,x,f,w,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,n,g p,f,y,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,x,s,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,f,s,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,f,s,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,k,s,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,f,y,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,x,s,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,y,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,x,s,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,f,s,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,k,y,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,f,s,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,f,s,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,f,s,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,f,y,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,x,y,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,f,s,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,x,y,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,x,s,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,f,y,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,f,y,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,x,y,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,f,y,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,x,s,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,f,y,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,f,s,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,x,y,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,x,s,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,k,s,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p e,x,s,c,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,f,s,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,f,y,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,x,y,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,x,s,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,x,y,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,f,s,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,f,y,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,k,s,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,f,y,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,f,s,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,x,s,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,f,y,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l e,b,f,w,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,n,g p,x,y,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,x,y,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,f,y,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,y,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l e,k,f,w,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,s,g p,x,s,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,f,s,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,x,s,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,x,s,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,k,s,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,x,y,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,x,s,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,x,y,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,x,s,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,x,s,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,f,y,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,f,s,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,x,s,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,f,s,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,x,s,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,f,y,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,k,s,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,f,s,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,k,s,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,f,s,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,f,s,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,x,y,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,k,y,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,f,y,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,k,y,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,f,y,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p e,b,s,g,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,n,g p,x,y,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,f,y,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,x,s,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,f,y,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,x,s,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,f,y,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p e,k,s,w,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,s,g p,f,y,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,x,s,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,f,y,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,x,s,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,f,y,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,f,s,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,x,y,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,f,y,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d e,b,f,g,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,n,g p,k,y,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,x,y,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,k,s,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,x,s,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p e,k,s,w,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,s,g p,f,s,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,k,y,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,k,y,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,f,s,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,f,y,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,f,y,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,x,y,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,f,y,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,x,y,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,x,s,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,f,s,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,x,s,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,f,s,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,f,y,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,x,y,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,x,s,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,x,s,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,k,y,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,x,y,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,f,y,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,x,y,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,f,s,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,k,y,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p e,k,s,g,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,s,g p,x,s,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,s,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,f,s,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,x,s,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,f,s,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,x,y,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p e,b,s,w,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,s,g p,f,s,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,x,y,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,f,y,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,f,s,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,f,s,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,x,y,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,x,s,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,f,s,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,x,y,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,x,y,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,s,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,f,s,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,x,s,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,f,s,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,k,y,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,x,y,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,k,s,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,x,s,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,x,s,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,f,y,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,k,s,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,x,s,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,f,y,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,k,s,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,f,y,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,x,y,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,x,y,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,f,y,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,k,y,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,x,s,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,x,s,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,x,s,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,k,y,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d e,x,f,g,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,s,g p,f,y,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,x,s,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,f,y,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,f,y,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,x,s,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,x,s,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,s,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,f,y,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,x,y,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,x,s,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,s,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,f,s,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,x,s,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,s,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,f,s,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,x,s,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,x,s,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,x,s,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,x,y,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,f,s,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,x,s,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p e,k,f,w,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,n,g p,x,s,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,f,y,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,f,y,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,f,y,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,f,s,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,o,v,l p,f,s,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,f,s,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,k,y,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,f,y,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,x,y,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,f,s,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,x,s,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,k,y,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,x,s,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,x,y,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,f,y,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,f,s,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,f,s,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p e,x,s,w,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,s,g p,f,y,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,f,s,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,x,y,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,x,s,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,x,y,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l e,k,f,g,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,s,g p,f,s,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p e,b,f,w,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,s,g p,f,s,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,x,y,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,f,s,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,f,s,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,f,s,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,x,y,e,f,m,f,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,f,y,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,f,s,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,f,y,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,f,y,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,y,c,l p,f,y,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,y,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,x,s,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,x,y,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,x,y,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,f,y,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,o,v,l p,f,s,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,x,y,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,x,y,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,x,s,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,x,s,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,f,s,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,s,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,k,y,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,x,s,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,f,y,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p e,k,s,w,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,n,g p,f,s,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,x,s,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,f,y,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,f,y,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,f,y,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,x,s,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,f,y,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,x,s,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,f,y,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,f,s,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,k,s,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,f,s,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,f,y,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,x,s,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,x,s,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,f,s,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,x,s,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,f,s,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,f,y,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,f,s,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,x,s,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,f,y,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,f,y,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,f,y,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,f,s,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,f,y,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,f,s,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,k,y,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,f,y,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,f,s,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,x,y,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d e,x,f,w,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,n,g p,x,s,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,x,s,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,x,s,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,x,s,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,x,s,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l e,x,f,g,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,n,g p,f,y,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,x,y,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,x,s,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,k,s,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,k,y,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,f,y,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,x,s,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,x,s,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,f,y,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p e,k,f,w,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,n,g p,k,y,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,x,y,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,x,s,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,x,y,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,y,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,f,s,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,f,y,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,f,y,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,f,y,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,f,y,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,f,s,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,f,s,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,f,y,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,f,s,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,b,v,l p,x,s,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,k,s,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,f,s,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,f,s,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,f,s,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,f,y,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,f,s,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,x,s,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,x,s,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,k,s,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,x,y,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,f,s,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,x,s,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,k,y,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,f,y,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,f,y,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,f,s,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,k,y,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,f,y,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,f,y,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,x,y,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,f,s,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,x,s,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,f,s,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,f,s,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p e,x,s,g,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,n,g p,k,y,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,x,s,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,x,s,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,f,y,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,k,y,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,k,y,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,x,y,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,k,s,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,x,y,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,s,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,f,s,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,f,s,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,f,s,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,f,y,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,x,s,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,x,s,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,x,s,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,x,s,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,x,s,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,x,s,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,x,s,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,s,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,k,y,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,x,s,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,k,y,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,f,s,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,f,s,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,x,s,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,f,y,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,f,y,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,x,y,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,k,s,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,x,y,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,f,s,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p e,b,f,g,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,s,g p,x,s,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,k,s,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,y,v,l p,f,s,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,f,y,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,x,y,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,k,y,c,f,m,a,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,x,s,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,x,s,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,x,s,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,f,s,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,s,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,f,y,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,x,y,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,f,s,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,x,s,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,k,y,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,x,y,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,x,s,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,f,s,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,y,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,k,s,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,f,s,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,f,y,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,f,y,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,f,y,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,x,s,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,f,s,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,x,s,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,k,y,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,f,s,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,f,s,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,x,s,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,x,s,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,f,y,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,x,s,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,f,s,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,x,s,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,f,s,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,x,s,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,x,s,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,x,y,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,x,s,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,f,s,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,x,s,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,f,y,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,x,s,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,f,s,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,f,y,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,x,y,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,k,y,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,x,y,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,f,s,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,f,s,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d e,x,f,g,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,s,g p,x,s,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,x,s,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,x,s,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,x,s,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,y,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d e,b,f,g,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,s,g p,f,y,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,f,y,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,f,s,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,f,y,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,x,y,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,f,y,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,x,s,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d e,k,f,g,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,s,g e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,o,c,l p,f,s,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,x,s,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,f,y,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,f,s,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,f,y,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,x,s,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d e,x,f,w,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,n,g p,f,s,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,x,s,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,x,s,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,k,y,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,f,s,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,x,y,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,f,s,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,x,s,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,x,y,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,f,s,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,f,y,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,y,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,s,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,f,s,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,k,y,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,x,s,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,x,y,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,f,y,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,x,s,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,f,s,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,f,s,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,f,s,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,f,y,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,f,s,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,f,y,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,f,s,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,y,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,x,s,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,k,y,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,x,s,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l e,x,s,g,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,n,g p,k,y,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,f,s,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,f,s,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,f,s,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,f,s,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,x,s,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,f,s,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,k,y,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,f,s,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,k,y,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,f,s,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,o,c,l p,x,s,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,f,y,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,f,y,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,k,y,n,f,m,f,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,x,s,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,f,s,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p e,k,s,w,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,s,g p,f,y,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,y,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,f,s,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,f,s,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,f,y,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,x,s,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,f,y,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,x,s,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,x,s,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,f,y,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,x,s,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,f,y,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,x,s,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,x,y,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d e,k,f,g,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,n,g p,x,s,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,k,y,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,k,y,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,x,y,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,f,s,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,x,s,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,f,s,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,f,y,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,x,s,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,x,y,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,f,s,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,x,s,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,f,s,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,y,v,l p,k,s,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,f,s,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,k,y,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p e,x,y,c,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,y,c,l e,k,s,g,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,n,g e,x,f,g,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,s,g p,x,s,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,k,y,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,o,c,l p,k,s,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,b,y,y,f,n,f,w,n,y,e,c,y,y,y,y,p,y,o,e,w,c,l p,x,s,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d e,b,s,g,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,n,g p,k,y,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,f,s,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,f,y,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,f,s,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d e,k,f,g,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,s,g p,k,s,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,k,s,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,f,s,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l e,b,f,g,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,n,g p,f,y,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,f,s,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,n,c,l e,x,y,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p p,f,s,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,k,y,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l e,b,s,w,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,n,g p,x,y,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,f,y,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,k,y,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d e,x,f,w,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,s,g e,b,s,w,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,n,g p,k,s,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l e,f,y,n,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p p,k,s,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,k,s,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,f,y,e,f,m,a,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,x,s,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,k,y,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,x,s,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,k,s,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,k,y,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p e,x,f,w,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,s,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,f,s,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,k,s,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,k,s,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,k,y,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l e,k,f,w,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,s,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,k,y,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,k,s,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,k,s,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,x,y,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,k,y,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d e,b,s,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,d p,f,s,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,k,y,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d e,x,s,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,d p,f,s,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,k,s,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,x,s,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p e,k,f,w,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,s,g p,f,y,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,x,s,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,s,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,k,s,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,k,s,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,x,s,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d e,b,s,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,p p,k,s,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,x,y,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,f,s,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,n,c,l e,k,s,g,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,n,g p,k,y,e,f,m,f,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d p,k,y,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,o,c,l p,f,y,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,k,y,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d e,k,f,w,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,s,g e,x,s,g,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,s,g e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,o,v,l p,k,y,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,k,y,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,k,s,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p e,x,s,w,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,s,g e,k,s,w,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,n,g e,k,s,w,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,s,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,x,s,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p e,k,s,g,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,s,g e,x,f,w,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,s,g p,k,y,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d e,b,s,w,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,s,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,f,s,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d e,k,s,g,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,s,g e,x,s,w,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,n,g p,f,y,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,x,s,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d e,x,f,w,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,s,g e,k,f,w,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,n,g p,f,s,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d e,f,s,g,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p p,k,s,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,b,c,l e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,n,c,l p,k,y,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,x,s,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,k,s,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l e,k,f,w,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,n,g e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,n,c,l p,k,y,c,f,m,f,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d e,x,f,g,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,s,g e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,o,v,l e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,b,v,l p,k,y,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p e,k,f,w,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,n,g e,x,f,g,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,s,g e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,n,v,l p,k,y,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,k,y,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,f,y,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p e,k,f,g,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,n,g p,f,y,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,f,y,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l e,k,s,g,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,s,g e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,y,c,l p,k,y,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,x,s,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,o,v,l p,k,s,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,k,s,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,x,s,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,k,y,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d e,x,s,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p p,f,s,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,x,y,n,f,m,a,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,k,s,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l e,k,s,g,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,s,g p,k,s,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,f,y,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,k,s,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,k,y,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d e,f,s,c,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p p,f,y,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,k,s,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,x,s,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,f,y,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,x,s,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,n,c,l p,f,s,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,x,y,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,x,y,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,x,s,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l e,b,f,g,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,y,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l e,k,f,g,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,n,g e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,n,v,l p,f,y,n,f,m,f,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,k,s,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,f,s,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,k,y,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,k,s,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,k,y,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l e,x,f,g,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,n,g p,k,y,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,x,y,c,f,m,a,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d p,k,y,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,k,y,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l e,b,s,w,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,s,g p,k,s,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,x,s,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,f,s,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,k,y,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,k,y,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d e,b,f,w,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,n,g p,k,y,n,f,m,a,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,f,y,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,k,s,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,k,y,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l e,x,y,g,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p p,f,s,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,k,y,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p e,k,f,w,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,n,g p,x,s,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,k,y,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,x,s,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d e,k,s,w,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,n,g p,f,y,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,k,s,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,f,y,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,y,v,l p,f,y,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,k,y,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,k,s,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,k,s,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,b,v,l e,k,s,g,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,s,g e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,n,v,l e,x,f,g,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,n,g p,k,s,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,f,y,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,k,s,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,k,s,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p e,b,s,w,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,n,g p,f,s,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d e,b,f,g,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,n,g p,x,s,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,x,y,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,f,y,c,f,m,f,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,f,s,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,x,y,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,f,s,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,f,y,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,f,s,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,x,s,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d e,k,s,g,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,s,g p,x,s,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,k,s,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,k,y,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,x,s,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p e,b,s,g,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,n,g p,x,s,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,f,s,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,k,s,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d e,b,s,g,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,s,g p,x,s,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,f,y,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,f,s,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,f,y,n,f,m,f,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d e,b,f,g,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,s,g p,f,s,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,k,s,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l e,k,s,g,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,n,g p,k,y,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,x,s,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,y,c,l p,k,y,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,f,y,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,b,c,l p,k,s,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,k,s,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,k,s,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,k,s,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p e,f,y,c,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,n,c,l e,b,s,w,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,n,g p,k,s,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p e,b,s,g,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,n,g p,k,y,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,k,y,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,y,c,l p,x,s,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,f,s,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,y,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d e,k,y,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,d p,f,s,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,k,s,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,f,y,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,f,s,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d e,k,f,g,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,n,g p,k,s,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d e,b,f,w,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,s,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l e,x,s,g,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,n,g e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,y,c,l p,k,s,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,k,y,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l e,k,f,g,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,n,g p,x,s,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,k,y,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l e,x,f,w,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,n,g p,k,y,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,k,s,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,k,y,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,k,y,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p e,k,s,g,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,n,g p,k,y,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l e,x,s,g,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,n,g e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,y,v,l e,k,s,g,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,n,g p,x,s,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,k,s,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,k,s,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p e,x,s,g,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,y,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,y,v,l e,k,s,w,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,n,g p,f,y,e,f,m,f,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d e,b,s,g,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,s,g p,f,y,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,b,c,l e,b,s,g,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,n,g e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,y,c,l e,b,s,g,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,n,g p,k,s,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,o,c,l p,k,s,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,f,s,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,k,s,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,k,s,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,y,v,l e,k,f,g,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,s,g e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,o,c,l p,k,s,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,k,y,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,k,y,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,k,s,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,n,c,l p,k,s,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,o,v,l p,k,s,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d e,k,s,w,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,y,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,k,y,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d e,k,f,g,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,s,g p,f,s,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p e,x,s,g,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,n,g p,k,y,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,f,s,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d e,x,f,w,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,n,g p,k,y,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,y,n,f,m,a,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d e,b,f,g,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,n,g p,k,y,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,k,s,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l e,k,f,g,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,n,g e,k,f,w,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,y,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d e,k,s,g,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,n,g p,k,s,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,k,y,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l e,k,s,w,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,y,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l e,b,s,w,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,s,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d e,x,s,w,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,n,g e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,n,v,l p,k,s,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,k,y,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p e,x,f,w,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,n,g p,x,y,e,f,m,a,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d p,k,s,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,k,s,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,b,c,l p,k,y,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l e,f,y,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,d e,k,s,g,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,n,g p,f,y,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,k,y,y,f,n,f,w,n,y,e,c,y,y,y,y,p,y,o,e,w,c,l p,k,y,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,k,y,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,n,c,l e,x,s,g,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p e,k,s,g,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,n,g p,f,y,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,k,y,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l e,b,f,w,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,n,g e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,o,c,l p,k,s,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d e,x,f,w,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,y,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l e,x,f,w,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,y,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,k,y,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p e,x,s,g,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,n,g e,x,s,w,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,n,g p,k,y,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,k,s,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,k,s,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d e,b,f,w,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,n,g p,f,s,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,k,s,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,k,s,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,x,y,n,f,m,f,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d p,k,y,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,y,c,l p,x,y,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,y,v,l e,b,s,w,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,n,g e,b,s,g,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,n,g p,k,y,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,k,s,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,k,s,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,k,s,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d e,b,f,w,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,s,g e,k,s,g,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,n,g p,f,y,e,f,m,f,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,k,y,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,k,y,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,f,s,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,k,y,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,k,y,c,f,m,f,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d p,k,y,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d e,k,s,w,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,n,g p,f,y,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l e,b,f,g,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,s,g p,f,s,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,k,s,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l e,k,s,g,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,s,g e,x,s,g,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,s,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,y,c,l e,f,y,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p e,b,s,w,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,n,g p,f,y,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,f,s,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l e,k,f,g,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,n,g e,x,f,w,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,s,g e,x,s,c,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p e,k,f,g,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,s,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,k,y,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,k,s,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,x,y,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,o,c,l p,f,y,y,f,n,f,w,n,w,e,c,y,y,y,y,p,y,o,e,w,c,l p,x,y,c,f,m,a,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,x,s,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d e,x,y,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p p,k,y,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p e,k,s,g,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,n,g e,b,s,g,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,s,g p,k,s,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,b,v,l e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,b,v,l e,f,s,n,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p e,k,s,g,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,s,g p,f,s,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,k,s,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,f,y,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,k,y,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,k,s,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,k,s,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p e,b,s,w,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,n,g p,k,y,n,f,m,f,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d p,k,y,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,y,v,l p,k,s,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p e,b,s,w,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,s,g e,x,s,g,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,s,g p,k,s,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,k,s,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,k,y,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p e,b,s,g,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,s,g p,k,y,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p e,b,f,w,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,s,g p,c,y,y,f,n,f,w,n,y,e,c,y,y,y,y,p,y,o,e,w,c,l p,x,s,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,k,y,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l e,x,s,g,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,s,g e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,y,v,l p,k,y,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,n,c,l p,k,y,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,k,y,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,k,s,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p e,b,s,g,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,s,g e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,n,c,l e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,n,v,l p,x,s,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d e,x,s,g,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p e,x,f,g,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,s,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l e,k,f,g,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,n,g p,k,s,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,k,y,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,k,y,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d e,f,s,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p p,k,y,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,k,y,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,b,c,l p,k,y,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,k,y,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,f,y,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,k,y,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,o,c,l p,f,s,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p e,k,s,g,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,s,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,k,s,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,o,v,l p,k,s,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l e,x,f,g,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,s,g e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,o,v,l p,f,s,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,k,s,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d e,f,y,n,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p e,x,f,g,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,n,g e,k,s,w,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,n,g e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,b,c,l p,k,y,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,k,y,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l e,k,y,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,p e,x,f,g,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,s,g p,k,s,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,k,y,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,k,y,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,f,y,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,b,v,l p,f,y,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,k,s,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,k,s,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,y,c,l e,x,f,g,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,n,g p,k,s,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,k,y,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p e,x,s,g,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,y,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,k,s,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,k,y,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,o,c,l e,b,s,g,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,s,g p,x,y,e,f,m,a,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,k,s,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,k,y,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,k,y,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,k,s,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,k,y,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,k,s,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,x,s,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,k,s,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d e,b,f,g,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,s,g p,k,y,n,f,m,a,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d e,f,s,n,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p p,k,s,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,f,y,y,f,n,f,w,n,y,e,c,y,y,y,y,p,y,o,e,w,c,l p,k,s,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,f,y,e,f,m,a,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d e,x,f,g,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,n,g p,k,y,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,k,s,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,f,y,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,y,c,l p,k,y,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,f,y,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,k,s,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,f,y,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,k,s,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,k,y,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p e,x,s,w,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,s,g e,x,s,g,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,s,g e,x,f,w,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,s,g p,k,s,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,k,s,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,k,y,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,k,s,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,k,y,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,k,y,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,k,s,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,k,s,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,o,c,l p,f,s,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,k,s,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l e,x,s,g,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,n,g e,x,f,w,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,n,g p,k,y,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,o,c,l p,k,y,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,k,y,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,k,y,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,k,y,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,k,s,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,b,c,l e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,n,c,l e,b,s,w,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,s,g p,k,s,n,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,n,c,l p,k,y,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d e,b,f,g,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,s,g e,b,s,g,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,n,g p,x,s,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,b,c,l e,x,s,w,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,n,g e,x,s,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,p e,k,s,g,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,s,g e,x,s,w,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,n,g p,f,y,c,f,m,f,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,y,c,l p,k,s,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,k,y,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l e,x,s,w,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,n,g e,k,f,w,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,s,g e,b,f,g,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,s,g e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,b,v,l p,k,y,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,f,y,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,n,v,l e,f,s,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p p,k,y,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p e,b,s,w,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,s,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p e,k,s,w,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,s,g p,k,y,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,k,s,n,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,b,c,l p,k,s,n,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l p,k,y,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,y,v,l e,x,f,w,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,n,g e,x,f,g,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,n,g e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,b,v,l p,k,s,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,k,y,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p e,x,s,w,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,y,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d e,x,f,g,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,s,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,f,y,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d p,k,s,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d e,k,s,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,p p,k,s,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,k,s,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p e,b,s,g,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,y,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,k,s,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p e,k,f,g,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,n,g p,k,y,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,k,s,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,k,y,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,k,s,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d e,k,f,w,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,n,g p,k,y,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,k,y,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d e,b,f,w,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,s,g e,x,s,g,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,n,g e,b,s,g,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,y,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,k,s,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,k,y,e,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d e,b,s,w,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,s,g p,f,s,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,k,s,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d e,k,s,w,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,s,g p,k,y,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,k,s,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,k,s,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d e,x,s,n,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p p,k,s,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,k,y,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,b,y,y,f,n,f,w,n,w,e,c,y,y,y,y,p,y,o,e,w,c,l p,k,y,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l e,x,s,n,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p p,k,s,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p e,k,f,g,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,s,g p,k,s,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,k,s,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,k,s,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l e,x,f,g,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,n,g e,b,s,w,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,n,g p,k,y,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,n,c,l p,k,y,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,k,s,e,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p e,b,s,g,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,s,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,o,v,l p,f,s,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,k,s,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,k,s,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l e,b,f,g,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,n,g e,k,s,w,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,s,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,f,y,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d e,x,s,w,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,s,g e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,b,c,l p,k,s,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,k,y,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,b,v,l e,b,f,w,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,s,g e,x,s,w,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,n,g p,f,y,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,k,y,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,x,y,e,f,m,f,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,y,c,l p,k,s,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,k,y,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d e,b,s,w,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,s,g e,b,s,g,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,s,g e,k,f,g,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,n,g e,k,f,g,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,n,g e,x,f,w,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,n,g p,k,y,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,f,y,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,k,y,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,f,s,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l e,b,s,w,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,s,g e,k,s,w,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,s,g e,b,f,w,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,n,g e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,b,c,l p,k,y,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,k,s,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,k,s,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,f,y,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,x,s,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,o,v,l e,k,f,w,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,s,g p,k,s,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d e,b,f,g,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,s,g p,k,y,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,y,c,l e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,n,v,l p,k,y,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,k,y,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p p,k,y,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,k,y,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d e,x,s,g,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,s,g p,k,y,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d e,f,y,c,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,n,v,l p,k,s,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,k,s,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,k,y,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p e,b,f,g,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,s,g p,k,y,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p e,b,f,w,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,s,g p,k,s,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l e,x,s,w,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,s,g p,k,y,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,k,y,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d e,x,s,w,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,n,g p,k,y,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,k,y,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,o,v,l e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,n,v,l p,k,s,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,k,s,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,n,c,l p,k,s,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,k,s,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,k,y,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,k,y,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,k,y,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l e,k,f,w,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,n,g e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,n,v,l p,k,s,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,b,v,l e,f,y,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,p p,k,y,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l e,f,s,g,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p e,x,s,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p p,c,y,y,f,n,f,w,n,w,e,c,y,y,y,y,p,y,o,e,w,c,l p,k,s,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p p,k,y,e,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,k,y,e,f,m,a,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,o,v,l p,k,s,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l e,x,s,w,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,s,g p,x,s,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,x,y,c,f,m,f,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,f,s,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,b,c,l e,b,y,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,d p,f,s,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,k,s,n,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p e,b,s,g,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,s,g e,x,y,n,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p p,f,s,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,y,c,l e,b,f,w,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,n,g e,x,f,w,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,n,g p,k,s,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,x,y,n,f,m,a,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d p,k,y,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,b,c,l p,k,s,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,x,s,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,k,s,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,k,y,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,k,y,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l p,k,s,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d e,b,f,g,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,n,g e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,y,v,l p,k,y,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,k,y,y,f,n,f,w,n,w,e,c,y,y,y,y,p,y,o,e,w,c,l e,k,s,w,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,n,g e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,y,c,l p,k,s,n,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p e,k,f,g,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,s,g e,k,f,w,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,n,g e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,b,c,l e,x,s,w,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,n,g e,b,s,g,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,n,g e,x,f,w,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,n,g e,k,f,w,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,n,g p,k,s,n,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,k,y,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d e,k,f,g,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,s,g e,x,s,w,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,s,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,k,y,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,k,y,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,n,v,l p,k,s,e,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p e,x,s,g,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,n,g e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,y,v,l e,b,s,w,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,n,g p,k,s,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,n,v,l p,k,s,n,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,k,s,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,k,y,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p e,b,f,w,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,y,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,k,s,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d e,b,s,g,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,s,g p,k,s,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,x,s,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,k,y,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l e,x,s,w,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,n,g e,x,s,w,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,s,g p,k,y,n,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p e,k,s,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,d p,k,s,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,k,y,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,o,v,l e,b,f,g,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,n,g p,k,s,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,k,s,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l p,f,y,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,f,y,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,y,c,l p,k,y,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d e,k,s,w,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,s,g e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,b,c,l p,k,y,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p p,k,s,n,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d e,k,s,w,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,n,g p,k,y,e,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l e,x,s,w,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,y,e,f,s,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,k,y,e,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,k,y,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,f,y,c,f,m,a,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,x,s,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d e,k,f,g,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,s,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,x,y,n,f,m,f,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,f,y,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,b,c,l p,k,s,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p e,b,f,g,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,n,g e,b,f,w,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,n,g e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,y,v,l p,k,y,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,o,c,l e,x,s,w,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,n,g p,k,s,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,k,s,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,p e,x,s,g,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,n,g e,b,s,g,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,n,g p,k,y,n,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d p,k,y,e,f,m,f,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,k,y,e,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,k,y,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p e,x,f,w,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,y,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,b,v,l p,k,y,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,k,s,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,y,v,l e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,n,v,l e,k,s,g,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,n,g e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,y,c,l p,k,y,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,b,v,l e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,n,c,l p,k,y,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,d e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,n,c,l p,k,s,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d e,b,f,g,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,n,g p,k,y,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,b,v,l p,k,s,n,f,s,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,l e,x,s,g,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,s,g e,x,s,g,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,s,g e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,b,v,l e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,b,c,l p,k,y,e,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d e,x,f,g,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,n,g p,k,s,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,k,y,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,k,y,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,k,y,n,f,s,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,k,y,e,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l e,x,s,w,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,n,g p,k,s,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,k,s,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p e,x,f,g,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,n,g e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,o,c,l e,b,s,w,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,n,g p,k,s,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,k,y,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,k,s,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,x,y,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,k,y,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,b,v,l e,x,s,g,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,s,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,k,y,e,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l e,k,s,w,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,n,g e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,b,v,l e,k,s,w,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,n,g p,k,s,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,k,y,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,k,s,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l p,k,s,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,x,s,n,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,n,c,l p,k,s,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,k,s,n,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d p,k,y,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l e,x,f,w,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,s,g p,f,s,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,k,s,n,f,y,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,k,s,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,b,v,l e,x,y,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,d p,k,y,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,k,s,e,f,s,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,l e,b,s,w,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,s,g p,k,y,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p p,k,s,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,p e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,n,c,l e,x,s,g,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,s,g e,x,s,g,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,n,g p,f,y,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,f,y,n,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d e,f,y,g,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p p,k,s,e,f,y,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d e,x,f,w,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,y,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,k,s,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p p,x,s,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p e,x,f,g,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,s,g e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,n,v,l p,x,y,e,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p e,b,f,w,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,s,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l e,x,f,g,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,s,g p,f,y,n,f,m,a,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,o,v,l e,b,s,g,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,n,g e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,o,v,l p,k,s,e,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,o,v,l e,x,f,g,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,n,g p,k,s,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p e,x,f,w,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,n,g e,f,y,p,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p p,k,y,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l e,k,f,g,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,n,g e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,y,c,l p,k,s,n,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d p,k,s,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l p,k,s,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,k,y,n,f,s,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,d e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,o,c,l p,k,y,n,f,s,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p e,k,f,w,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,s,g p,k,y,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p e,f,s,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,p p,k,s,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p e,x,f,g,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,s,g p,k,y,e,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,d p,k,y,e,f,y,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,k,s,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,o,c,l e,k,s,w,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,n,g e,b,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,o,c,l e,f,y,g,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p p,k,y,e,f,m,a,c,b,w,e,c,k,y,c,c,p,w,n,n,w,c,d p,x,y,e,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,k,y,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,y,v,l e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,o,c,l e,x,y,c,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,l p,k,s,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l p,k,y,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,k,y,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p e,f,s,c,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,v,p e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,n,c,l e,b,f,w,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,n,g e,k,f,g,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,s,g e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,o,c,l e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,o,c,l e,k,f,w,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,n,g p,k,y,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,l e,b,f,w,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,s,g p,k,y,n,f,y,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,k,y,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,k,y,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,y,v,l e,x,y,n,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p e,b,s,w,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,n,g p,f,y,n,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,d p,k,s,n,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,k,s,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,y,c,l e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,n,v,l e,b,s,w,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,s,g p,x,y,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p e,b,f,w,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,s,g e,b,f,w,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,n,g e,b,f,w,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,n,g e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,o,v,l p,k,y,e,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,p e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,o,v,l p,k,s,e,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,d p,k,y,c,f,m,a,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d p,k,s,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d e,x,s,g,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,n,g e,f,s,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,d e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,y,c,l e,b,y,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,p p,x,s,n,f,f,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,b,c,l p,f,s,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p p,k,y,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p e,k,s,g,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,n,g p,k,y,n,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l e,k,f,g,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,s,g e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,o,c,l p,k,s,e,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,y,v,l p,k,s,n,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,k,y,n,f,s,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,n,v,l e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,n,c,l e,x,y,n,f,n,f,c,b,w,e,b,y,y,n,n,p,w,t,p,w,y,p e,x,s,w,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,s,g e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,o,v,l p,f,s,n,f,f,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,x,y,e,f,s,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,d p,k,y,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,k,s,e,f,f,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,k,s,e,f,f,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,p e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,n,v,l e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,y,v,l e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,y,v,l p,k,s,n,f,s,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,b,v,l e,k,s,g,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,s,g e,k,f,w,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,s,g p,k,s,e,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,p e,b,f,w,f,n,f,w,b,g,e,?,k,k,w,w,p,w,t,p,w,n,g e,x,s,w,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,s,g e,b,f,w,f,n,f,w,b,p,e,?,s,k,w,w,p,w,t,p,w,s,g p,k,y,n,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,d p,f,s,n,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l p,f,y,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,k,s,e,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,p p,k,y,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,y,c,l e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,n,v,l p,k,y,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,l p,k,s,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l e,x,f,g,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,n,g e,k,s,w,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,s,g p,k,y,e,f,f,f,c,n,b,t,?,s,k,p,p,p,w,o,e,w,v,p p,x,s,n,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,d p,k,y,n,f,f,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,l e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,b,c,l e,b,f,w,f,n,f,w,b,p,e,?,k,s,w,w,p,w,t,p,w,n,g e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,b,v,l p,k,y,e,f,y,f,c,n,b,t,?,k,k,p,w,p,w,o,e,w,v,d e,x,y,g,t,n,f,c,b,w,e,b,s,s,w,w,p,w,t,p,w,y,p p,k,s,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,y,v,l p,k,y,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,p e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,b,c,l e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,b,v,l e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,y,c,l p,k,y,e,f,y,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p e,b,f,g,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,n,g p,k,s,e,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,k,s,n,f,y,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d p,k,y,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,l p,k,s,n,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,d e,x,f,w,f,n,f,w,b,w,e,?,s,k,w,w,p,w,t,p,w,s,g e,f,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,o,v,l p,k,y,n,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d e,x,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,n,v,l e,b,f,g,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,n,g e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,y,v,l e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,o,v,l p,k,s,e,f,s,f,c,n,b,t,?,s,k,w,p,p,w,o,e,w,v,l p,k,s,n,f,f,f,c,n,b,t,?,s,s,w,p,p,w,o,e,w,v,p p,k,s,n,f,s,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,k,s,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,k,y,n,f,y,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l e,k,f,w,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,s,g p,k,y,e,f,f,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,l e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,b,v,l p,k,s,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p e,b,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,b,c,l e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,b,c,l e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,n,c,l p,k,y,e,f,s,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,l e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,y,v,l p,k,y,e,f,f,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,p e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,y,v,l e,b,f,g,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,n,g e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,o,c,l e,b,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,y,c,l e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,o,v,l e,b,f,g,f,n,f,w,b,g,e,?,s,s,w,w,p,w,t,p,w,s,g p,k,y,e,f,f,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l p,k,s,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,d p,k,y,n,f,f,f,c,n,b,t,?,k,s,w,w,p,w,o,e,w,v,p p,k,s,e,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,p p,k,y,n,f,y,f,c,n,b,t,?,s,s,w,w,p,w,o,e,w,v,l e,b,f,g,f,n,f,w,b,p,e,?,k,k,w,w,p,w,t,p,w,s,g e,k,f,w,f,n,f,w,b,g,e,?,s,k,w,w,p,w,t,p,w,s,g e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,n,o,p,o,v,l p,x,s,e,f,f,f,c,n,b,t,?,k,s,w,p,p,w,o,e,w,v,p e,k,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,n,v,l p,k,y,e,f,f,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d p,k,s,n,f,f,f,c,n,b,t,?,k,s,p,p,p,w,o,e,w,v,d p,k,y,e,f,f,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,p p,k,y,e,f,y,f,c,n,b,t,?,s,s,p,p,p,w,o,e,w,v,p p,x,s,n,f,y,f,c,n,b,t,?,k,k,w,w,p,w,o,e,w,v,d e,b,s,g,f,n,f,w,b,g,e,?,k,s,w,w,p,w,t,p,w,n,g p,x,y,c,f,m,f,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d e,k,f,w,f,n,f,w,b,w,e,?,k,s,w,w,p,w,t,p,w,n,g p,k,y,n,f,s,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,l p,k,s,e,f,y,f,c,n,b,t,?,k,k,w,p,p,w,o,e,w,v,d e,k,f,w,f,n,f,w,b,w,e,?,k,k,w,w,p,w,t,p,w,s,g e,f,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,b,v,l p,k,s,e,f,s,f,c,n,b,t,?,s,s,p,w,p,w,o,e,w,v,p e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,n,c,l e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,o,c,l e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,n,v,l e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,y,v,l e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,n,v,l e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,n,c,l p,k,y,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,l e,b,s,w,f,n,f,w,b,w,e,?,s,s,w,w,p,w,t,p,w,n,g e,x,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,o,o,p,n,v,l e,k,s,w,f,n,f,w,b,p,e,?,s,s,w,w,p,w,t,p,w,n,g e,k,s,n,f,n,a,c,b,o,e,?,s,s,o,o,p,n,o,p,b,v,l p,k,y,e,f,y,f,c,n,b,t,?,k,k,p,p,p,w,o,e,w,v,d p,f,y,c,f,m,a,c,b,y,e,c,k,y,c,c,p,w,n,n,w,c,d e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,o,v,l p,k,y,n,f,s,f,c,n,b,t,?,s,k,p,w,p,w,o,e,w,v,l p,k,s,e,f,y,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d p,k,y,n,f,f,f,c,n,b,t,?,k,s,p,w,p,w,o,e,w,v,d e,k,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,b,c,l e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,n,o,p,b,v,l e,f,s,n,f,n,a,c,b,n,e,?,s,s,o,o,p,o,o,p,b,c,l p,k,y,n,f,y,f,c,n,b,t,?,s,k,w,w,p,w,o,e,w,v,l e,x,s,n,f,n,a,c,b,y,e,?,s,s,o,o,p,o,o,p,o,c,l xgboost-1.5.2/demo/CLI/binary_classification/agaricus-lepiota.fmap000066400000000000000000000042321417122711700252000ustar00rootroot00000000000000 1. cap-shape: bell=b,conical=c,convex=x,flat=f,knobbed=k,sunken=s 2. cap-surface: fibrous=f,grooves=g,scaly=y,smooth=s 3. cap-color: brown=n,buff=b,cinnamon=c,gray=g,green=r,pink=p,purple=u,red=e,white=w,yellow=y 4. bruises?: bruises=t,no=f 5. odor: almond=a,anise=l,creosote=c,fishy=y,foul=f, musty=m,none=n,pungent=p,spicy=s 6. gill-attachment: attached=a,descending=d,free=f,notched=n 7. gill-spacing: close=c,crowded=w,distant=d 8. gill-size: broad=b,narrow=n 9. gill-color: black=k,brown=n,buff=b,chocolate=h,gray=g, green=r,orange=o,pink=p,purple=u,red=e, white=w,yellow=y 10. stalk-shape: enlarging=e,tapering=t 11. stalk-root: bulbous=b,club=c,cup=u,equal=e, rhizomorphs=z,rooted=r,missing=? 12. stalk-surface-above-ring: fibrous=f,scaly=y,silky=k,smooth=s 13. stalk-surface-below-ring: fibrous=f,scaly=y,silky=k,smooth=s 14. stalk-color-above-ring: brown=n,buff=b,cinnamon=c,gray=g,orange=o, pink=p,red=e,white=w,yellow=y 15. stalk-color-below-ring: brown=n,buff=b,cinnamon=c,gray=g,orange=o, pink=p,red=e,white=w,yellow=y 16. veil-type: partial=p,universal=u 17. veil-color: brown=n,orange=o,white=w,yellow=y 18. ring-number: none=n,one=o,two=t 19. ring-type: cobwebby=c,evanescent=e,flaring=f,large=l, none=n,pendant=p,sheathing=s,zone=z 20. spore-print-color: black=k,brown=n,buff=b,chocolate=h,green=r, orange=o,purple=u,white=w,yellow=y 21. population: abundant=a,clustered=c,numerous=n, scattered=s,several=v,solitary=y 22. habitat: grasses=g,leaves=l,meadows=m,paths=p, urban=u,waste=w,woods=d xgboost-1.5.2/demo/CLI/binary_classification/agaricus-lepiota.names000066400000000000000000000152401417122711700253610ustar00rootroot000000000000001. Title: Mushroom Database 2. Sources: (a) Mushroom records drawn from The Audubon Society Field Guide to North American Mushrooms (1981). G. H. Lincoff (Pres.), New York: Alfred A. Knopf (b) Donor: Jeff Schlimmer (Jeffrey.Schlimmer@a.gp.cs.cmu.edu) (c) Date: 27 April 1987 3. Past Usage: 1. Schlimmer,J.S. (1987). Concept Acquisition Through Representational Adjustment (Technical Report 87-19). Doctoral disseration, Department of Information and Computer Science, University of California, Irvine. --- STAGGER: asymptoted to 95% classification accuracy after reviewing 1000 instances. 2. Iba,W., Wogulis,J., & Langley,P. (1988). Trading off Simplicity and Coverage in Incremental Concept Learning. In Proceedings of the 5th International Conference on Machine Learning, 73-79. Ann Arbor, Michigan: Morgan Kaufmann. -- approximately the same results with their HILLARY algorithm 3. In the following references a set of rules (given below) were learned for this data set which may serve as a point of comparison for other researchers. Duch W, Adamczak R, Grabczewski K (1996) Extraction of logical rules from training data using backpropagation networks, in: Proc. of the The 1st Online Workshop on Soft Computing, 19-30.Aug.1996, pp. 25-30, available on-line at: http://www.bioele.nuee.nagoya-u.ac.jp/wsc1/ Duch W, Adamczak R, Grabczewski K, Ishikawa M, Ueda H, Extraction of crisp logical rules using constrained backpropagation networks - comparison of two new approaches, in: Proc. of the European Symposium on Artificial Neural Networks (ESANN'97), Bruge, Belgium 16-18.4.1997, pp. xx-xx Wlodzislaw Duch, Department of Computer Methods, Nicholas Copernicus University, 87-100 Torun, Grudziadzka 5, Poland e-mail: duch@phys.uni.torun.pl WWW http://www.phys.uni.torun.pl/kmk/ Date: Mon, 17 Feb 1997 13:47:40 +0100 From: Wlodzislaw Duch Organization: Dept. of Computer Methods, UMK I have attached a file containing logical rules for mushrooms. It should be helpful for other people since only in the last year I have seen about 10 papers analyzing this dataset and obtaining quite complex rules. We will try to contribute other results later. With best regards, Wlodek Duch ________________________________________________________________ Logical rules for the mushroom data sets. Logical rules given below seem to be the simplest possible for the mushroom dataset and therefore should be treated as benchmark results. Disjunctive rules for poisonous mushrooms, from most general to most specific: P_1) odor=NOT(almond.OR.anise.OR.none) 120 poisonous cases missed, 98.52% accuracy P_2) spore-print-color=green 48 cases missed, 99.41% accuracy P_3) odor=none.AND.stalk-surface-below-ring=scaly.AND. (stalk-color-above-ring=NOT.brown) 8 cases missed, 99.90% accuracy P_4) habitat=leaves.AND.cap-color=white 100% accuracy Rule P_4) may also be P_4') population=clustered.AND.cap_color=white These rule involve 6 attributes (out of 22). Rules for edible mushrooms are obtained as negation of the rules given above, for example the rule: odor=(almond.OR.anise.OR.none).AND.spore-print-color=NOT.green gives 48 errors, or 99.41% accuracy on the whole dataset. Several slightly more complex variations on these rules exist, involving other attributes, such as gill_size, gill_spacing, stalk_surface_above_ring, but the rules given above are the simplest we have found. 4. Relevant Information: This data set includes descriptions of hypothetical samples corresponding to 23 species of gilled mushrooms in the Agaricus and Lepiota Family (pp. 500-525). Each species is identified as definitely edible, definitely poisonous, or of unknown edibility and not recommended. This latter class was combined with the poisonous one. The Guide clearly states that there is no simple rule for determining the edibility of a mushroom; no rule like ``leaflets three, let it be'' for Poisonous Oak and Ivy. 5. Number of Instances: 8124 6. Number of Attributes: 22 (all nominally valued) 7. Attribute Information: (classes: edible=e, poisonous=p) 1. cap-shape: bell=b,conical=c,convex=x,flat=f, knobbed=k,sunken=s 2. cap-surface: fibrous=f,grooves=g,scaly=y,smooth=s 3. cap-color: brown=n,buff=b,cinnamon=c,gray=g,green=r, pink=p,purple=u,red=e,white=w,yellow=y 4. bruises?: bruises=t,no=f 5. odor: almond=a,anise=l,creosote=c,fishy=y,foul=f, musty=m,none=n,pungent=p,spicy=s 6. gill-attachment: attached=a,descending=d,free=f,notched=n 7. gill-spacing: close=c,crowded=w,distant=d 8. gill-size: broad=b,narrow=n 9. gill-color: black=k,brown=n,buff=b,chocolate=h,gray=g, green=r,orange=o,pink=p,purple=u,red=e, white=w,yellow=y 10. stalk-shape: enlarging=e,tapering=t 11. stalk-root: bulbous=b,club=c,cup=u,equal=e, rhizomorphs=z,rooted=r,missing=? 12. stalk-surface-above-ring: fibrous=f,scaly=y,silky=k,smooth=s 13. stalk-surface-below-ring: fibrous=f,scaly=y,silky=k,smooth=s 14. stalk-color-above-ring: brown=n,buff=b,cinnamon=c,gray=g,orange=o, pink=p,red=e,white=w,yellow=y 15. stalk-color-below-ring: brown=n,buff=b,cinnamon=c,gray=g,orange=o, pink=p,red=e,white=w,yellow=y 16. veil-type: partial=p,universal=u 17. veil-color: brown=n,orange=o,white=w,yellow=y 18. ring-number: none=n,one=o,two=t 19. ring-type: cobwebby=c,evanescent=e,flaring=f,large=l, none=n,pendant=p,sheathing=s,zone=z 20. spore-print-color: black=k,brown=n,buff=b,chocolate=h,green=r, orange=o,purple=u,white=w,yellow=y 21. population: abundant=a,clustered=c,numerous=n, scattered=s,several=v,solitary=y 22. habitat: grasses=g,leaves=l,meadows=m,paths=p, urban=u,waste=w,woods=d 8. Missing Attribute Values: 2480 of them (denoted by "?"), all for attribute #11. 9. Class Distribution: -- edible: 4208 (51.8%) -- poisonous: 3916 (48.2%) -- total: 8124 instances xgboost-1.5.2/demo/CLI/binary_classification/mapfeat.py000077500000000000000000000022261417122711700230750ustar00rootroot00000000000000#!/usr/bin/python def loadfmap( fname ): fmap = {} nmap = {} for l in open( fname ): arr = l.split() if arr[0].find('.') != -1: idx = int( arr[0].strip('.') ) assert idx not in fmap fmap[ idx ] = {} ftype = arr[1].strip(':') content = arr[2] else: content = arr[0] for it in content.split(','): if it.strip() == '': continue k , v = it.split('=') fmap[ idx ][ v ] = len(nmap) nmap[ len(nmap) ] = ftype+'='+k return fmap, nmap def write_nmap( fo, nmap ): for i in range( len(nmap) ): fo.write('%d\t%s\ti\n' % (i, nmap[i]) ) # start here fmap, nmap = loadfmap( 'agaricus-lepiota.fmap' ) fo = open( 'featmap.txt', 'w' ) write_nmap( fo, nmap ) fo.close() fo = open( 'agaricus.txt', 'w' ) for l in open( 'agaricus-lepiota.data' ): arr = l.split(',') if arr[0] == 'p': fo.write('1') else: assert arr[0] == 'e' fo.write('0') for i in range( 1,len(arr) ): fo.write( ' %d:1' % fmap[i][arr[i].strip()] ) fo.write('\n') fo.close() xgboost-1.5.2/demo/CLI/binary_classification/mknfold.py000077500000000000000000000007621417122711700231150ustar00rootroot00000000000000#!/usr/bin/python import sys import random if len(sys.argv) < 2: print ('Usage: [nfold = 5]') exit(0) random.seed( 10 ) k = int( sys.argv[2] ) if len(sys.argv) > 3: nfold = int( sys.argv[3] ) else: nfold = 5 fi = open( sys.argv[1], 'r' ) ftr = open( sys.argv[1]+'.train', 'w' ) fte = open( sys.argv[1]+'.test', 'w' ) for l in fi: if random.randint( 1 , nfold ) == k: fte.write( l ) else: ftr.write( l ) fi.close() ftr.close() fte.close() xgboost-1.5.2/demo/CLI/binary_classification/mushroom.conf000066400000000000000000000016451417122711700236270ustar00rootroot00000000000000# General Parameters, see comment for each definition # choose the booster, can be gbtree or gblinear booster = gbtree # choose logistic regression loss function for binary classification objective = binary:logistic # Tree Booster Parameters # step size shrinkage eta = 1.0 # minimum loss reduction required to make a further partition gamma = 1.0 # minimum sum of instance weight(hessian) needed in a child min_child_weight = 1 # maximum depth of a tree max_depth = 3 # Task Parameters # the number of round to do boosting num_round = 2 # 0 means do not save any model except the final round model save_period = 2 # The path of training data data = "agaricus.txt.train" # The path of validation data, used to monitor training process, here [test] sets name of the validation set eval[test] = "agaricus.txt.test" # evaluate on training data as well each round eval_train = 1 # The path of test data test:data = "agaricus.txt.test" xgboost-1.5.2/demo/CLI/binary_classification/runexp.sh000077500000000000000000000011501417122711700227560ustar00rootroot00000000000000#!/bin/bash # map feature using indicator encoding, also produce featmap.txt python mapfeat.py # split train and test python mknfold.py agaricus.txt 1 XGBOOST=../../../xgboost # training and output the models $XGBOOST mushroom.conf # output prediction task=pred $XGBOOST mushroom.conf task=pred model_in=0002.model # print the boosters of 00002.model in dump.raw.txt $XGBOOST mushroom.conf task=dump model_in=0002.model name_dump=dump.raw.txt # use the feature map in printing for better visualization $XGBOOST mushroom.conf task=dump model_in=0002.model fmap=featmap.txt name_dump=dump.nice.txt cat dump.nice.txt xgboost-1.5.2/demo/CLI/distributed-training/000077500000000000000000000000001417122711700206755ustar00rootroot00000000000000xgboost-1.5.2/demo/CLI/distributed-training/README.md000066400000000000000000000021031417122711700221500ustar00rootroot00000000000000Distributed XGBoost Training ============================ This is an tutorial of Distributed XGBoost Training. Currently xgboost supports distributed training via CLI program with the configuration file. There is also plan push distributed python and other language bindings, please open an issue if you are interested in contributing. Build XGBoost with Distributed Filesystem Support ------------------------------------------------- To use distributed xgboost, you only need to turn the options on to build with distributed filesystems(HDFS or S3) in cmake. ``` cmake -DUSE_HDFS=ON -DUSE_S3=ON -DUSE_AZURE=ON ``` Step by Step Tutorial on AWS ---------------------------- Checkout [this tutorial](https://xgboost.readthedocs.org/en/latest/tutorials/aws_yarn.html) for running distributed xgboost. Model Analysis -------------- XGBoost is exchangeable across all bindings and platforms. This means you can use python or R to analyze the learnt model and do prediction. For example, you can use the [plot_model.ipynb](plot_model.ipynb) to visualize the learnt model. xgboost-1.5.2/demo/CLI/distributed-training/mushroom.aws.conf000066400000000000000000000015271417122711700242130ustar00rootroot00000000000000# General Parameters, see comment for each definition # choose the booster, can be gbtree or gblinear booster = gbtree # choose logistic regression loss function for binary classification objective = binary:logistic # Tree Booster Parameters # step size shrinkage eta = 1.0 # minimum loss reduction required to make a further partition gamma = 1.0 # minimum sum of instance weight(hessian) needed in a child min_child_weight = 1 # maximum depth of a tree max_depth = 3 # Task Parameters # the number of round to do boosting num_round = 2 # 0 means do not save any model except the final round model save_period = 0 # The path of training data data = "s3://mybucket/xgb-demo/train" # The path of validation data, used to monitor training process, here [test] sets name of the validation set # evaluate on training data as well each round eval_train = 1 xgboost-1.5.2/demo/CLI/distributed-training/plot_model.ipynb000066400000000000000000000040101417122711700240710ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# XGBoost Model Analysis\n", "\n", "This notebook can be used to load and analysis model learnt from all xgboost bindings, including distributed training. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import sys\n", "import os\n", "%matplotlib inline " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Please change the ```pkg_path``` and ```model_file``` to be correct path" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "pkg_path = '../../python-package/'\n", "model_file = 's3://my-bucket/xgb-demo/model/0002.model'\n", "sys.path.insert(0, pkg_path)\n", "import xgboost as xgb" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Plot the Feature Importance" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# plot the first two trees.\n", "bst = xgb.Booster(model_file=model_file)\n", "xgb.plot_importance(bst)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Plot the First Tree" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "tree_id = 0\n", "xgb.to_graphviz(bst, tree_id)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.3" } }, "nbformat": 4, "nbformat_minor": 0 } xgboost-1.5.2/demo/CLI/distributed-training/run_aws.sh000066400000000000000000000007141417122711700227110ustar00rootroot00000000000000# This is the example script to run distributed xgboost on AWS. # Change the following two lines for configuration export BUCKET=mybucket # submit the job to YARN ../../../dmlc-core/tracker/dmlc-submit --cluster=yarn --num-workers=2 --worker-cores=2\ ../../../xgboost mushroom.aws.conf nthread=2\ data=s3://${BUCKET}/xgb-demo/train\ eval[test]=s3://${BUCKET}/xgb-demo/test\ model_dir=s3://${BUCKET}/xgb-demo/model xgboost-1.5.2/demo/CLI/regression/000077500000000000000000000000001417122711700167225ustar00rootroot00000000000000xgboost-1.5.2/demo/CLI/regression/README.md000066400000000000000000000021411417122711700201770ustar00rootroot00000000000000Regression ==== Using XGBoost for regression is very similar to using it for binary classification. We suggest that you can refer to the [binary classification demo](../binary_classification) first. In XGBoost if we use negative log likelihood as the loss function for regression, the training procedure is same as training binary classifier of XGBoost. ### Tutorial The dataset we used is the [computer hardware dataset from UCI repository](https://archive.ics.uci.edu/ml/datasets/Computer+Hardware). The demo for regression is almost the same as the [binary classification demo](../binary_classification), except a little difference in general parameter: ``` # General parameter # this is the only difference with classification, use reg:squarederror to do linear regression # when labels are in [0,1] we can also use reg:logistic objective = reg:squarederror ... ``` The input format is same as binary classification, except that the label is now the target regression values. We use linear regression here, if we want use objective = reg:logistic logistic regression, the label needed to be pre-scaled into [0,1]. xgboost-1.5.2/demo/CLI/regression/machine.conf000066400000000000000000000017031417122711700211760ustar00rootroot00000000000000# General Parameters, see comment for each definition # choose the tree booster, can also change to gblinear booster = gbtree # this is the only difference with classification, use reg:squarederror to do linear classification # when labels are in [0,1] we can also use reg:logistic objective = reg:squarederror # Tree Booster Parameters # step size shrinkage eta = 1.0 # minimum loss reduction required to make a further partition gamma = 1.0 # minimum sum of instance weight(hessian) needed in a child min_child_weight = 1 # maximum depth of a tree max_depth = 3 # Task parameters # the number of round to do boosting num_round = 2 # 0 means do not save any model except the final round model save_period = 0 # The path of training data data = "machine.txt.train" # The path of validation data, used to monitor training process, here [test] sets name of the validation set eval[test] = "machine.txt.test" # The path of test data test:data = "machine.txt.test" xgboost-1.5.2/demo/CLI/regression/machine.data000066400000000000000000000210261417122711700211620ustar00rootroot00000000000000adviser,32/60,125,256,6000,256,16,128,198,199 amdahl,470v/7,29,8000,32000,32,8,32,269,253 amdahl,470v/7a,29,8000,32000,32,8,32,220,253 amdahl,470v/7b,29,8000,32000,32,8,32,172,253 amdahl,470v/7c,29,8000,16000,32,8,16,132,132 amdahl,470v/b,26,8000,32000,64,8,32,318,290 amdahl,580-5840,23,16000,32000,64,16,32,367,381 amdahl,580-5850,23,16000,32000,64,16,32,489,381 amdahl,580-5860,23,16000,64000,64,16,32,636,749 amdahl,580-5880,23,32000,64000,128,32,64,1144,1238 apollo,dn320,400,1000,3000,0,1,2,38,23 apollo,dn420,400,512,3500,4,1,6,40,24 basf,7/65,60,2000,8000,65,1,8,92,70 basf,7/68,50,4000,16000,65,1,8,138,117 bti,5000,350,64,64,0,1,4,10,15 bti,8000,200,512,16000,0,4,32,35,64 burroughs,b1955,167,524,2000,8,4,15,19,23 burroughs,b2900,143,512,5000,0,7,32,28,29 burroughs,b2925,143,1000,2000,0,5,16,31,22 burroughs,b4955,110,5000,5000,142,8,64,120,124 burroughs,b5900,143,1500,6300,0,5,32,30,35 burroughs,b5920,143,3100,6200,0,5,20,33,39 burroughs,b6900,143,2300,6200,0,6,64,61,40 burroughs,b6925,110,3100,6200,0,6,64,76,45 c.r.d,68/10-80,320,128,6000,0,1,12,23,28 c.r.d,universe:2203t,320,512,2000,4,1,3,69,21 c.r.d,universe:68,320,256,6000,0,1,6,33,28 c.r.d,universe:68/05,320,256,3000,4,1,3,27,22 c.r.d,universe:68/137,320,512,5000,4,1,5,77,28 c.r.d,universe:68/37,320,256,5000,4,1,6,27,27 cdc,cyber:170/750,25,1310,2620,131,12,24,274,102 cdc,cyber:170/760,25,1310,2620,131,12,24,368,102 cdc,cyber:170/815,50,2620,10480,30,12,24,32,74 cdc,cyber:170/825,50,2620,10480,30,12,24,63,74 cdc,cyber:170/835,56,5240,20970,30,12,24,106,138 cdc,cyber:170/845,64,5240,20970,30,12,24,208,136 cdc,omega:480-i,50,500,2000,8,1,4,20,23 cdc,omega:480-ii,50,1000,4000,8,1,5,29,29 cdc,omega:480-iii,50,2000,8000,8,1,5,71,44 cambex,1636-1,50,1000,4000,8,3,5,26,30 cambex,1636-10,50,1000,8000,8,3,5,36,41 cambex,1641-1,50,2000,16000,8,3,5,40,74 cambex,1641-11,50,2000,16000,8,3,6,52,74 cambex,1651-1,50,2000,16000,8,3,6,60,74 dec,decsys:10:1091,133,1000,12000,9,3,12,72,54 dec,decsys:20:2060,133,1000,8000,9,3,12,72,41 dec,microvax-1,810,512,512,8,1,1,18,18 dec,vax:11/730,810,1000,5000,0,1,1,20,28 dec,vax:11/750,320,512,8000,4,1,5,40,36 dec,vax:11/780,200,512,8000,8,1,8,62,38 dg,eclipse:c/350,700,384,8000,0,1,1,24,34 dg,eclipse:m/600,700,256,2000,0,1,1,24,19 dg,eclipse:mv/10000,140,1000,16000,16,1,3,138,72 dg,eclipse:mv/4000,200,1000,8000,0,1,2,36,36 dg,eclipse:mv/6000,110,1000,4000,16,1,2,26,30 dg,eclipse:mv/8000,110,1000,12000,16,1,2,60,56 dg,eclipse:mv/8000-ii,220,1000,8000,16,1,2,71,42 formation,f4000/100,800,256,8000,0,1,4,12,34 formation,f4000/200,800,256,8000,0,1,4,14,34 formation,f4000/200ap,800,256,8000,0,1,4,20,34 formation,f4000/300,800,256,8000,0,1,4,16,34 formation,f4000/300ap,800,256,8000,0,1,4,22,34 four-phase,2000/260,125,512,1000,0,8,20,36,19 gould,concept:32/8705,75,2000,8000,64,1,38,144,75 gould,concept:32/8750,75,2000,16000,64,1,38,144,113 gould,concept:32/8780,75,2000,16000,128,1,38,259,157 hp,3000/30,90,256,1000,0,3,10,17,18 hp,3000/40,105,256,2000,0,3,10,26,20 hp,3000/44,105,1000,4000,0,3,24,32,28 hp,3000/48,105,2000,4000,8,3,19,32,33 hp,3000/64,75,2000,8000,8,3,24,62,47 hp,3000/88,75,3000,8000,8,3,48,64,54 hp,3000/iii,175,256,2000,0,3,24,22,20 harris,100,300,768,3000,0,6,24,36,23 harris,300,300,768,3000,6,6,24,44,25 harris,500,300,768,12000,6,6,24,50,52 harris,600,300,768,4500,0,1,24,45,27 harris,700,300,384,12000,6,1,24,53,50 harris,80,300,192,768,6,6,24,36,18 harris,800,180,768,12000,6,1,31,84,53 honeywell,dps:6/35,330,1000,3000,0,2,4,16,23 honeywell,dps:6/92,300,1000,4000,8,3,64,38,30 honeywell,dps:6/96,300,1000,16000,8,2,112,38,73 honeywell,dps:7/35,330,1000,2000,0,1,2,16,20 honeywell,dps:7/45,330,1000,4000,0,3,6,22,25 honeywell,dps:7/55,140,2000,4000,0,3,6,29,28 honeywell,dps:7/65,140,2000,4000,0,4,8,40,29 honeywell,dps:8/44,140,2000,4000,8,1,20,35,32 honeywell,dps:8/49,140,2000,32000,32,1,20,134,175 honeywell,dps:8/50,140,2000,8000,32,1,54,66,57 honeywell,dps:8/52,140,2000,32000,32,1,54,141,181 honeywell,dps:8/62,140,2000,32000,32,1,54,189,181 honeywell,dps:8/20,140,2000,4000,8,1,20,22,32 ibm,3033:s,57,4000,16000,1,6,12,132,82 ibm,3033:u,57,4000,24000,64,12,16,237,171 ibm,3081,26,16000,32000,64,16,24,465,361 ibm,3081:d,26,16000,32000,64,8,24,465,350 ibm,3083:b,26,8000,32000,0,8,24,277,220 ibm,3083:e,26,8000,16000,0,8,16,185,113 ibm,370/125-2,480,96,512,0,1,1,6,15 ibm,370/148,203,1000,2000,0,1,5,24,21 ibm,370/158-3,115,512,6000,16,1,6,45,35 ibm,38/3,1100,512,1500,0,1,1,7,18 ibm,38/4,1100,768,2000,0,1,1,13,20 ibm,38/5,600,768,2000,0,1,1,16,20 ibm,38/7,400,2000,4000,0,1,1,32,28 ibm,38/8,400,4000,8000,0,1,1,32,45 ibm,4321,900,1000,1000,0,1,2,11,18 ibm,4331-1,900,512,1000,0,1,2,11,17 ibm,4331-11,900,1000,4000,4,1,2,18,26 ibm,4331-2,900,1000,4000,8,1,2,22,28 ibm,4341,900,2000,4000,0,3,6,37,28 ibm,4341-1,225,2000,4000,8,3,6,40,31 ibm,4341-10,225,2000,4000,8,3,6,34,31 ibm,4341-11,180,2000,8000,8,1,6,50,42 ibm,4341-12,185,2000,16000,16,1,6,76,76 ibm,4341-2,180,2000,16000,16,1,6,66,76 ibm,4341-9,225,1000,4000,2,3,6,24,26 ibm,4361-4,25,2000,12000,8,1,4,49,59 ibm,4361-5,25,2000,12000,16,3,5,66,65 ibm,4381-1,17,4000,16000,8,6,12,100,101 ibm,4381-2,17,4000,16000,32,6,12,133,116 ibm,8130-a,1500,768,1000,0,0,0,12,18 ibm,8130-b,1500,768,2000,0,0,0,18,20 ibm,8140,800,768,2000,0,0,0,20,20 ipl,4436,50,2000,4000,0,3,6,27,30 ipl,4443,50,2000,8000,8,3,6,45,44 ipl,4445,50,2000,8000,8,1,6,56,44 ipl,4446,50,2000,16000,24,1,6,70,82 ipl,4460,50,2000,16000,24,1,6,80,82 ipl,4480,50,8000,16000,48,1,10,136,128 magnuson,m80/30,100,1000,8000,0,2,6,16,37 magnuson,m80/31,100,1000,8000,24,2,6,26,46 magnuson,m80/32,100,1000,8000,24,3,6,32,46 magnuson,m80/42,50,2000,16000,12,3,16,45,80 magnuson,m80/43,50,2000,16000,24,6,16,54,88 magnuson,m80/44,50,2000,16000,24,6,16,65,88 microdata,seq.ms/3200,150,512,4000,0,8,128,30,33 nas,as/3000,115,2000,8000,16,1,3,50,46 nas,as/3000-n,115,2000,4000,2,1,5,40,29 nas,as/5000,92,2000,8000,32,1,6,62,53 nas,as/5000-e,92,2000,8000,32,1,6,60,53 nas,as/5000-n,92,2000,8000,4,1,6,50,41 nas,as/6130,75,4000,16000,16,1,6,66,86 nas,as/6150,60,4000,16000,32,1,6,86,95 nas,as/6620,60,2000,16000,64,5,8,74,107 nas,as/6630,60,4000,16000,64,5,8,93,117 nas,as/6650,50,4000,16000,64,5,10,111,119 nas,as/7000,72,4000,16000,64,8,16,143,120 nas,as/7000-n,72,2000,8000,16,6,8,105,48 nas,as/8040,40,8000,16000,32,8,16,214,126 nas,as/8050,40,8000,32000,64,8,24,277,266 nas,as/8060,35,8000,32000,64,8,24,370,270 nas,as/9000-dpc,38,16000,32000,128,16,32,510,426 nas,as/9000-n,48,4000,24000,32,8,24,214,151 nas,as/9040,38,8000,32000,64,8,24,326,267 nas,as/9060,30,16000,32000,256,16,24,510,603 ncr,v8535:ii,112,1000,1000,0,1,4,8,19 ncr,v8545:ii,84,1000,2000,0,1,6,12,21 ncr,v8555:ii,56,1000,4000,0,1,6,17,26 ncr,v8565:ii,56,2000,6000,0,1,8,21,35 ncr,v8565:ii-e,56,2000,8000,0,1,8,24,41 ncr,v8575:ii,56,4000,8000,0,1,8,34,47 ncr,v8585:ii,56,4000,12000,0,1,8,42,62 ncr,v8595:ii,56,4000,16000,0,1,8,46,78 ncr,v8635,38,4000,8000,32,16,32,51,80 ncr,v8650,38,4000,8000,32,16,32,116,80 ncr,v8655,38,8000,16000,64,4,8,100,142 ncr,v8665,38,8000,24000,160,4,8,140,281 ncr,v8670,38,4000,16000,128,16,32,212,190 nixdorf,8890/30,200,1000,2000,0,1,2,25,21 nixdorf,8890/50,200,1000,4000,0,1,4,30,25 nixdorf,8890/70,200,2000,8000,64,1,5,41,67 perkin-elmer,3205,250,512,4000,0,1,7,25,24 perkin-elmer,3210,250,512,4000,0,4,7,50,24 perkin-elmer,3230,250,1000,16000,1,1,8,50,64 prime,50-2250,160,512,4000,2,1,5,30,25 prime,50-250-ii,160,512,2000,2,3,8,32,20 prime,50-550-ii,160,1000,4000,8,1,14,38,29 prime,50-750-ii,160,1000,8000,16,1,14,60,43 prime,50-850-ii,160,2000,8000,32,1,13,109,53 siemens,7.521,240,512,1000,8,1,3,6,19 siemens,7.531,240,512,2000,8,1,5,11,22 siemens,7.536,105,2000,4000,8,3,8,22,31 siemens,7.541,105,2000,6000,16,6,16,33,41 siemens,7.551,105,2000,8000,16,4,14,58,47 siemens,7.561,52,4000,16000,32,4,12,130,99 siemens,7.865-2,70,4000,12000,8,6,8,75,67 siemens,7.870-2,59,4000,12000,32,6,12,113,81 siemens,7.872-2,59,8000,16000,64,12,24,188,149 siemens,7.875-2,26,8000,24000,32,8,16,173,183 siemens,7.880-2,26,8000,32000,64,12,16,248,275 siemens,7.881-2,26,8000,32000,128,24,32,405,382 sperry,1100/61-h1,116,2000,8000,32,5,28,70,56 sperry,1100/81,50,2000,32000,24,6,26,114,182 sperry,1100/82,50,2000,32000,48,26,52,208,227 sperry,1100/83,50,2000,32000,112,52,104,307,341 sperry,1100/84,50,4000,32000,112,52,104,397,360 sperry,1100/93,30,8000,64000,96,12,176,915,919 sperry,1100/94,30,8000,64000,128,12,176,1150,978 sperry,80/3,180,262,4000,0,1,3,12,24 sperry,80/4,180,512,4000,0,1,3,14,24 sperry,80/5,180,262,4000,0,1,3,18,24 sperry,80/6,180,512,4000,0,1,3,21,24 sperry,80/8,124,1000,8000,0,1,8,42,37 sperry,90/80-model-3,98,1000,8000,32,2,8,46,50 sratus,32,125,2000,8000,0,2,14,52,41 wang,vs-100,480,512,8000,32,0,0,67,47 wang,vs-90,480,1000,4000,0,0,0,45,25 xgboost-1.5.2/demo/CLI/regression/machine.names000066400000000000000000000055271417122711700213640ustar00rootroot000000000000001. Title: Relative CPU Performance Data 2. Source Information -- Creators: Phillip Ein-Dor and Jacob Feldmesser -- Ein-Dor: Faculty of Management; Tel Aviv University; Ramat-Aviv; Tel Aviv, 69978; Israel -- Donor: David W. Aha (aha@ics.uci.edu) (714) 856-8779 -- Date: October, 1987 3. Past Usage: 1. Ein-Dor and Feldmesser (CACM 4/87, pp 308-317) -- Results: -- linear regression prediction of relative cpu performance -- Recorded 34% average deviation from actual values 2. Kibler,D. & Aha,D. (1988). Instance-Based Prediction of Real-Valued Attributes. In Proceedings of the CSCSI (Canadian AI) Conference. -- Results: -- instance-based prediction of relative cpu performance -- similar results; no transformations required - Predicted attribute: cpu relative performance (numeric) 4. Relevant Information: -- The estimated relative performance values were estimated by the authors using a linear regression method. See their article (pp 308-313) for more details on how the relative performance values were set. 5. Number of Instances: 209 6. Number of Attributes: 10 (6 predictive attributes, 2 non-predictive, 1 goal field, and the linear regression's guess) 7. Attribute Information: 1. vendor name: 30 (adviser, amdahl,apollo, basf, bti, burroughs, c.r.d, cambex, cdc, dec, dg, formation, four-phase, gould, honeywell, hp, ibm, ipl, magnuson, microdata, nas, ncr, nixdorf, perkin-elmer, prime, siemens, sperry, sratus, wang) 2. Model Name: many unique symbols 3. MYCT: machine cycle time in nanoseconds (integer) 4. MMIN: minimum main memory in kilobytes (integer) 5. MMAX: maximum main memory in kilobytes (integer) 6. CACH: cache memory in kilobytes (integer) 7. CHMIN: minimum channels in units (integer) 8. CHMAX: maximum channels in units (integer) 9. PRP: published relative performance (integer) 10. ERP: estimated relative performance from the original article (integer) 8. Missing Attribute Values: None 9. Class Distribution: the class value (PRP) is continuously valued. PRP Value Range: Number of Instances in Range: 0-20 31 21-100 121 101-200 27 201-300 13 301-400 7 401-500 4 501-600 2 above 600 4 Summary Statistics: Min Max Mean SD PRP Correlation MCYT: 17 1500 203.8 260.3 -0.3071 MMIN: 64 32000 2868.0 3878.7 0.7949 MMAX: 64 64000 11796.1 11726.6 0.8630 CACH: 0 256 25.2 40.6 0.6626 CHMIN: 0 52 4.7 6.8 0.6089 CHMAX: 0 176 18.2 26.0 0.6052 PRP: 6 1150 105.6 160.8 1.0000 ERP: 15 1238 99.3 154.8 0.9665 xgboost-1.5.2/demo/CLI/regression/mapfeat.py000077500000000000000000000013211417122711700207110ustar00rootroot00000000000000#!/usr/bin/python fo = open('machine.txt', 'w') cnt = 6 fmap = {} for l in open('machine.data'): arr = l.split(',') fo.write(arr[8]) for i in range(0, 6): fo.write(' %d:%s' % (i, arr[i + 2])) if arr[0] not in fmap: fmap[arr[0]] = cnt cnt += 1 fo.write(' %d:1' % fmap[arr[0]]) fo.write('\n') fo.close() # create feature map for machine data fo = open('featmap.txt', 'w') # list from machine.names names = [ 'vendor', 'MYCT', 'MMIN', 'MMAX', 'CACH', 'CHMIN', 'CHMAX', 'PRP', 'ERP' ] for i in range(0, 6): fo.write('%d\t%s\tint\n' % (i, names[i + 1])) for v, k in sorted(fmap.items(), key=lambda x: x[1]): fo.write('%d\tvendor=%s\ti\n' % (k, v)) fo.close() xgboost-1.5.2/demo/CLI/regression/mknfold.py000077500000000000000000000007411417122711700207330ustar00rootroot00000000000000#!/usr/bin/python import sys import random if len(sys.argv) < 2: print('Usage: [nfold = 5]') exit(0) random.seed(10) k = int(sys.argv[2]) if len(sys.argv) > 3: nfold = int(sys.argv[3]) else: nfold = 5 fi = open(sys.argv[1], 'r') ftr = open(sys.argv[1] + '.train', 'w') fte = open(sys.argv[1] + '.test', 'w') for l in fi: if random.randint(1, nfold) == k: fte.write(l) else: ftr.write(l) fi.close() ftr.close() fte.close() xgboost-1.5.2/demo/CLI/regression/runexp.sh000077500000000000000000000012671417122711700206100ustar00rootroot00000000000000#!/bin/bash # map the data to features. For convenience we only use 7 original attributes and encode them as features in a trivial way python mapfeat.py # split train and test python mknfold.py machine.txt 1 # training and output the models ../../xgboost machine.conf # output predictions of test data ../../xgboost machine.conf task=pred model_in=0002.model # print the boosters of 0002.model in dump.raw.txt ../../xgboost machine.conf task=dump model_in=0002.model name_dump=dump.raw.txt # print the boosters of 0002.model in dump.nice.txt with feature map ../../xgboost machine.conf task=dump model_in=0002.model fmap=featmap.txt name_dump=dump.nice.txt # cat the result cat dump.nice.txt xgboost-1.5.2/demo/CLI/yearpredMSD/000077500000000000000000000000001417122711700167215ustar00rootroot00000000000000xgboost-1.5.2/demo/CLI/yearpredMSD/README.md000066400000000000000000000006701417122711700202030ustar00rootroot00000000000000Demonstrating how to use XGBoost on [Year Prediction task of Million Song Dataset](https://archive.ics.uci.edu/ml/datasets/YearPredictionMSD) 1. Run runexp.sh ```bash ./runexp.sh ``` You can also use the script to prepare LIBSVM format, and run the [Distributed Version](../../multi-node). Note that though that normally you only need to use single machine for dataset at this scale, and use distributed version for larger scale dataset. xgboost-1.5.2/demo/CLI/yearpredMSD/csv2libsvm.py000077500000000000000000000003171417122711700213710ustar00rootroot00000000000000import sys fo = open(sys.argv[2], 'w') for l in open(sys.argv[1]): arr = l.split(',') fo.write('%s' % arr[0]) for i in range(len(arr) - 1): fo.write(' %d:%s' % (i, arr[i+1])) fo.close() xgboost-1.5.2/demo/CLI/yearpredMSD/runexp.sh000077500000000000000000000012141417122711700205770ustar00rootroot00000000000000#!/bin/bash if [ -f YearPredictionMSD.txt ] then echo "use existing data to run experiment" else echo "getting data from uci, make sure you are connected to internet" wget https://archive.ics.uci.edu/ml/machine-learning-databases/00203/YearPredictionMSD.txt.zip unzip YearPredictionMSD.txt.zip fi echo "start making data.." # map feature using indicator encoding, also produce featmap.txt python csv2libsvm.py YearPredictionMSD.txt yearpredMSD.libsvm head -n 463715 yearpredMSD.libsvm > yearpredMSD.libsvm.train tail -n 51630 yearpredMSD.libsvm > yearpredMSD.libsvm.test echo "finish making the data" ../../../xgboost yearpredMSD.conf xgboost-1.5.2/demo/CLI/yearpredMSD/yearpredMSD.conf000066400000000000000000000017551417122711700217570ustar00rootroot00000000000000# General Parameters, see comment for each definition # choose the tree booster, can also change to gblinear booster = gbtree # this is the only difference with classification, use reg:squarederror to do linear classification # when labels are in [0,1] we can also use reg:logistic objective = reg:squarederror # Tree Booster Parameters # step size shrinkage eta = 1.0 # minimum loss reduction required to make a further partition gamma = 1.0 # minimum sum of instance weight(hessian) needed in a child min_child_weight = 1 # maximum depth of a tree max_depth = 5 base_score = 2001 # Task parameters # the number of round to do boosting num_round = 100 # 0 means do not save any model except the final round model save_period = 0 # The path of training data data = "yearpredMSD.libsvm.train" # The path of validation data, used to monitor training process, here [test] sets name of the validation set eval[test] = "yearpredMSD.libsvm.test" # The path of test data #test:data = "yearpredMSD.libsvm.test" xgboost-1.5.2/demo/README.md000066400000000000000000000427771417122711700154330ustar00rootroot00000000000000Awesome XGBoost =============== This page contains a curated list of examples, tutorials, blogs about XGBoost usecases. It is inspired by [awesome-MXNet](https://github.com/dmlc/mxnet/blob/master/example/README.md), [awesome-php](https://github.com/ziadoz/awesome-php) and [awesome-machine-learning](https://github.com/josephmisiti/awesome-machine-learning). Please send a pull request if you find things that belongs to here. Contents -------- - [Code Examples](#code-examples) - [Features Walkthrough](#features-walkthrough) - [Basic Examples by Tasks](#basic-examples-by-tasks) - [Benchmarks](#benchmarks) - [Machine Learning Challenge Winning Solutions](#machine-learning-challenge-winning-solutions) - [Tutorials](#tutorials) - [Usecases](#usecases) - [Tools using XGBoost](#tools-using-xgboost) - [Integrations with 3rd party software](#integrations-with-3rd-party-software) - [Awards](#awards) - [Windows Binaries](#windows-binaries) Code Examples ------------- ### Features Walkthrough This is a list of short codes introducing different functionalities of xgboost packages. * Basic walkthrough of packages [python](guide-python/basic_walkthrough.py) [R](../R-package/demo/basic_walkthrough.R) [Julia](https://github.com/antinucleon/XGBoost.jl/blob/master/demo/basic_walkthrough.jl) [PHP](https://github.com/bpachev/xgboost-php/blob/master/demo/titanic_demo.php) * Customize loss function, and evaluation metric [python](guide-python/custom_objective.py) [R](../R-package/demo/custom_objective.R) [Julia](https://github.com/antinucleon/XGBoost.jl/blob/master/demo/custom_objective.jl) * Boosting from existing prediction [python](guide-python/boost_from_prediction.py) [R](../R-package/demo/boost_from_prediction.R) [Julia](https://github.com/antinucleon/XGBoost.jl/blob/master/demo/boost_from_prediction.jl) * Predicting using first n trees [python](guide-python/predict_first_ntree.py) [R](../R-package/demo/predict_first_ntree.R) [Julia](https://github.com/antinucleon/XGBoost.jl/blob/master/demo/predict_first_ntree.jl) * Generalized Linear Model [python](guide-python/generalized_linear_model.py) [R](../R-package/demo/generalized_linear_model.R) [Julia](https://github.com/antinucleon/XGBoost.jl/blob/master/demo/generalized_linear_model.jl) * Cross validation [python](guide-python/cross_validation.py) [R](../R-package/demo/cross_validation.R) [Julia](https://github.com/antinucleon/XGBoost.jl/blob/master/demo/cross_validation.jl) * Predicting leaf indices [python](guide-python/predict_leaf_indices.py) [R](../R-package/demo/predict_leaf_indices.R) ### Basic Examples by Tasks Most of examples in this section are based on CLI or python version. However, the parameter settings can be applied to all versions - [Binary classification](CLI/binary_classification) - [Multiclass classification](multiclass_classification) - [Regression](CLI/regression) - [Learning to Rank](rank) ### Benchmarks - [Starter script for Kaggle Higgs Boson](kaggle-higgs) - [Kaggle Tradeshift winning solution by daxiongshu](https://github.com/daxiongshu/kaggle-tradeshift-winning-solution) - [Benchmarking the most commonly used open source tools for binary classification](https://github.com/szilard/benchm-ml#boosting-gradient-boosted-treesgradient-boosting-machines) ## Machine Learning Challenge Winning Solutions XGBoost is extensively used by machine learning practitioners to create state of art data science solutions, this is a list of machine learning winning solutions with XGBoost. Please send pull requests if you find ones that are missing here. - Benedikt Schifferer, Gilberto Titericz, Chris Deotte, Christof Henkel, Kazuki Onodera, Jiwei Liu, Bojan Tunguz, Even Oldridge, Gabriel De Souza Pereira Moreira and Ahmet Erdem, 1st place winner of [Twitter RecSys Challenge 2020](https://recsys-twitter.com/) conducted from June,20-August,20. [GPU Accelerated Feature Engineering and Training for Recommender Systems](https://medium.com/rapids-ai/winning-solution-of-recsys2020-challenge-gpu-accelerated-feature-engineering-and-training-for-cd67c5a87b1f) - Eugene Khvedchenya,Jessica Fridrich, Jan Butora, Yassine Yousfi 1st place winner in [ALASKA2 Image Steganalysis](https://www.kaggle.com/c/alaska2-image-steganalysis/overview). Link to [discussion](https://www.kaggle.com/c/alaska2-image-steganalysis/discussion/168546) - Dan Ofer, Seffi Cohen, Noa Dagan, Nurit, 1st place in WiDS Datathon 2020. Link to [discussion](https://www.kaggle.com/c/widsdatathon2020/discussion/133189) - Chris Deotte, Konstantin Yakovlev 1st place in [IEEE-CIS Fraud Detection](https://www.kaggle.com/c/ieee-fraud-detection/overview). Link to [discussion](https://www.kaggle.com/c/ieee-fraud-detection/discussion/111308) - Giba, Lucasz, 1st place winner in [Santander Value Prediction Challenge](https://www.kaggle.com/c/santander-value-prediction-challenge) organized on August,2018. Solution [discussion](https://www.kaggle.com/c/santander-value-prediction-challenge/discussion/65272) and [code](https://www.kaggle.com/titericz/winner-model-giba-single-xgb-lb0-5178/comments) - Beluga, 2nd place and Evgeny Nekrasov, 3rd place winner in Statoil/C-CORE Iceberg Classifier Challenge'2018. Link to [discussion](https://www.kaggle.com/c/statoil-iceberg-classifier-challenge/discussion/48294) - Radek Osmulski, 1st place of the [iMaterialist Challenge (Fashion) at FGVC5](https://www.kaggle.com/c/imaterialist-challenge-fashion-2018/overview). Link to [the winning solution](https://www.kaggle.com/c/imaterialist-challenge-fashion-2018/discussion/57944). - Maksims Volkovs, Guangwei Yu and Tomi Poutanen, 1st place of the [2017 ACM RecSys challenge](http://2017.recsyschallenge.com/). Link to [paper](http://www.cs.toronto.edu/~mvolkovs/recsys2017_challenge.pdf). - Vlad Sandulescu, Mihai Chiru, 1st place of the [KDD Cup 2016 competition](https://kddcup2016.azurewebsites.net). Link to [the arxiv paper](http://arxiv.org/abs/1609.02728). - Marios Michailidis, Mathias Müller and HJ van Veen, 1st place of the [Dato Truely Native? competition](https://www.kaggle.com/c/dato-native). Link to [the Kaggle interview](http://blog.kaggle.com/2015/12/03/dato-winners-interview-1st-place-mad-professors/). - Vlad Mironov, Alexander Guschin, 1st place of the [CERN LHCb experiment Flavour of Physics competition](https://www.kaggle.com/c/flavours-of-physics). Link to [the Kaggle interview](http://blog.kaggle.com/2015/11/30/flavour-of-physics-technical-write-up-1st-place-go-polar-bears/). - Josef Slavicek, 3rd place of the [CERN LHCb experiment Flavour of Physics competition](https://www.kaggle.com/c/flavours-of-physics). Link to [the Kaggle interview](http://blog.kaggle.com/2015/11/23/flavour-of-physics-winners-interview-3rd-place-josef-slavicek/). - Mario Filho, Josef Feigl, Lucas, Gilberto, 1st place of the [Caterpillar Tube Pricing competition](https://www.kaggle.com/c/caterpillar-tube-pricing). Link to [the Kaggle interview](http://blog.kaggle.com/2015/09/22/caterpillar-winners-interview-1st-place-gilberto-josef-leustagos-mario/). - Qingchen Wang, 1st place of the [Liberty Mutual Property Inspection](https://www.kaggle.com/c/liberty-mutual-group-property-inspection-prediction). Link to [the Kaggle interview](http://blog.kaggle.com/2015/09/28/liberty-mutual-property-inspection-winners-interview-qingchen-wang/). - Chenglong Chen, 1st place of the [Crowdflower Search Results Relevance](https://www.kaggle.com/c/crowdflower-search-relevance). Link to [the winning solution](https://www.kaggle.com/c/crowdflower-search-relevance/forums/t/15186/1st-place-winner-solution-chenglong-chen/). - Alexandre Barachant (“Cat”) and Rafał Cycoń (“Dog”), 1st place of the [Grasp-and-Lift EEG Detection](https://www.kaggle.com/c/grasp-and-lift-eeg-detection). Link to [the Kaggle interview](http://blog.kaggle.com/2015/10/12/grasp-and-lift-eeg-winners-interview-1st-place-cat-dog/). - Halla Yang, 2nd place of the [Recruit Coupon Purchase Prediction Challenge](https://www.kaggle.com/c/coupon-purchase-prediction). Link to [the Kaggle interview](http://blog.kaggle.com/2015/10/21/recruit-coupon-purchase-winners-interview-2nd-place-halla-yang/). - Owen Zhang, 1st place of the [Avito Context Ad Clicks competition](https://www.kaggle.com/c/avito-context-ad-clicks). Link to [the Kaggle interview](http://blog.kaggle.com/2015/08/26/avito-winners-interview-1st-place-owen-zhang/). - Keiichi Kuroyanagi, 2nd place of the [Airbnb New User Bookings](https://www.kaggle.com/c/airbnb-recruiting-new-user-bookings). Link to [the Kaggle interview](http://blog.kaggle.com/2016/03/17/airbnb-new-user-bookings-winners-interview-2nd-place-keiichi-kuroyanagi-keiku/). - Marios Michailidis, Mathias Müller and Ning Situ, 1st place [Homesite Quote Conversion](https://www.kaggle.com/c/homesite-quote-conversion). Link to [the Kaggle interview](http://blog.kaggle.com/2016/04/08/homesite-quote-conversion-winners-write-up-1st-place-kazanova-faron-clobber/). - Gilberto Titericz, Stanislav Semenov, 1st place in challenge to classify products into the correct category organized by Otto Group in 2015. Link to [challenge](https://www.kaggle.com/c/otto-group-product-classification-challenge). Link to [kaggle winning solution](https://www.kaggle.com/c/otto-group-product-classification-challenge/discussion/14335) - Darius Barušauskas, 1st place winner in [Predicting Red Hat Business Value](https://www.kaggle.com/c/predicting-red-hat-business-value). Link to [interview](https://medium.com/kaggle-blog/red-hat-business-value-competition-1st-place-winners-interview-darius-baru%C5%A1auskas-646692a2841b). Link to [discussion](https://www.kaggle.com/c/predicting-red-hat-business-value/discussion/23786) - David Austin, Weimin Wang, 1st place winner in [Iceberg-classifier-challenge](https://www.kaggle.com/c/statoil-iceberg-classifier-challenge/leaderboard) Link to [discussion](https://www.kaggle.com/c/statoil-iceberg-classifier-challenge/discussion/48241) - Kazuki Onodera, Kazuki Fujikawa, 2nd place winner in [OpenVaccine: COVID-19 mRNA Vaccine Degradation Prediction](https://www.kaggle.com/c/stanford-covid-vaccine/overview) Link to [Discussion](https://www.kaggle.com/c/stanford-covid-vaccine/discussion/189709) - Prarthana Bhat, 2nd place winner in [DYD Competition](https://datahack.analyticsvidhya.com/contest/date-your-data/). Link to [Solution](https://github.com/analyticsvidhya/DateYourData/blob/master/Prathna_Bhat_Model.R). ## Talks - [XGBoost: A Scalable Tree Boosting System](http://datascience.la/xgboost-workshop-and-meetup-talk-with-tianqi-chen/) (video+slides) by Tianqi Chen at the Los Angeles Data Science meetup ## Tutorials - [XGBoost Training with Dask, using Saturn Cloud](https://www.saturncloud.io/docs/tutorials/xgboost/) - [Machine Learning with XGBoost on Qubole Spark Cluster](https://www.qubole.com/blog/machine-learning-xgboost-qubole-spark-cluster/) - [XGBoost Official RMarkdown Tutorials](https://xgboost.readthedocs.org/en/latest/R-package/index.html#tutorials) - [An Introduction to XGBoost R Package](http://dmlc.ml/rstats/2016/03/10/xgboost.html) by Tong He - [Open Source Tools & Data Science Competitions](http://www.slideshare.net/odsc/owen-zhangopen-sourcetoolsanddscompetitions1) by Owen Zhang - XGBoost parameter tuning tips * [Feature Importance Analysis with XGBoost in Tax audit](http://fr.slideshare.net/MichaelBENESTY/feature-importance-analysis-with-xgboost-in-tax-audit) * [Winning solution of Kaggle Higgs competition: what a single model can do](http://no2147483647.wordpress.com/2014/09/17/winning-solution-of-kaggle-higgs-competition-what-a-single-model-can-do/) - [XGBoost - eXtreme Gradient Boosting](http://www.slideshare.net/ShangxuanZhang/xgboost) by Tong He - [How to use XGBoost algorithm in R in easy steps](http://www.analyticsvidhya.com/blog/2016/01/xgboost-algorithm-easy-steps/) by TAVISH SRIVASTAVA ([Chinese Translation 中文翻译](https://segmentfault.com/a/1190000004421821) by [HarryZhu](https://segmentfault.com/u/harryprince)) - [Kaggle Solution: What’s Cooking ? (Text Mining Competition)](http://www.analyticsvidhya.com/blog/2015/12/kaggle-solution-cooking-text-mining-competition/) by MANISH SARASWAT - Better Optimization with Repeated Cross Validation and the XGBoost model - Machine Learning with R) by Manuel Amunategui ([Youtube Link](https://www.youtube.com/watch?v=Og7CGAfSr_Y)) ([GitHub Link](https://github.com/amunategui/BetterCrossValidation)) - [XGBoost Rossman Parameter Tuning](https://www.kaggle.com/khozzy/rossmann-store-sales/xgboost-parameter-tuning-template/run/90168/notebook) by [Norbert Kozlowski](https://www.kaggle.com/khozzy) - [Featurizing log data before XGBoost](http://www.slideshare.net/DataRobot/featurizing-log-data-before-xgboost) by Xavier Conort, Owen Zhang etc - [West Nile Virus Competition Benchmarks & Tutorials](http://blog.kaggle.com/2015/07/21/west-nile-virus-competition-benchmarks-tutorials/) by [Anna Montoya](http://blog.kaggle.com/author/annamontoya/) - [Ensemble Decision Tree with XGBoost](https://www.kaggle.com/binghsu/predict-west-nile-virus/xgboost-starter-code-python-0-69) by [Bing Xu](https://www.kaggle.com/binghsu) - [Notes on eXtreme Gradient Boosting](http://startup.ml/blog/xgboost) by ARSHAK NAVRUZYAN ([iPython Notebook](https://github.com/startupml/koan/blob/master/eXtreme%20Gradient%20Boosting.ipynb)) - [Complete Guide to Parameter Tuning in XGBoost](http://www.analyticsvidhya.com/blog/2016/03/complete-guide-parameter-tuning-xgboost-with-codes-python/) by Aarshay Jain - [Practical XGBoost in Python online course](http://education.parrotprediction.teachable.com/courses/practical-xgboost-in-python) by Parrot Prediction - [Spark and XGBoost using Scala](http://www.elenacuoco.com/2016/10/10/scala-spark-xgboost-classification/) by Elena Cuoco ## Usecases If you have particular usecase of xgboost that you would like to highlight. Send a PR to add a one sentence description:) - XGBoost is used in [Kaggle Script](https://www.kaggle.com/scripts) to solve data science challenges. - Distribute XGBoost as Rest API server from Jupyter notebook with [BentoML](https://github.com/bentoml/bentoml). [Link to notebook](https://github.com/bentoml/BentoML/blob/master/examples/xgboost-predict-titanic-survival/XGBoost-titanic-survival-prediction.ipynb) - [Seldon predictive service powered by XGBoost](http://docs.seldon.io/iris-demo.html) - XGBoost Distributed is used in [ODPS Cloud Service by Alibaba](https://yq.aliyun.com/articles/6355) (in Chinese) - XGBoost is incoporated as part of [Graphlab Create](https://dato.com/products/create/) for scalable machine learning. - [Hanjing Su](https://www.52cs.org) from Tencent data platform team: "We use distributed XGBoost for click through prediction in wechat shopping and lookalikes. The problems involve hundreds millions of users and thousands of features. XGBoost is cleanly designed and can be easily integrated into our production environment, reducing our cost in developments." - [CNevd](https://github.com/CNevd) from autohome.com ad platform team: "Distributed XGBoost is used for click through rate prediction in our display advertising, XGBoost is highly efficient and flexible and can be easily used on our distributed platform, our ctr made a great improvement with hundred millions samples and millions features due to this awesome XGBoost" ## Tools using XGBoost - [BayesBoost](https://github.com/mpearmain/BayesBoost) - Bayesian Optimization using xgboost and sklearn API - [FLAML](https://github.com/microsoft/FLAML) - An open source AutoML library designed to automatically produce accurate machine learning models with low computational cost. FLAML includes [XGBoost as one of the default learners](https://github.com/microsoft/FLAML/blob/main/flaml/model.py) and can also be used as a fast hyperparameter tuning tool for XGBoost ([code example](https://github.com/microsoft/FLAML/blob/main/notebook/flaml_xgboost.ipynb)). - [gp_xgboost_gridsearch](https://github.com/vatsan/gp_xgboost_gridsearch) - In-database parallel grid-search for XGBoost on [Greenplum](https://github.com/greenplum-db/gpdb) using PL/Python - [tpot](https://github.com/rhiever/tpot) - A Python tool that automatically creates and optimizes machine learning pipelines using genetic programming. ## Integrations with 3rd party software Open source integrations with XGBoost: * [Neptune.ai](http://neptune.ai/) - Experiment management and collaboration tool for ML/DL/RL specialists. Integration has a form of the [XGBoost callback](https://docs.neptune.ai/integrations/xgboost.html) that automatically logs training and evaluation metrics, as well as saved model (booster), feature importance chart and visualized trees. * [Optuna](https://optuna.org/) - An open source hyperparameter optimization framework to automate hyperparameter search. Optuna integrates with XGBoost in the [XGBoostPruningCallback](https://optuna.readthedocs.io/en/stable/reference/integration.html#optuna.integration.XGBoostPruningCallback) that let users easily prune unpromising trials. * [dtreeviz](https://github.com/parrt/dtreeviz) - A python library for decision tree visualization and model interpretation. Starting from version 1.0, dtreeviz is able to visualize tree ensembles produced by XGBoost. ## Awards - [John Chambers Award](http://stat-computing.org/awards/jmc/winners.html) - 2016 Winner: XGBoost R Package, by Tong He (Simon Fraser University) and Tianqi Chen (University of Washington) - [InfoWorld’s 2019 Technology of the Year Award](https://www.infoworld.com/article/3336072/application-development/infoworlds-2019-technology-of-the-year-award-winners.html) ## Windows Binaries Unofficial windows binaries and instructions on how to use them are hosted on [Guido Tapia's blog](http://www.picnet.com.au/blogs/guido/post/2016/09/22/xgboost-windows-x64-binaries-for-download/) xgboost-1.5.2/demo/aft_survival/000077500000000000000000000000001417122711700166405ustar00rootroot00000000000000xgboost-1.5.2/demo/aft_survival/aft_survival_demo.py000066400000000000000000000042331417122711700227250ustar00rootroot00000000000000""" Demo for survival analysis (regression) using Accelerated Failure Time (AFT) model """ import os from sklearn.model_selection import ShuffleSplit import pandas as pd import numpy as np import xgboost as xgb # The Veterans' Administration Lung Cancer Trial # The Statistical Analysis of Failure Time Data by Kalbfleisch J. and Prentice R (1980) CURRENT_DIR = os.path.dirname(__file__) df = pd.read_csv(os.path.join(CURRENT_DIR, '../data/veterans_lung_cancer.csv')) print('Training data:') print(df) # Split features and labels y_lower_bound = df['Survival_label_lower_bound'] y_upper_bound = df['Survival_label_upper_bound'] X = df.drop(['Survival_label_lower_bound', 'Survival_label_upper_bound'], axis=1) # Split data into training and validation sets rs = ShuffleSplit(n_splits=2, test_size=.7, random_state=0) train_index, valid_index = next(rs.split(X)) dtrain = xgb.DMatrix(X.values[train_index, :]) dtrain.set_float_info('label_lower_bound', y_lower_bound[train_index]) dtrain.set_float_info('label_upper_bound', y_upper_bound[train_index]) dvalid = xgb.DMatrix(X.values[valid_index, :]) dvalid.set_float_info('label_lower_bound', y_lower_bound[valid_index]) dvalid.set_float_info('label_upper_bound', y_upper_bound[valid_index]) # Train gradient boosted trees using AFT loss and metric params = {'verbosity': 0, 'objective': 'survival:aft', 'eval_metric': 'aft-nloglik', 'tree_method': 'hist', 'learning_rate': 0.05, 'aft_loss_distribution': 'normal', 'aft_loss_distribution_scale': 1.20, 'max_depth': 6, 'lambda': 0.01, 'alpha': 0.02} bst = xgb.train(params, dtrain, num_boost_round=10000, evals=[(dtrain, 'train'), (dvalid, 'valid')], early_stopping_rounds=50) # Run prediction on the validation set df = pd.DataFrame({'Label (lower bound)': y_lower_bound[valid_index], 'Label (upper bound)': y_upper_bound[valid_index], 'Predicted label': bst.predict(dvalid)}) print(df) # Show only data points with right-censored labels print(df[np.isinf(df['Label (upper bound)'])]) # Save trained model bst.save_model('aft_model.json') xgboost-1.5.2/demo/aft_survival/aft_survival_demo_with_optuna.py000066400000000000000000000067341417122711700253560ustar00rootroot00000000000000""" Demo for survival analysis (regression) using Accelerated Failure Time (AFT) model, using Optuna to tune hyperparameters """ from sklearn.model_selection import ShuffleSplit import pandas as pd import numpy as np import xgboost as xgb import optuna # The Veterans' Administration Lung Cancer Trial # The Statistical Analysis of Failure Time Data by Kalbfleisch J. and Prentice R (1980) df = pd.read_csv('../data/veterans_lung_cancer.csv') print('Training data:') print(df) # Split features and labels y_lower_bound = df['Survival_label_lower_bound'] y_upper_bound = df['Survival_label_upper_bound'] X = df.drop(['Survival_label_lower_bound', 'Survival_label_upper_bound'], axis=1) # Split data into training and validation sets rs = ShuffleSplit(n_splits=2, test_size=.7, random_state=0) train_index, valid_index = next(rs.split(X)) dtrain = xgb.DMatrix(X.values[train_index, :]) dtrain.set_float_info('label_lower_bound', y_lower_bound[train_index]) dtrain.set_float_info('label_upper_bound', y_upper_bound[train_index]) dvalid = xgb.DMatrix(X.values[valid_index, :]) dvalid.set_float_info('label_lower_bound', y_lower_bound[valid_index]) dvalid.set_float_info('label_upper_bound', y_upper_bound[valid_index]) # Define hyperparameter search space base_params = {'verbosity': 0, 'objective': 'survival:aft', 'eval_metric': 'aft-nloglik', 'tree_method': 'hist'} # Hyperparameters common to all trials def objective(trial): params = {'learning_rate': trial.suggest_loguniform('learning_rate', 0.01, 1.0), 'aft_loss_distribution': trial.suggest_categorical('aft_loss_distribution', ['normal', 'logistic', 'extreme']), 'aft_loss_distribution_scale': trial.suggest_loguniform('aft_loss_distribution_scale', 0.1, 10.0), 'max_depth': trial.suggest_int('max_depth', 3, 8), 'lambda': trial.suggest_loguniform('lambda', 1e-8, 1.0), 'alpha': trial.suggest_loguniform('alpha', 1e-8, 1.0)} # Search space params.update(base_params) pruning_callback = optuna.integration.XGBoostPruningCallback(trial, 'valid-aft-nloglik') bst = xgb.train(params, dtrain, num_boost_round=10000, evals=[(dtrain, 'train'), (dvalid, 'valid')], early_stopping_rounds=50, verbose_eval=False, callbacks=[pruning_callback]) if bst.best_iteration >= 25: return bst.best_score else: return np.inf # Reject models with < 25 trees # Run hyperparameter search study = optuna.create_study(direction='minimize') study.optimize(objective, n_trials=200) print('Completed hyperparameter tuning with best aft-nloglik = {}.'.format(study.best_trial.value)) params = {} params.update(base_params) params.update(study.best_trial.params) # Re-run training with the best hyperparameter combination print('Re-running the best trial... params = {}'.format(params)) bst = xgb.train(params, dtrain, num_boost_round=10000, evals=[(dtrain, 'train'), (dvalid, 'valid')], early_stopping_rounds=50) # Run prediction on the validation set df = pd.DataFrame({'Label (lower bound)': y_lower_bound[valid_index], 'Label (upper bound)': y_upper_bound[valid_index], 'Predicted label': bst.predict(dvalid)}) print(df) # Show only data points with right-censored labels print(df[np.isinf(df['Label (upper bound)'])]) # Save trained model bst.save_model('aft_best_model.json') xgboost-1.5.2/demo/aft_survival/aft_survival_viz_demo.py000066400000000000000000000067001417122711700236160ustar00rootroot00000000000000""" Visual demo for survival analysis (regression) with Accelerated Failure Time (AFT) model. This demo uses 1D toy data and visualizes how XGBoost fits a tree ensemble. The ensemble model starts out as a flat line and evolves into a step function in order to account for all ranged labels. """ import numpy as np import xgboost as xgb import matplotlib.pyplot as plt plt.rcParams.update({'font.size': 13}) # Function to visualize censored labels def plot_censored_labels(X, y_lower, y_upper): def replace_inf(x, target_value): x[np.isinf(x)] = target_value return x plt.plot(X, y_lower, 'o', label='y_lower', color='blue') plt.plot(X, y_upper, 'o', label='y_upper', color='fuchsia') plt.vlines(X, ymin=replace_inf(y_lower, 0.01), ymax=replace_inf(y_upper, 1000), label='Range for y', color='gray') # Toy data X = np.array([1, 2, 3, 4, 5]).reshape((-1, 1)) INF = np.inf y_lower = np.array([ 10, 15, -INF, 30, 100]) y_upper = np.array([INF, INF, 20, 50, INF]) # Visualize toy data plt.figure(figsize=(5, 4)) plot_censored_labels(X, y_lower, y_upper) plt.ylim((6, 200)) plt.legend(loc='lower right') plt.title('Toy data') plt.xlabel('Input feature') plt.ylabel('Label') plt.yscale('log') plt.tight_layout() plt.show(block=True) # Will be used to visualize XGBoost model grid_pts = np.linspace(0.8, 5.2, 1000).reshape((-1, 1)) # Train AFT model using XGBoost dmat = xgb.DMatrix(X) dmat.set_float_info('label_lower_bound', y_lower) dmat.set_float_info('label_upper_bound', y_upper) params = {'max_depth': 3, 'objective':'survival:aft', 'min_child_weight': 0} accuracy_history = [] def plot_intermediate_model_callback(env): """Custom callback to plot intermediate models""" # Compute y_pred = prediction using the intermediate model, at current boosting iteration y_pred = env.model.predict(dmat) # "Accuracy" = the number of data points whose ranged label (y_lower, y_upper) includes # the corresponding predicted label (y_pred) acc = np.sum(np.logical_and(y_pred >= y_lower, y_pred <= y_upper)/len(X) * 100) accuracy_history.append(acc) # Plot ranged labels as well as predictions by the model plt.subplot(5, 3, env.iteration + 1) plot_censored_labels(X, y_lower, y_upper) y_pred_grid_pts = env.model.predict(xgb.DMatrix(grid_pts)) plt.plot(grid_pts, y_pred_grid_pts, 'r-', label='XGBoost AFT model', linewidth=4) plt.title('Iteration {}'.format(env.iteration), x=0.5, y=0.8) plt.xlim((0.8, 5.2)) plt.ylim((1 if np.min(y_pred) < 6 else 6, 200)) plt.yscale('log') res = {} plt.figure(figsize=(12,13)) bst = xgb.train(params, dmat, 15, [(dmat, 'train')], evals_result=res, callbacks=[plot_intermediate_model_callback]) plt.tight_layout() plt.legend(loc='lower center', ncol=4, bbox_to_anchor=(0.5, 0), bbox_transform=plt.gcf().transFigure) plt.tight_layout() # Plot negative log likelihood over boosting iterations plt.figure(figsize=(8,3)) plt.subplot(1, 2, 1) plt.plot(res['train']['aft-nloglik'], 'b-o', label='aft-nloglik') plt.xlabel('# Boosting Iterations') plt.legend(loc='best') # Plot "accuracy" over boosting iterations # "Accuracy" = the number of data points whose ranged label (y_lower, y_upper) includes # the corresponding predicted label (y_pred) plt.subplot(1, 2, 2) plt.plot(accuracy_history, 'r-o', label='Accuracy (%)') plt.xlabel('# Boosting Iterations') plt.legend(loc='best') plt.tight_layout() plt.show() xgboost-1.5.2/demo/c-api/000077500000000000000000000000001417122711700151245ustar00rootroot00000000000000xgboost-1.5.2/demo/c-api/.gitignore000066400000000000000000000000131417122711700171060ustar00rootroot00000000000000c-api-demo xgboost-1.5.2/demo/c-api/CMakeLists.txt000066400000000000000000000010511417122711700176610ustar00rootroot00000000000000cmake_minimum_required(VERSION 3.13) project(xgboost-c-examples) add_subdirectory(basic) add_subdirectory(external-memory) add_subdirectory(inference) enable_testing() add_test( NAME test_xgboost_demo_c_basic COMMAND api-demo WORKING_DIRECTORY ${xgboost-c-examples_BINARY_DIR} ) add_test( NAME test_xgboost_demo_c_external_memory COMMAND external-memory-demo WORKING_DIRECTORY ${xgboost-c-examples_BINARY_DIR} ) add_test( NAME test_xgboost_demo_c_inference COMMAND inference-demo WORKING_DIRECTORY ${xgboost-c-examples_BINARY_DIR} ) xgboost-1.5.2/demo/c-api/basic/000077500000000000000000000000001417122711700162055ustar00rootroot00000000000000xgboost-1.5.2/demo/c-api/basic/CMakeLists.txt000066400000000000000000000006611417122711700207500ustar00rootroot00000000000000project(api-demo LANGUAGES C VERSION 0.0.1) find_package(xgboost REQUIRED) # xgboost is built as static libraries, all cxx dependencies need to be linked into the # executable. if (XGBOOST_BUILD_STATIC_LIB) enable_language(CXX) # find again for those cxx libraries. find_package(xgboost REQUIRED) endif(XGBOOST_BUILD_STATIC_LIB) add_executable(api-demo c-api-demo.c) target_link_libraries(api-demo PRIVATE xgboost::xgboost) xgboost-1.5.2/demo/c-api/basic/Makefile000066400000000000000000000006201417122711700176430ustar00rootroot00000000000000SRC=c-api-demo.c TGT=c-api-demo cc=cc CFLAGS ?=-O3 XGBOOST_ROOT ?=../.. INCLUDE_DIR=-I$(XGBOOST_ROOT)/include -I$(XGBOOST_ROOT)/dmlc-core/include -I$(XGBOOST_ROOT)/rabit/include LIB_DIR=-L$(XGBOOST_ROOT)/lib build: $(TGT) $(TGT): $(SRC) Makefile $(cc) $(CFLAGS) $(INCLUDE_DIR) $(LIB_DIR) -o $(TGT) $(SRC) -lxgboost run: $(TGT) LD_LIBRARY_PATH=$(XGBOOST_ROOT)/lib ./$(TGT) clean: rm -f $(TGT) xgboost-1.5.2/demo/c-api/basic/README.md000066400000000000000000000017071417122711700174710ustar00rootroot00000000000000C-APIs === **XGBoost** implements a C API originally designed for various language bindings. For detailed reference, please check xgboost/c_api.h. Here is a demonstration of using the API. # CMake If you use **CMake** for your project, you can either install **XGBoost** somewhere in your system and tell CMake to find it by calling `find_package(xgboost)`, or put **XGBoost** inside your project's source tree and call **CMake** command: `add_subdirectory(xgboost)`. To use `find_package()`, put the following in your **CMakeLists.txt**: ``` CMake find_package(xgboost REQUIRED) add_executable(api-demo c-api-demo.c) target_link_libraries(api-demo xgboost::xgboost) ``` If you want to put XGBoost inside your project (like git submodule), use this instead: ``` CMake add_subdirectory(xgboost) add_executable(api-demo c-api-demo.c) target_link_libraries(api-demo xgboost) ``` # make You can start by modifying the makefile in this directory to fit your need. xgboost-1.5.2/demo/c-api/basic/c-api-demo.c000066400000000000000000000137471417122711700203000ustar00rootroot00000000000000/*! * Copyright 2019 XGBoost contributors * * \file c-api-demo.c * \brief A simple example of using xgboost C API. */ #include #include #include #include #define safe_xgboost(call) { \ int err = (call); \ if (err != 0) { \ fprintf(stderr, "%s:%d: error in %s: %s\n", __FILE__, __LINE__, #call, XGBGetLastError()); \ exit(1); \ } \ } int main(int argc, char** argv) { int silent = 0; int use_gpu = 0; // set to 1 to use the GPU for training // load the data DMatrixHandle dtrain, dtest; safe_xgboost(XGDMatrixCreateFromFile("../../data/agaricus.txt.train", silent, &dtrain)); safe_xgboost(XGDMatrixCreateFromFile("../../data/agaricus.txt.test", silent, &dtest)); // create the booster BoosterHandle booster; DMatrixHandle eval_dmats[2] = {dtrain, dtest}; safe_xgboost(XGBoosterCreate(eval_dmats, 2, &booster)); // configure the training // available parameters are described here: // https://xgboost.readthedocs.io/en/latest/parameter.html safe_xgboost(XGBoosterSetParam(booster, "tree_method", use_gpu ? "gpu_hist" : "hist")); if (use_gpu) { // set the GPU to use; // this is not necessary, but provided here as an illustration safe_xgboost(XGBoosterSetParam(booster, "gpu_id", "0")); } else { // avoid evaluating objective and metric on a GPU safe_xgboost(XGBoosterSetParam(booster, "gpu_id", "-1")); } safe_xgboost(XGBoosterSetParam(booster, "objective", "binary:logistic")); safe_xgboost(XGBoosterSetParam(booster, "min_child_weight", "1")); safe_xgboost(XGBoosterSetParam(booster, "gamma", "0.1")); safe_xgboost(XGBoosterSetParam(booster, "max_depth", "3")); safe_xgboost(XGBoosterSetParam(booster, "verbosity", silent ? "0" : "1")); // train and evaluate for 10 iterations int n_trees = 10; const char* eval_names[2] = {"train", "test"}; const char* eval_result = NULL; for (int i = 0; i < n_trees; ++i) { safe_xgboost(XGBoosterUpdateOneIter(booster, i, dtrain)); safe_xgboost(XGBoosterEvalOneIter(booster, i, eval_dmats, eval_names, 2, &eval_result)); printf("%s\n", eval_result); } bst_ulong num_feature = 0; safe_xgboost(XGBoosterGetNumFeature(booster, &num_feature)); printf("num_feature: %lu\n", (unsigned long)(num_feature)); // predict bst_ulong out_len = 0; const float* out_result = NULL; int n_print = 10; safe_xgboost(XGBoosterPredict(booster, dtest, 0, 0, 0, &out_len, &out_result)); printf("y_pred: "); for (int i = 0; i < n_print; ++i) { printf("%1.4f ", out_result[i]); } printf("\n"); // print true labels safe_xgboost(XGDMatrixGetFloatInfo(dtest, "label", &out_len, &out_result)); printf("y_test: "); for (int i = 0; i < n_print; ++i) { printf("%1.4f ", out_result[i]); } printf("\n"); { printf("Dense Matrix Example (XGDMatrixCreateFromMat): "); const float values[] = {0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0}; DMatrixHandle dmat; safe_xgboost(XGDMatrixCreateFromMat(values, 1, 127, 0.0, &dmat)); bst_ulong out_len = 0; const float* out_result = NULL; safe_xgboost(XGBoosterPredict(booster, dmat, 0, 0, 0, &out_len, &out_result)); assert(out_len == 1); printf("%1.4f \n", out_result[0]); safe_xgboost(XGDMatrixFree(dmat)); } { printf("Sparse Matrix Example (XGDMatrixCreateFromCSREx): "); const size_t indptr[] = {0, 22}; const unsigned indices[] = {1, 9, 19, 21, 24, 34, 36, 39, 42, 53, 56, 65, 69, 77, 86, 88, 92, 95, 102, 106, 117, 122}; const float data[] = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0}; DMatrixHandle dmat; safe_xgboost(XGDMatrixCreateFromCSREx(indptr, indices, data, 2, 22, 127, &dmat)); bst_ulong out_len = 0; const float* out_result = NULL; safe_xgboost(XGBoosterPredict(booster, dmat, 0, 0, 0, &out_len, &out_result)); assert(out_len == 1); printf("%1.4f \n", out_result[0]); safe_xgboost(XGDMatrixFree(dmat)); } { printf("Sparse Matrix Example (XGDMatrixCreateFromCSCEx): "); const size_t col_ptr[] = {0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22}; const unsigned indices[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; const float data[] = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0}; DMatrixHandle dmat; safe_xgboost(XGDMatrixCreateFromCSCEx(col_ptr, indices, data, 128, 22, 1, &dmat)); bst_ulong out_len = 0; const float* out_result = NULL; safe_xgboost(XGBoosterPredict(booster, dmat, 0, 0, 0, &out_len, &out_result)); assert(out_len == 1); printf("%1.4f \n", out_result[0]); safe_xgboost(XGDMatrixFree(dmat)); } // free everything safe_xgboost(XGBoosterFree(booster)); safe_xgboost(XGDMatrixFree(dtrain)); safe_xgboost(XGDMatrixFree(dtest)); return 0; } xgboost-1.5.2/demo/c-api/external-memory/000077500000000000000000000000001417122711700202545ustar00rootroot00000000000000xgboost-1.5.2/demo/c-api/external-memory/CMakeLists.txt000066400000000000000000000003721417122711700230160ustar00rootroot00000000000000cmake_minimum_required(VERSION 3.13) project(external-memory-demo LANGUAGES C VERSION 0.0.1) find_package(xgboost REQUIRED) add_executable(external-memory-demo external_memory.c) target_link_libraries(external-memory-demo PRIVATE xgboost::xgboost) xgboost-1.5.2/demo/c-api/external-memory/README.md000066400000000000000000000017031417122711700215340ustar00rootroot00000000000000Defining a Custom Data Iterator to Load Data from External Memory ================================================================= A simple demo for using custom data iterator with XGBoost. The feature is still **experimental** and not ready for production use. If you are not familiar with C API, please read its introduction in our tutorials and visit the basic demo first. Defining Data Iterator ---------------------- In the example, we define a custom data iterator with 2 methods: `reset` and `next`. The `next` method passes data into XGBoost and tells XGBoost whether the iterator has reached its end, and the `reset` method resets iterations. One important detail when using the C API for data iterator is users need to make sure that the data passed into `next` method must be kept in memory until the next iteration or `reset` is called. The external memory DMatrix is not limited to training, but also valid for other features like prediction.xgboost-1.5.2/demo/c-api/external-memory/external_memory.c000066400000000000000000000131671417122711700236420ustar00rootroot00000000000000/*! * Copyright 2021 XGBoost contributors * * \brief A simple example of using xgboost data callback API. */ #include #include #include #include #define safe_xgboost(err) \ if ((err) != 0) { \ fprintf(stderr, "%s:%d: error in %s: %s\n", __FILE__, __LINE__, #err, \ XGBGetLastError()); \ exit(1); \ } #define N_BATCHS 32 #define BATCH_LEN 512 /* Shorthands. */ typedef DMatrixHandle DMatrix; typedef BoosterHandle Booster; typedef struct _DataIter { /* Data of each batch. */ float **data; /* Labels of each batch */ float **labels; /* Length of each batch. */ size_t *lengths; /* Total number of batches. */ size_t n; /* Current iteration. */ size_t cur_it; /* Private fields */ DMatrix _proxy; char _array[128]; } DataIter; #define safe_malloc(ptr) \ if ((ptr) == NULL) { \ fprintf(stderr, "%s:%d: Failed to allocate memory.\n", __FILE__, \ __LINE__); \ exit(1); \ } /** * Initialize with random data for demo. In practice the data should be loaded * from external memory. We just demonstrate how to use the iterator in * XGBoost. * * \param batch_size Number of elements for each batch. The demo here is only using 1 * column. * \param n_batches Number of batches. */ void DataIterator_Init(DataIter *self, size_t batch_size, size_t n_batches) { self->n = n_batches; self->lengths = (size_t *)malloc(self->n * sizeof(size_t)); safe_malloc(self->lengths); for (size_t i = 0; i < self->n; ++i) { self->lengths[i] = batch_size; } self->data = (float **)malloc(self->n * sizeof(float *)); safe_malloc(self->data); self->labels = (float **)malloc(self->n * sizeof(float *)); safe_malloc(self->labels); /* Generate some random data. */ for (size_t i = 0; i < self->n; ++i) { self->data[i] = (float *)malloc(self->lengths[i] * sizeof(float)); safe_malloc(self->data[i]); for (size_t j = 0; j < self->lengths[i]; ++j) { float x = (float)rand() / (float)(RAND_MAX); self->data[i][j] = x; } self->labels[i] = (float *)malloc(self->lengths[i] * sizeof(float)); safe_malloc(self->labels[i]); for (size_t j = 0; j < self->lengths[i]; ++j) { float y = (float)rand() / (float)(RAND_MAX); self->labels[i][j] = y; } } self->cur_it = 0; safe_xgboost(XGProxyDMatrixCreate(&self->_proxy)); } void DataIterator_Free(DataIter *self) { for (size_t i = 0; i < self->n; ++i) { free(self->data[i]); free(self->labels[i]); } free(self->data); free(self->lengths); free(self->labels); safe_xgboost(XGDMatrixFree(self->_proxy)); }; int DataIterator_Next(DataIterHandle handle) { DataIter *self = (DataIter *)(handle); if (self->cur_it == self->n) { self->cur_it = 0; return 0; /* At end */ } /* A JSON string encoding array interface (standard from numpy). */ char array[] = "{\"data\": [%lu, false], \"shape\":[%lu, 1], \"typestr\": " "\"_array, '\0', sizeof(self->_array)); sprintf(self->_array, array, (size_t)self->data[self->cur_it], self->lengths[self->cur_it]); safe_xgboost(XGProxyDMatrixSetDataDense(self->_proxy, self->_array)); /* The data passed in the iterator must remain valid (not being freed until the next * iteration or reset) */ safe_xgboost(XGDMatrixSetDenseInfo(self->_proxy, "label", self->labels[self->cur_it], self->lengths[self->cur_it], 1)); self->cur_it++; return 1; /* Continue. */ } void DataIterator_Reset(DataIterHandle handle) { DataIter *self = (DataIter *)(handle); self->cur_it = 0; } /** * Train a regression model and save it into JSON model file. */ void TrainModel(DMatrix Xy) { /* Create booster for training. */ Booster booster; DMatrix cache[] = {Xy}; safe_xgboost(XGBoosterCreate(cache, 1, &booster)); /* Use approx for external memory training. */ safe_xgboost(XGBoosterSetParam(booster, "tree_method", "approx")); safe_xgboost(XGBoosterSetParam(booster, "objective", "reg:squarederror")); /* Start training. */ const char *validation_names[1] = {"train"}; const char *validation_result = NULL; size_t n_rounds = 10; for (size_t i = 0; i < n_rounds; ++i) { safe_xgboost(XGBoosterUpdateOneIter(booster, i, Xy)); safe_xgboost(XGBoosterEvalOneIter(booster, i, cache, validation_names, 1, &validation_result)); printf("%s\n", validation_result); } /* Save the model to a JSON file. */ safe_xgboost(XGBoosterSaveModel(booster, "model.json")); safe_xgboost(XGBoosterFree(booster)); } int main() { DataIter iter; DataIterator_Init(&iter, BATCH_LEN, N_BATCHS); /* Create DMatrix from iterator. During training, some cache files with the * prefix "cache-" will be generated in current directory */ char config[] = "{\"missing\": NaN, \"cache_prefix\": \"cache\"}"; DMatrix Xy; safe_xgboost(XGDMatrixCreateFromCallback( &iter, iter._proxy, DataIterator_Reset, DataIterator_Next, config, &Xy)); TrainModel(Xy); safe_xgboost(XGDMatrixFree(Xy)); DataIterator_Free(&iter); return 0; } xgboost-1.5.2/demo/c-api/inference/000077500000000000000000000000001417122711700170625ustar00rootroot00000000000000xgboost-1.5.2/demo/c-api/inference/CMakeLists.txt000066400000000000000000000007471417122711700216320ustar00rootroot00000000000000cmake_minimum_required(VERSION 3.13) project(inference-demo LANGUAGES C VERSION 0.0.1) find_package(xgboost REQUIRED) # xgboost is built as static libraries, all cxx dependencies need to be linked into the # executable. if (XGBOOST_BUILD_STATIC_LIB) enable_language(CXX) # find again for those cxx libraries. find_package(xgboost REQUIRED) endif(XGBOOST_BUILD_STATIC_LIB) add_executable(inference-demo inference.c) target_link_libraries(inference-demo PRIVATE xgboost::xgboost) xgboost-1.5.2/demo/c-api/inference/inference.c000066400000000000000000000154141417122711700211710ustar00rootroot00000000000000/*! * Copyright 2021 XGBoost contributors * * \brief A simple example of using prediction functions. */ #include #include #include #include #define safe_xgboost(err) \ if ((err) != 0) { \ fprintf(stderr, "%s:%d: error in %s: %s\n", __FILE__, __LINE__, #err, \ XGBGetLastError()); \ exit(1); \ } #define safe_malloc(ptr) \ if ((ptr) == NULL) { \ fprintf(stderr, "%s:%d: Failed to allocate memory.\n", __FILE__, \ __LINE__); \ exit(1); \ } #define N_SAMPLES 128 #define N_FEATURES 16 typedef BoosterHandle Booster; typedef DMatrixHandle DMatrix; /* Row-major matrix */ struct _Matrix { float *data; size_t shape[2]; /* private members */ char _array_intrerface[256]; }; /* A custom data type for demo. */ typedef struct _Matrix *Matrix; /* Initialize matrix, copy data from `data` if it's not NULL. */ void Matrix_Create(Matrix *self, float const *data, size_t n_samples, size_t n_features) { if (self == NULL) { fprintf(stderr, "Invalid pointer to %s\n", __func__); exit(-1); } *self = (Matrix)malloc(sizeof(struct _Matrix)); safe_malloc(*self); (*self)->data = (float *)malloc(n_samples * n_features * sizeof(float)); safe_malloc((*self)->data); (*self)->shape[0] = n_samples; (*self)->shape[1] = n_features; if (data != NULL) { memcpy((*self)->data, data, (*self)->shape[0] * (*self)->shape[1] * sizeof(float)); } } /* Generate random matrix. */ void Matrix_Random(Matrix *self, size_t n_samples, size_t n_features) { Matrix_Create(self, NULL, n_samples, n_features); for (size_t i = 0; i < n_samples * n_features; ++i) { float x = (float)rand() / (float)(RAND_MAX); (*self)->data[i] = x; } } /* Array interface specified by numpy. */ char const *Matrix_ArrayInterface(Matrix self) { char const template[] = "{\"data\": [%lu, true], \"shape\": [%lu, %lu], " "\"typestr\": \"_array_intrerface, '\0', sizeof(self->_array_intrerface)); sprintf(self->_array_intrerface, template, (size_t)self->data, self->shape[0], self->shape[1]); return self->_array_intrerface; } size_t Matrix_NSamples(Matrix self) { return self->shape[0]; } size_t Matrix_NFeatures(Matrix self) { return self->shape[1]; } float Matrix_At(Matrix self, size_t i, size_t j) { return self->data[i * self->shape[1] + j]; } void Matrix_Print(Matrix self) { for (size_t i = 0; i < Matrix_NSamples(self); i++) { for (size_t j = 0; j < Matrix_NFeatures(self); ++j) { printf("%f, ", Matrix_At(self, i, j)); } } printf("\n"); } void Matrix_Free(Matrix self) { if (self != NULL) { if (self->data != NULL) { self->shape[0] = 0; self->shape[1] = 0; free(self->data); self->data = NULL; } free(self); } } int main() { Matrix X; Matrix y; Matrix_Random(&X, N_SAMPLES, N_FEATURES); Matrix_Random(&y, N_SAMPLES, 1); char const *X_interface = Matrix_ArrayInterface(X); char config[] = "{\"nthread\": 16, \"missing\": NaN}"; DMatrix Xy; /* Dense means "dense matrix". */ safe_xgboost(XGDMatrixCreateFromDense(X_interface, config, &Xy)); /* Label must be in a contigious array. */ safe_xgboost(XGDMatrixSetDenseInfo(Xy, "label", y->data, y->shape[0], 1)); DMatrix cache[] = {Xy}; Booster booster; /* Train a booster for demo. */ safe_xgboost(XGBoosterCreate(cache, 1, &booster)); size_t n_rounds = 10; for (size_t i = 0; i < n_rounds; ++i) { safe_xgboost(XGBoosterUpdateOneIter(booster, i, Xy)); } /* Save the trained model in JSON format. */ safe_xgboost(XGBoosterSaveModel(booster, "model.json")); safe_xgboost(XGBoosterFree(booster)); /* Load it back for inference. The save and load is not required, only shown here for * demonstration purpose. */ safe_xgboost(XGBoosterCreate(NULL, 0, &booster)); safe_xgboost(XGBoosterLoadModel(booster, "model.json")); { /* Run prediction with DMatrix object. */ char const config[] = "{\"training\": false, \"type\": 0, " "\"iteration_begin\": 0, \"iteration_end\": 0, \"strict_shape\": true}"; /* Shape of output prediction */ uint64_t const *out_shape; /* Dimension of output prediction */ uint64_t out_dim; /* Pointer to a thread local contigious array, assigned in prediction function. */ float const *out_results; safe_xgboost(XGBoosterPredictFromDMatrix(booster, Xy, config, &out_shape, &out_dim, &out_results)); if (out_dim != 2 || out_shape[0] != N_SAMPLES || out_shape[1] != 1) { fprintf(stderr, "Regression model should output prediction as vector."); exit(-1); } Matrix predt; /* Always copy output from XGBoost before calling next API function. */ Matrix_Create(&predt, out_results, out_shape[0], out_shape[1]); printf("Results from prediction\n"); Matrix_Print(predt); Matrix_Free(predt); } { /* Run inplace prediction, which is faster and more memory efficient, but supports * only basic inference types. */ char const config[] = "{\"type\": 0, \"iteration_begin\": 0, " "\"iteration_end\": 0, \"strict_shape\": true, " "\"cache_id\": 0, \"missing\": NaN}"; /* Shape of output prediction */ uint64_t const *out_shape; /* Dimension of output prediction */ uint64_t out_dim; /* Pointer to a thread local contigious array, assigned in prediction function. */ float const *out_results; char const *X_interface = Matrix_ArrayInterface(X); safe_xgboost(XGBoosterPredictFromDense(booster, X_interface, config, NULL, &out_shape, &out_dim, &out_results)); if (out_dim != 2 || out_shape[0] != N_SAMPLES || out_shape[1] != 1) { fprintf(stderr, "Regression model should output prediction as vector, %lu, %lu", out_dim, out_shape[0]); exit(-1); } Matrix predt; /* Always copy output from XGBoost before calling next API function. */ Matrix_Create(&predt, out_results, out_shape[0], out_shape[1]); printf("Results from inplace prediction\n"); Matrix_Print(predt); Matrix_Free(predt); } XGBoosterFree(booster); XGDMatrixFree(Xy); Matrix_Free(X); Matrix_Free(y); return 0; } xgboost-1.5.2/demo/dask/000077500000000000000000000000001417122711700150555ustar00rootroot00000000000000xgboost-1.5.2/demo/dask/README.md000066400000000000000000000002531417122711700163340ustar00rootroot00000000000000Dask ==== This directory contains some demonstrations for using `dask` with `XGBoost`. For an overview, see https://xgboost.readthedocs.io/en/latest/tutorials/dask.html .xgboost-1.5.2/demo/dask/callbacks.py000066400000000000000000000056071417122711700173560ustar00rootroot00000000000000"""Example of using callbacks in Dask""" import numpy as np import xgboost as xgb from xgboost.dask import DaskDMatrix from dask.distributed import Client from dask.distributed import LocalCluster from dask_ml.datasets import make_regression from dask_ml.model_selection import train_test_split def probability_for_going_backward(epoch): return 0.999 / (1.0 + 0.05 * np.log(1.0 + epoch)) # All callback functions must inherit from TrainingCallback class CustomEarlyStopping(xgb.callback.TrainingCallback): """A custom early stopping class where early stopping is determined stochastically. In the beginning, allow the metric to become worse with a probability of 0.999. As boosting progresses, the probability should be adjusted downward""" def __init__(self, *, validation_set, target_metric, maximize, seed): self.validation_set = validation_set self.target_metric = target_metric self.maximize = maximize self.seed = seed self.rng = np.random.default_rng(seed=seed) if maximize: self.better = lambda x, y: x > y else: self.better = lambda x, y: x < y def after_iteration(self, model, epoch, evals_log): metric_history = evals_log[self.validation_set][self.target_metric] if len(metric_history) < 2 or self.better( metric_history[-1], metric_history[-2] ): return False # continue training p = probability_for_going_backward(epoch) go_backward = self.rng.choice(2, size=(1,), replace=True, p=[1 - p, p]).astype( np.bool )[0] print( "The validation metric went into the wrong direction. " + f"Stopping training with probability {1 - p}..." ) if go_backward: return False # continue training else: return True # stop training def main(client): m = 100000 n = 100 X, y = make_regression(n_samples=m, n_features=n, chunks=200, random_state=0) X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0) dtrain = DaskDMatrix(client, X_train, y_train) dtest = DaskDMatrix(client, X_test, y_test) output = xgb.dask.train( client, { "verbosity": 1, "tree_method": "hist", "objective": "reg:squarederror", "eval_metric": "rmse", "max_depth": 6, "learning_rate": 1.0, }, dtrain, num_boost_round=1000, evals=[(dtrain, "train"), (dtest, "test")], callbacks=[ CustomEarlyStopping( validation_set="test", target_metric="rmse", maximize=False, seed=0 ) ], ) if __name__ == "__main__": # or use other clusters for scaling with LocalCluster(n_workers=4, threads_per_worker=1) as cluster: with Client(cluster) as client: main(client) xgboost-1.5.2/demo/dask/cpu_survival.py000066400000000000000000000046341417122711700201600ustar00rootroot00000000000000import xgboost as xgb import os from xgboost.dask import DaskDMatrix import dask.dataframe as dd from dask.distributed import Client from dask.distributed import LocalCluster def main(client): # Load an example survival data from CSV into a Dask data frame. # The Veterans' Administration Lung Cancer Trial # The Statistical Analysis of Failure Time Data by Kalbfleisch J. and Prentice R (1980) CURRENT_DIR = os.path.dirname(__file__) df = dd.read_csv(os.path.join(CURRENT_DIR, os.pardir, 'data', 'veterans_lung_cancer.csv')) # DaskDMatrix acts like normal DMatrix, works as a proxy for local # DMatrix scatter around workers. # For AFT survival, you'd need to extract the lower and upper bounds for the label # and pass them as arguments to DaskDMatrix. y_lower_bound = df['Survival_label_lower_bound'] y_upper_bound = df['Survival_label_upper_bound'] X = df.drop(['Survival_label_lower_bound', 'Survival_label_upper_bound'], axis=1) dtrain = DaskDMatrix(client, X, label_lower_bound=y_lower_bound, label_upper_bound=y_upper_bound) # Use train method from xgboost.dask instead of xgboost. This # distributed version of train returns a dictionary containing the # resulting booster and evaluation history obtained from # evaluation metrics. params = {'verbosity': 1, 'objective': 'survival:aft', 'eval_metric': 'aft-nloglik', 'learning_rate': 0.05, 'aft_loss_distribution_scale': 1.20, 'aft_loss_distribution': 'normal', 'max_depth': 6, 'lambda': 0.01, 'alpha': 0.02} output = xgb.dask.train(client, params, dtrain, num_boost_round=100, evals=[(dtrain, 'train')]) bst = output['booster'] history = output['history'] # you can pass output directly into `predict` too. prediction = xgb.dask.predict(client, bst, dtrain) print('Evaluation history: ', history) # Uncomment the following line to save the model to the disk # bst.save_model('survival_model.json') return prediction if __name__ == '__main__': # or use other clusters for scaling with LocalCluster(n_workers=7, threads_per_worker=4) as cluster: with Client(cluster) as client: main(client) xgboost-1.5.2/demo/dask/cpu_training.py000066400000000000000000000026131417122711700201130ustar00rootroot00000000000000import xgboost as xgb from xgboost.dask import DaskDMatrix from dask.distributed import Client from dask.distributed import LocalCluster from dask import array as da def main(client): # generate some random data for demonstration m = 100000 n = 100 X = da.random.random(size=(m, n), chunks=100) y = da.random.random(size=(m, ), chunks=100) # DaskDMatrix acts like normal DMatrix, works as a proxy for local # DMatrix scatter around workers. dtrain = DaskDMatrix(client, X, y) # Use train method from xgboost.dask instead of xgboost. This # distributed version of train returns a dictionary containing the # resulting booster and evaluation history obtained from # evaluation metrics. output = xgb.dask.train(client, {'verbosity': 1, 'tree_method': 'hist'}, dtrain, num_boost_round=4, evals=[(dtrain, 'train')]) bst = output['booster'] history = output['history'] # you can pass output directly into `predict` too. prediction = xgb.dask.predict(client, bst, dtrain) print('Evaluation history:', history) return prediction if __name__ == '__main__': # or use other clusters for scaling with LocalCluster(n_workers=7, threads_per_worker=4) as cluster: with Client(cluster) as client: main(client) xgboost-1.5.2/demo/dask/gpu_training.py000066400000000000000000000061111417122711700201140ustar00rootroot00000000000000from dask_cuda import LocalCUDACluster from dask.distributed import Client from dask import array as da import xgboost as xgb from xgboost import dask as dxgb from xgboost.dask import DaskDMatrix import cupy as cp import argparse def using_dask_matrix(client: Client, X, y): # DaskDMatrix acts like normal DMatrix, works as a proxy for local # DMatrix scatter around workers. dtrain = DaskDMatrix(client, X, y) # Use train method from xgboost.dask instead of xgboost. This # distributed version of train returns a dictionary containing the # resulting booster and evaluation history obtained from # evaluation metrics. output = xgb.dask.train(client, {'verbosity': 2, # Golden line for GPU training 'tree_method': 'gpu_hist'}, dtrain, num_boost_round=4, evals=[(dtrain, 'train')]) bst = output['booster'] history = output['history'] # you can pass output directly into `predict` too. prediction = xgb.dask.predict(client, bst, dtrain) print('Evaluation history:', history) return prediction def using_quantile_device_dmatrix(client: Client, X, y): '''`DaskDeviceQuantileDMatrix` is a data type specialized for `gpu_hist`, tree method that reduces memory overhead. When training on GPU pipeline, it's preferred over `DaskDMatrix`. .. versionadded:: 1.2.0 ''' # Input must be on GPU for `DaskDeviceQuantileDMatrix`. X = X.map_blocks(cp.array) y = y.map_blocks(cp.array) # `DaskDeviceQuantileDMatrix` is used instead of `DaskDMatrix`, be careful # that it can not be used for anything else than training. dtrain = dxgb.DaskDeviceQuantileDMatrix(client, X, y) output = xgb.dask.train(client, {'verbosity': 2, 'tree_method': 'gpu_hist'}, dtrain, num_boost_round=4) prediction = xgb.dask.predict(client, output, X) return prediction if __name__ == '__main__': parser = argparse.ArgumentParser() parser.add_argument( '--ddqdm', choices=[0, 1], type=int, default=1, help='''Whether should we use `DaskDeviceQuantileDMatrix`''') args = parser.parse_args() # `LocalCUDACluster` is used for assigning GPU to XGBoost processes. Here # `n_workers` represents the number of GPUs since we use one GPU per worker # process. with LocalCUDACluster(n_workers=2, threads_per_worker=4) as cluster: with Client(cluster) as client: # generate some random data for demonstration m = 100000 n = 100 X = da.random.random(size=(m, n), chunks=100) y = da.random.random(size=(m, ), chunks=100) if args.ddqdm == 1: print('Using DaskDeviceQuantileDMatrix') from_ddqdm = using_quantile_device_dmatrix(client, X, y) else: print('Using DMatrix') from_dmatrix = using_dask_matrix(client, X, y) xgboost-1.5.2/demo/dask/sklearn_cpu_training.py000066400000000000000000000022361417122711700216330ustar00rootroot00000000000000'''Dask interface demo: Use scikit-learn regressor interface with CPU histogram tree method.''' from dask.distributed import Client from dask.distributed import LocalCluster from dask import array as da import xgboost def main(client): # generate some random data for demonstration n = 100 m = 10000 partition_size = 100 X = da.random.random((m, n), partition_size) y = da.random.random(m, partition_size) regressor = xgboost.dask.DaskXGBRegressor(verbosity=1, n_estimators=2) regressor.set_params(tree_method='hist') # assigning client here is optional regressor.client = client regressor.fit(X, y, eval_set=[(X, y)]) prediction = regressor.predict(X) bst = regressor.get_booster() history = regressor.evals_result() print('Evaluation history:', history) # returned prediction is always a dask array. assert isinstance(prediction, da.Array) return bst # returning the trained model if __name__ == '__main__': # or use other clusters for scaling with LocalCluster(n_workers=4, threads_per_worker=1) as cluster: with Client(cluster) as client: main(client) xgboost-1.5.2/demo/dask/sklearn_gpu_training.py000066400000000000000000000024261417122711700216400ustar00rootroot00000000000000'''Dask interface demo: Use scikit-learn regressor interface with GPU histogram tree method.''' from dask.distributed import Client # It's recommended to use dask_cuda for GPU assignment from dask_cuda import LocalCUDACluster from dask import array as da import xgboost def main(client): # generate some random data for demonstration n = 100 m = 1000000 partition_size = 10000 X = da.random.random((m, n), partition_size) y = da.random.random(m, partition_size) regressor = xgboost.dask.DaskXGBRegressor(verbosity=1) regressor.set_params(tree_method='gpu_hist') # assigning client here is optional regressor.client = client regressor.fit(X, y, eval_set=[(X, y)]) prediction = regressor.predict(X) bst = regressor.get_booster() history = regressor.evals_result() print('Evaluation history:', history) # returned prediction is always a dask array. assert isinstance(prediction, da.Array) return bst # returning the trained model if __name__ == '__main__': # With dask cuda, one can scale up XGBoost to arbitrary GPU clusters. # `LocalCUDACluster` used here is only for demonstration purpose. with LocalCUDACluster() as cluster: with Client(cluster) as client: main(client) xgboost-1.5.2/demo/data/000077500000000000000000000000001417122711700150445ustar00rootroot00000000000000xgboost-1.5.2/demo/data/README.md000066400000000000000000000002041417122711700163170ustar00rootroot00000000000000This folder contains processed example dataset used by the demos. 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95:1 102:1 110:1 115:1 121:1 xgboost-1.5.2/demo/data/featmap.txt000066400000000000000000000062031417122711700172230ustar00rootroot000000000000000 cap-shape=bell i 1 cap-shape=conical i 2 cap-shape=convex i 3 cap-shape=flat i 4 cap-shape=knobbed i 5 cap-shape=sunken i 6 cap-surface=fibrous i 7 cap-surface=grooves i 8 cap-surface=scaly i 9 cap-surface=smooth i 10 cap-color=brown i 11 cap-color=buff i 12 cap-color=cinnamon i 13 cap-color=gray i 14 cap-color=green i 15 cap-color=pink i 16 cap-color=purple i 17 cap-color=red i 18 cap-color=white i 19 cap-color=yellow i 20 bruises?=bruises i 21 bruises?=no i 22 odor=almond i 23 odor=anise i 24 odor=creosote i 25 odor=fishy i 26 odor=foul i 27 odor=musty i 28 odor=none i 29 odor=pungent i 30 odor=spicy i 31 gill-attachment=attached i 32 gill-attachment=descending i 33 gill-attachment=free i 34 gill-attachment=notched i 35 gill-spacing=close i 36 gill-spacing=crowded i 37 gill-spacing=distant i 38 gill-size=broad i 39 gill-size=narrow i 40 gill-color=black i 41 gill-color=brown i 42 gill-color=buff i 43 gill-color=chocolate i 44 gill-color=gray i 45 gill-color=green i 46 gill-color=orange i 47 gill-color=pink i 48 gill-color=purple i 49 gill-color=red i 50 gill-color=white i 51 gill-color=yellow i 52 stalk-shape=enlarging i 53 stalk-shape=tapering i 54 stalk-root=bulbous i 55 stalk-root=club i 56 stalk-root=cup i 57 stalk-root=equal i 58 stalk-root=rhizomorphs i 59 stalk-root=rooted i 60 stalk-root=missing i 61 stalk-surface-above-ring=fibrous i 62 stalk-surface-above-ring=scaly i 63 stalk-surface-above-ring=silky i 64 stalk-surface-above-ring=smooth i 65 stalk-surface-below-ring=fibrous i 66 stalk-surface-below-ring=scaly i 67 stalk-surface-below-ring=silky i 68 stalk-surface-below-ring=smooth i 69 stalk-color-above-ring=brown i 70 stalk-color-above-ring=buff i 71 stalk-color-above-ring=cinnamon i 72 stalk-color-above-ring=gray i 73 stalk-color-above-ring=orange i 74 stalk-color-above-ring=pink i 75 stalk-color-above-ring=red i 76 stalk-color-above-ring=white i 77 stalk-color-above-ring=yellow i 78 stalk-color-below-ring=brown i 79 stalk-color-below-ring=buff i 80 stalk-color-below-ring=cinnamon i 81 stalk-color-below-ring=gray i 82 stalk-color-below-ring=orange i 83 stalk-color-below-ring=pink i 84 stalk-color-below-ring=red i 85 stalk-color-below-ring=white i 86 stalk-color-below-ring=yellow i 87 veil-type=partial i 88 veil-type=universal i 89 veil-color=brown i 90 veil-color=orange i 91 veil-color=white i 92 veil-color=yellow i 93 ring-number=none i 94 ring-number=one i 95 ring-number=two i 96 ring-type=cobwebby i 97 ring-type=evanescent i 98 ring-type=flaring i 99 ring-type=large i 100 ring-type=none i 101 ring-type=pendant i 102 ring-type=sheathing i 103 ring-type=zone i 104 spore-print-color=black i 105 spore-print-color=brown i 106 spore-print-color=buff i 107 spore-print-color=chocolate i 108 spore-print-color=green i 109 spore-print-color=orange i 110 spore-print-color=purple i 111 spore-print-color=white i 112 spore-print-color=yellow i 113 population=abundant i 114 population=clustered i 115 population=numerous i 116 population=scattered i 117 population=several i 118 population=solitary i 119 habitat=grasses i 120 habitat=leaves i 121 habitat=meadows i 122 habitat=paths i 123 habitat=urban i 124 habitat=waste i 125 habitat=woods i xgboost-1.5.2/demo/data/gen_autoclaims.R000066400000000000000000000010331417122711700201560ustar00rootroot00000000000000site <- 'http://cran.r-project.org' if (!require('dummies')) install.packages('dummies', repos=site) if (!require('insuranceData')) install.packages('insuranceData', repos=site) library(dummies) library(insuranceData) data(AutoClaims) data = AutoClaims data$STATE = as.factor(data$STATE) data$CLASS = as.factor(data$CLASS) data$GENDER = as.factor(data$GENDER) data.dummy <- dummy.data.frame(data, dummy.class='factor', omit.constants=TRUE); write.table(data.dummy, 'autoclaims.csv', sep=',', row.names=F, col.names=F, quote=F) xgboost-1.5.2/demo/data/veterans_lung_cancer.csv000066400000000000000000000133141417122711700217520ustar00rootroot00000000000000Survival_label_lower_bound,Survival_label_upper_bound,Age_in_years,Karnofsky_score,Months_from_Diagnosis,Celltype=adeno,Celltype=large,Celltype=smallcell,Celltype=squamous,Prior_therapy=no,Prior_therapy=yes,Treatment=standard,Treatment=test 72.0,72.0,69.0,60.0,7.0,0,0,0,1,1,0,1,0 411.0,411.0,64.0,70.0,5.0,0,0,0,1,0,1,1,0 228.0,228.0,38.0,60.0,3.0,0,0,0,1,1,0,1,0 126.0,126.0,63.0,60.0,9.0,0,0,0,1,0,1,1,0 118.0,118.0,65.0,70.0,11.0,0,0,0,1,0,1,1,0 10.0,10.0,49.0,20.0,5.0,0,0,0,1,1,0,1,0 82.0,82.0,69.0,40.0,10.0,0,0,0,1,0,1,1,0 110.0,110.0,68.0,80.0,29.0,0,0,0,1,1,0,1,0 314.0,314.0,43.0,50.0,18.0,0,0,0,1,1,0,1,0 100.0,inf,70.0,70.0,6.0,0,0,0,1,1,0,1,0 42.0,42.0,81.0,60.0,4.0,0,0,0,1,1,0,1,0 8.0,8.0,63.0,40.0,58.0,0,0,0,1,0,1,1,0 144.0,144.0,63.0,30.0,4.0,0,0,0,1,1,0,1,0 25.0,inf,52.0,80.0,9.0,0,0,0,1,0,1,1,0 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44.0,44.0,70.0,60.0,13.0,0,0,0,1,0,1,0,1 283.0,283.0,51.0,90.0,2.0,0,0,0,1,1,0,0,1 15.0,15.0,40.0,50.0,13.0,0,0,0,1,0,1,0,1 25.0,25.0,69.0,30.0,2.0,0,0,1,0,1,0,0,1 103.0,inf,36.0,70.0,22.0,0,0,1,0,0,1,0,1 21.0,21.0,71.0,20.0,4.0,0,0,1,0,1,0,0,1 13.0,13.0,62.0,30.0,2.0,0,0,1,0,1,0,0,1 87.0,87.0,60.0,60.0,2.0,0,0,1,0,1,0,0,1 2.0,2.0,44.0,40.0,36.0,0,0,1,0,0,1,0,1 20.0,20.0,54.0,30.0,9.0,0,0,1,0,0,1,0,1 7.0,7.0,66.0,20.0,11.0,0,0,1,0,1,0,0,1 24.0,24.0,49.0,60.0,8.0,0,0,1,0,1,0,0,1 99.0,99.0,72.0,70.0,3.0,0,0,1,0,1,0,0,1 8.0,8.0,68.0,80.0,2.0,0,0,1,0,1,0,0,1 99.0,99.0,62.0,85.0,4.0,0,0,1,0,1,0,0,1 61.0,61.0,71.0,70.0,2.0,0,0,1,0,1,0,0,1 25.0,25.0,70.0,70.0,2.0,0,0,1,0,1,0,0,1 95.0,95.0,61.0,70.0,1.0,0,0,1,0,1,0,0,1 80.0,80.0,71.0,50.0,17.0,0,0,1,0,1,0,0,1 51.0,51.0,59.0,30.0,87.0,0,0,1,0,0,1,0,1 29.0,29.0,67.0,40.0,8.0,0,0,1,0,1,0,0,1 24.0,24.0,60.0,40.0,2.0,1,0,0,0,1,0,0,1 18.0,18.0,69.0,40.0,5.0,1,0,0,0,0,1,0,1 83.0,inf,57.0,99.0,3.0,1,0,0,0,1,0,0,1 31.0,31.0,39.0,80.0,3.0,1,0,0,0,1,0,0,1 51.0,51.0,62.0,60.0,5.0,1,0,0,0,1,0,0,1 90.0,90.0,50.0,60.0,22.0,1,0,0,0,0,1,0,1 52.0,52.0,43.0,60.0,3.0,1,0,0,0,1,0,0,1 73.0,73.0,70.0,60.0,3.0,1,0,0,0,1,0,0,1 8.0,8.0,66.0,50.0,5.0,1,0,0,0,1,0,0,1 36.0,36.0,61.0,70.0,8.0,1,0,0,0,1,0,0,1 48.0,48.0,81.0,10.0,4.0,1,0,0,0,1,0,0,1 7.0,7.0,58.0,40.0,4.0,1,0,0,0,1,0,0,1 140.0,140.0,63.0,70.0,3.0,1,0,0,0,1,0,0,1 186.0,186.0,60.0,90.0,3.0,1,0,0,0,1,0,0,1 84.0,84.0,62.0,80.0,4.0,1,0,0,0,0,1,0,1 19.0,19.0,42.0,50.0,10.0,1,0,0,0,1,0,0,1 45.0,45.0,69.0,40.0,3.0,1,0,0,0,1,0,0,1 80.0,80.0,63.0,40.0,4.0,1,0,0,0,1,0,0,1 52.0,52.0,45.0,60.0,4.0,0,1,0,0,1,0,0,1 164.0,164.0,68.0,70.0,15.0,0,1,0,0,0,1,0,1 19.0,19.0,39.0,30.0,4.0,0,1,0,0,0,1,0,1 53.0,53.0,66.0,60.0,12.0,0,1,0,0,1,0,0,1 15.0,15.0,63.0,30.0,5.0,0,1,0,0,1,0,0,1 43.0,43.0,49.0,60.0,11.0,0,1,0,0,0,1,0,1 340.0,340.0,64.0,80.0,10.0,0,1,0,0,0,1,0,1 133.0,133.0,65.0,75.0,1.0,0,1,0,0,1,0,0,1 111.0,111.0,64.0,60.0,5.0,0,1,0,0,1,0,0,1 231.0,231.0,67.0,70.0,18.0,0,1,0,0,0,1,0,1 378.0,378.0,65.0,80.0,4.0,0,1,0,0,1,0,0,1 49.0,49.0,37.0,30.0,3.0,0,1,0,0,1,0,0,1 xgboost-1.5.2/demo/gpu_acceleration/000077500000000000000000000000001417122711700174375ustar00rootroot00000000000000xgboost-1.5.2/demo/gpu_acceleration/README.md000066400000000000000000000007061417122711700207210ustar00rootroot00000000000000# GPU Acceleration Demo `cover_type.py` shows how to train a model on the [forest cover type](https://archive.ics.uci.edu/ml/datasets/covertype) dataset using GPU acceleration. The forest cover type dataset has 581,012 rows and 54 features, making it time consuming to process. We compare the run-time and accuracy of the GPU and CPU histogram algorithms. `shap.ipynb` demonstrates using GPU acceleration to compute SHAP values for feature importance. xgboost-1.5.2/demo/gpu_acceleration/cover_type.py000066400000000000000000000024631417122711700221750ustar00rootroot00000000000000import xgboost as xgb from sklearn.datasets import fetch_covtype from sklearn.model_selection import train_test_split import time # Fetch dataset using sklearn cov = fetch_covtype() X = cov.data y = cov.target # Create 0.75/0.25 train/test split X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, train_size=0.75, random_state=42) # Specify sufficient boosting iterations to reach a minimum num_round = 3000 # Leave most parameters as default param = {'objective': 'multi:softmax', # Specify multiclass classification 'num_class': 8, # Number of possible output classes 'tree_method': 'gpu_hist' # Use GPU accelerated algorithm } # Convert input data from numpy to XGBoost format dtrain = xgb.DMatrix(X_train, label=y_train) dtest = xgb.DMatrix(X_test, label=y_test) gpu_res = {} # Store accuracy result tmp = time.time() # Train model xgb.train(param, dtrain, num_round, evals=[(dtest, 'test')], evals_result=gpu_res) print("GPU Training Time: %s seconds" % (str(time.time() - tmp))) # Repeat for CPU algorithm tmp = time.time() param['tree_method'] = 'hist' cpu_res = {} xgb.train(param, dtrain, num_round, evals=[(dtest, 'test')], evals_result=cpu_res) print("CPU Training Time: %s seconds" % (str(time.time() - tmp))) xgboost-1.5.2/demo/gpu_acceleration/shap.ipynb000066400000000000000000001506071417122711700214460ustar00rootroot00000000000000{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ".. _california_housing_dataset:\n", "\n", "California Housing dataset\n", "--------------------------\n", "\n", "**Data Set Characteristics:**\n", "\n", " :Number of Instances: 20640\n", "\n", " :Number of Attributes: 8 numeric, predictive attributes and the target\n", "\n", " :Attribute Information:\n", " - MedInc median income in block\n", " - HouseAge median house age in block\n", " - AveRooms average number of rooms\n", " - AveBedrms average number of bedrooms\n", " - Population block population\n", " - AveOccup average house occupancy\n", " - Latitude house block latitude\n", " - Longitude house block longitude\n", "\n", " :Missing Attribute Values: None\n", "\n", "This dataset was obtained from the StatLib repository.\n", "http://lib.stat.cmu.edu/datasets/\n", "\n", "The target variable is the median house value for California districts.\n", "\n", "This dataset was derived from the 1990 U.S. census, using one row per census\n", "block group. A block group is the smallest geographical unit for which the U.S.\n", "Census Bureau publishes sample data (a block group typically has a population\n", "of 600 to 3,000 people).\n", "\n", "It can be downloaded/loaded using the\n", ":func:`sklearn.datasets.fetch_california_housing` function.\n", "\n", ".. topic:: References\n", "\n", " - Pace, R. Kelley and Ronald Barry, Sparse Spatial Autoregressions,\n", " Statistics and Probability Letters, 33 (1997) 291-297\n", "\n", "Wall time: 28.9 s\n" ] } ], "source": [ "import numpy as np\n", "import xgboost as xgb\n", "from sklearn.datasets import fetch_california_housing\n", "\n", "# Fetch dataset using sklearn\n", "data = fetch_california_housing()\n", "print( data.DESCR)\n", "X = data.data\n", "y = data.target\n", "\n", "num_round = 500\n", "\n", "param = {\n", " \"eta\": 0.05,\n", " \"max_depth\": 10,\n", " \"tree_method\": \"gpu_hist\",\n", "}\n", "\n", "# GPU accelerated training\n", "dtrain = xgb.DMatrix(X, label=y, feature_names=data.feature_names)\n", "%time model = xgb.train(param, dtrain,num_round)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 3.73 s\n" ] } ], "source": [ "%%time\n", "# Compute shap values using GPU with xgboost\n", "# model.set_param({\"predictor\":\"cpu_predictor\"})\n", "model.set_param({\"predictor\": \"gpu_predictor\"})\n", "shap_values = model.predict(dtrain, pred_contribs=True)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 49.3 s\n" ] } ], "source": [ "%%time\n", "# Compute shap interaction values using GPU\n", "shap_interaction_values = model.predict(dtrain, pred_interactions=True)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 3.69 s\n" ] }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# We can use the shap package\n", "import shap\n", "\n", "\n", "# shap will call the GPU accelerated version as long as the predictor parameter is set to \"gpu_predictor\"\n", "model.set_param({\"predictor\": \"gpu_predictor\"})\n", "explainer = shap.TreeExplainer(model)\n", "%time shap_values = explainer.shap_values(X)\n", "\n", "# visualize the first prediction's explanation\n", "shap.force_plot(\n", " explainer.expected_value,\n", " shap_values[0, :],\n", " X[0, :],\n", " feature_names=data.feature_names,\n", " matplotlib=True\n", ")" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Show a summary of feature importance\n", "shap.summary_plot(shap_values, X, plot_type=\"bar\", feature_names=data.feature_names)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 } xgboost-1.5.2/demo/guide-python/000077500000000000000000000000001417122711700165475ustar00rootroot00000000000000xgboost-1.5.2/demo/guide-python/README.md000066400000000000000000000016771417122711700200410ustar00rootroot00000000000000XGBoost Python Feature Walkthrough ================================== * [Basic walkthrough of wrappers](basic_walkthrough.py) * [Customize loss function, and evaluation metric](custom_objective.py) * [Re-implement RMSLE as customized metric and objective](custom_rmsle.py) * [Re-Implement `multi:softmax` objective as customized objective](custom_softmax.py) * [Boosting from existing prediction](boost_from_prediction.py) * [Predicting using first n trees](predict_first_ntree.py) * [Generalized Linear Model](generalized_linear_model.py) * [Cross validation](cross_validation.py) * [Predicting leaf indices](predict_leaf_indices.py) * [Sklearn Wrapper](sklearn_examples.py) * [Sklearn Parallel](sklearn_parallel.py) * [Sklearn access evals result](sklearn_evals_result.py) * [Access evals result](evals_result.py) * [External Memory](external_memory.py) * [Training continuation](continuation.py) * [Feature weights for column sampling](feature_weights.py) xgboost-1.5.2/demo/guide-python/basic_walkthrough.py000066400000000000000000000060031417122711700226200ustar00rootroot00000000000000import numpy as np import scipy.sparse import pickle import xgboost as xgb import os # Make sure the demo knows where to load the data. CURRENT_DIR = os.path.dirname(os.path.abspath(__file__)) XGBOOST_ROOT_DIR = os.path.dirname(os.path.dirname(CURRENT_DIR)) DEMO_DIR = os.path.join(XGBOOST_ROOT_DIR, 'demo') # simple example # load file from text file, also binary buffer generated by xgboost dtrain = xgb.DMatrix(os.path.join(DEMO_DIR, 'data', 'agaricus.txt.train?indexing_mode=1')) dtest = xgb.DMatrix(os.path.join(DEMO_DIR, 'data', 'agaricus.txt.test?indexing_mode=1')) # specify parameters via map, definition are same as c++ version param = {'max_depth': 2, 'eta': 1, 'objective': 'binary:logistic'} # specify validations set to watch performance watchlist = [(dtest, 'eval'), (dtrain, 'train')] num_round = 2 bst = xgb.train(param, dtrain, num_round, watchlist) # this is prediction preds = bst.predict(dtest) labels = dtest.get_label() print('error=%f' % (sum(1 for i in range(len(preds)) if int(preds[i] > 0.5) != labels[i]) / float(len(preds)))) bst.save_model('0001.model') # dump model bst.dump_model('dump.raw.txt') # dump model with feature map bst.dump_model('dump.nice.txt', os.path.join(DEMO_DIR, 'data/featmap.txt')) # save dmatrix into binary buffer dtest.save_binary('dtest.buffer') # save model bst.save_model('xgb.model') # load model and data in bst2 = xgb.Booster(model_file='xgb.model') dtest2 = xgb.DMatrix('dtest.buffer') preds2 = bst2.predict(dtest2) # assert they are the same assert np.sum(np.abs(preds2 - preds)) == 0 # alternatively, you can pickle the booster pks = pickle.dumps(bst2) # load model and data in bst3 = pickle.loads(pks) preds3 = bst3.predict(dtest2) # assert they are the same assert np.sum(np.abs(preds3 - preds)) == 0 ### # build dmatrix from scipy.sparse print('start running example of build DMatrix from scipy.sparse CSR Matrix') labels = [] row = [] col = [] dat = [] i = 0 for l in open(os.path.join(DEMO_DIR, 'data', 'agaricus.txt.train')): arr = l.split() labels.append(int(arr[0])) for it in arr[1:]: k, v = it.split(':') row.append(i) col.append(int(k)) dat.append(float(v)) i += 1 csr = scipy.sparse.csr_matrix((dat, (row, col))) dtrain = xgb.DMatrix(csr, label=labels) watchlist = [(dtest, 'eval'), (dtrain, 'train')] bst = xgb.train(param, dtrain, num_round, watchlist) print('start running example of build DMatrix from scipy.sparse CSC Matrix') # we can also construct from csc matrix csc = scipy.sparse.csc_matrix((dat, (row, col))) dtrain = xgb.DMatrix(csc, label=labels) watchlist = [(dtest, 'eval'), (dtrain, 'train')] bst = xgb.train(param, dtrain, num_round, watchlist) print('start running example of build DMatrix from numpy array') # NOTE: npymat is numpy array, we will convert it into scipy.sparse.csr_matrix # in internal implementation then convert to DMatrix npymat = csr.todense() dtrain = xgb.DMatrix(npymat, label=labels) watchlist = [(dtest, 'eval'), (dtrain, 'train')] bst = xgb.train(param, dtrain, num_round, watchlist) xgboost-1.5.2/demo/guide-python/boost_from_prediction.py000066400000000000000000000020421417122711700235100ustar00rootroot00000000000000import os import xgboost as xgb CURRENT_DIR = os.path.dirname(__file__) dtrain = xgb.DMatrix(os.path.join(CURRENT_DIR, '../data/agaricus.txt.train')) dtest = xgb.DMatrix(os.path.join(CURRENT_DIR, '../data/agaricus.txt.test')) watchlist = [(dtest, 'eval'), (dtrain, 'train')] ### # advanced: start from a initial base prediction # print('start running example to start from a initial prediction') # specify parameters via map, definition are same as c++ version param = {'max_depth': 2, 'eta': 1, 'objective': 'binary:logistic'} # train xgboost for 1 round bst = xgb.train(param, dtrain, 1, watchlist) # Note: we need the margin value instead of transformed prediction in # set_base_margin # do predict with output_margin=True, will always give you margin values # before logistic transformation ptrain = bst.predict(dtrain, output_margin=True) ptest = bst.predict(dtest, output_margin=True) dtrain.set_base_margin(ptrain) dtest.set_base_margin(ptest) print('this is result of running from initial prediction') bst = xgb.train(param, dtrain, 1, watchlist) xgboost-1.5.2/demo/guide-python/callbacks.py000066400000000000000000000107141417122711700210430ustar00rootroot00000000000000''' Demo for using and defining callback functions. .. versionadded:: 1.3.0 ''' import xgboost as xgb import tempfile import os import numpy as np from sklearn.datasets import load_breast_cancer from sklearn.model_selection import train_test_split from matplotlib import pyplot as plt import argparse class Plotting(xgb.callback.TrainingCallback): '''Plot evaluation result during training. Only for demonstration purpose as it's quite slow to draw. ''' def __init__(self, rounds): self.fig = plt.figure() self.ax = self.fig.add_subplot(111) self.rounds = rounds self.lines = {} self.fig.show() self.x = np.linspace(0, self.rounds, self.rounds) plt.ion() def _get_key(self, data, metric): return f'{data}-{metric}' def after_iteration(self, model, epoch, evals_log): '''Update the plot.''' if not self.lines: for data, metric in evals_log.items(): for metric_name, log in metric.items(): key = self._get_key(data, metric_name) expanded = log + [0] * (self.rounds - len(log)) self.lines[key], = self.ax.plot(self.x, expanded, label=key) self.ax.legend() else: # https://pythonspot.com/matplotlib-update-plot/ for data, metric in evals_log.items(): for metric_name, log in metric.items(): key = self._get_key(data, metric_name) expanded = log + [0] * (self.rounds - len(log)) self.lines[key].set_ydata(expanded) self.fig.canvas.draw() # False to indicate training should not stop. return False def custom_callback(): '''Demo for defining a custom callback function that plots evaluation result during training.''' X, y = load_breast_cancer(return_X_y=True) X_train, X_valid, y_train, y_valid = train_test_split(X, y, random_state=0) D_train = xgb.DMatrix(X_train, y_train) D_valid = xgb.DMatrix(X_valid, y_valid) num_boost_round = 100 plotting = Plotting(num_boost_round) # Pass it to the `callbacks` parameter as a list. xgb.train( { 'objective': 'binary:logistic', 'eval_metric': ['error', 'rmse'], 'tree_method': 'gpu_hist' }, D_train, evals=[(D_train, 'Train'), (D_valid, 'Valid')], num_boost_round=num_boost_round, callbacks=[plotting]) def check_point_callback(): # only for demo, set a larger value (like 100) in practice as checkpointing is quite # slow. rounds = 2 def check(as_pickle): for i in range(0, 10, rounds): if i == 0: continue if as_pickle: path = os.path.join(tmpdir, 'model_' + str(i) + '.pkl') else: path = os.path.join(tmpdir, 'model_' + str(i) + '.json') assert(os.path.exists(path)) X, y = load_breast_cancer(return_X_y=True) m = xgb.DMatrix(X, y) # Check point to a temporary directory for demo with tempfile.TemporaryDirectory() as tmpdir: # Use callback class from xgboost.callback # Feel free to subclass/customize it to suit your need. check_point = xgb.callback.TrainingCheckPoint(directory=tmpdir, iterations=rounds, name='model') xgb.train({'objective': 'binary:logistic'}, m, num_boost_round=10, verbose_eval=False, callbacks=[check_point]) check(False) # This version of checkpoint saves everything including parameters and # model. See: doc/tutorials/saving_model.rst check_point = xgb.callback.TrainingCheckPoint(directory=tmpdir, iterations=rounds, as_pickle=True, name='model') xgb.train({'objective': 'binary:logistic'}, m, num_boost_round=10, verbose_eval=False, callbacks=[check_point]) check(True) if __name__ == '__main__': parser = argparse.ArgumentParser() parser.add_argument('--plot', default=1, type=int) args = parser.parse_args() check_point_callback() if args.plot: custom_callback() xgboost-1.5.2/demo/guide-python/categorical.py000066400000000000000000000050261417122711700214010ustar00rootroot00000000000000"""Experimental support for categorical data. After 1.5 XGBoost `gpu_hist` tree method has experimental support for one-hot encoding based tree split. In before, users need to run an encoder themselves before passing the data into XGBoost, which creates a sparse matrix and potentially increase memory usage. This demo showcases the experimental categorical data support, more advanced features are planned. .. versionadded:: 1.5.0 """ import pandas as pd import numpy as np import xgboost as xgb from typing import Tuple def make_categorical( n_samples: int, n_features: int, n_categories: int, onehot: bool ) -> Tuple[pd.DataFrame, pd.Series]: """Make some random data for demo.""" rng = np.random.RandomState(1994) pd_dict = {} for i in range(n_features + 1): c = rng.randint(low=0, high=n_categories, size=n_samples) pd_dict[str(i)] = pd.Series(c, dtype=np.int64) df = pd.DataFrame(pd_dict) label = df.iloc[:, 0] df = df.iloc[:, 1:] for i in range(0, n_features): label += df.iloc[:, i] label += 1 df = df.astype("category") categories = np.arange(0, n_categories) for col in df.columns: df[col] = df[col].cat.set_categories(categories) if onehot: return pd.get_dummies(df), label return df, label def main() -> None: # Use builtin categorical data support # For scikit-learn interface, the input data must be pandas DataFrame or cudf # DataFrame with categorical features X, y = make_categorical(100, 10, 4, False) # Specify `enable_categorical` to True. reg = xgb.XGBRegressor(tree_method="gpu_hist", enable_categorical=True) reg.fit(X, y, eval_set=[(X, y)]) # Pass in already encoded data X_enc, y_enc = make_categorical(100, 10, 4, True) reg_enc = xgb.XGBRegressor(tree_method="gpu_hist") reg_enc.fit(X_enc, y_enc, eval_set=[(X_enc, y_enc)]) reg_results = np.array(reg.evals_result()["validation_0"]["rmse"]) reg_enc_results = np.array(reg_enc.evals_result()["validation_0"]["rmse"]) # Check that they have same results np.testing.assert_allclose(reg_results, reg_enc_results) # Convert to DMatrix for SHAP value booster: xgb.Booster = reg.get_booster() m = xgb.DMatrix(X, enable_categorical=True) # specify categorical data support. SHAP = booster.predict(m, pred_contribs=True) margin = booster.predict(m, output_margin=True) np.testing.assert_allclose( np.sum(SHAP, axis=len(SHAP.shape) - 1), margin, rtol=1e-3 ) if __name__ == "__main__": main() xgboost-1.5.2/demo/guide-python/continuation.py000066400000000000000000000075411417122711700216420ustar00rootroot00000000000000""" Demo for training continuation. """ from sklearn.datasets import load_breast_cancer import xgboost import pickle import tempfile import os def training_continuation(tmpdir: str, use_pickle: bool) -> None: """Basic training continuation.""" # Train 128 iterations in 1 session X, y = load_breast_cancer(return_X_y=True) clf = xgboost.XGBClassifier(n_estimators=128, use_label_encoder=False) clf.fit(X, y, eval_set=[(X, y)], eval_metric="logloss") print("Total boosted rounds:", clf.get_booster().num_boosted_rounds()) # Train 128 iterations in 2 sessions, with the first one runs for 32 iterations and # the second one runs for 96 iterations clf = xgboost.XGBClassifier(n_estimators=32, use_label_encoder=False) clf.fit(X, y, eval_set=[(X, y)], eval_metric="logloss") assert clf.get_booster().num_boosted_rounds() == 32 # load back the model, this could be a checkpoint if use_pickle: path = os.path.join(tmpdir, "model-first-32.pkl") with open(path, "wb") as fd: pickle.dump(clf, fd) with open(path, "rb") as fd: loaded = pickle.load(fd) else: path = os.path.join(tmpdir, "model-first-32.json") clf.save_model(path) loaded = xgboost.XGBClassifier() loaded.load_model(path) clf = xgboost.XGBClassifier(n_estimators=128 - 32) clf.fit(X, y, eval_set=[(X, y)], eval_metric="logloss", xgb_model=loaded) print("Total boosted rounds:", clf.get_booster().num_boosted_rounds()) assert clf.get_booster().num_boosted_rounds() == 128 def training_continuation_early_stop(tmpdir: str, use_pickle: bool) -> None: """Training continuation with early stopping.""" early_stopping_rounds = 5 early_stop = xgboost.callback.EarlyStopping( rounds=early_stopping_rounds, save_best=True ) n_estimators = 512 X, y = load_breast_cancer(return_X_y=True) clf = xgboost.XGBClassifier(n_estimators=n_estimators, use_label_encoder=False) clf.fit(X, y, eval_set=[(X, y)], eval_metric="logloss", callbacks=[early_stop]) print("Total boosted rounds:", clf.get_booster().num_boosted_rounds()) best = clf.best_iteration # Train 512 iterations in 2 sessions, with the first one runs for 128 iterations and # the second one runs until early stop. clf = xgboost.XGBClassifier(n_estimators=128, use_label_encoder=False) # Reinitialize the early stop callback early_stop = xgboost.callback.EarlyStopping( rounds=early_stopping_rounds, save_best=True ) clf.fit(X, y, eval_set=[(X, y)], eval_metric="logloss", callbacks=[early_stop]) assert clf.get_booster().num_boosted_rounds() == 128 # load back the model, this could be a checkpoint if use_pickle: path = os.path.join(tmpdir, "model-first-128.pkl") with open(path, "wb") as fd: pickle.dump(clf, fd) with open(path, "rb") as fd: loaded = pickle.load(fd) else: path = os.path.join(tmpdir, "model-first-128.json") clf.save_model(path) loaded = xgboost.XGBClassifier(use_label_encoder=False) loaded.load_model(path) early_stop = xgboost.callback.EarlyStopping( rounds=early_stopping_rounds, save_best=True ) clf = xgboost.XGBClassifier( n_estimators=n_estimators - 128, use_label_encoder=False ) clf.fit( X, y, eval_set=[(X, y)], eval_metric="logloss", callbacks=[early_stop], xgb_model=loaded, ) print("Total boosted rounds:", clf.get_booster().num_boosted_rounds()) assert clf.best_iteration == best if __name__ == "__main__": with tempfile.TemporaryDirectory() as tmpdir: training_continuation_early_stop(tmpdir, False) training_continuation_early_stop(tmpdir, True) training_continuation(tmpdir, True) training_continuation(tmpdir, False) xgboost-1.5.2/demo/guide-python/cross_validation.py000066400000000000000000000044771417122711700225000ustar00rootroot00000000000000import os import numpy as np import xgboost as xgb # load data in do training CURRENT_DIR = os.path.dirname(__file__) dtrain = xgb.DMatrix(os.path.join(CURRENT_DIR, '../data/agaricus.txt.train')) param = {'max_depth':2, 'eta':1, 'objective':'binary:logistic'} num_round = 2 print('running cross validation') # do cross validation, this will print result out as # [iteration] metric_name:mean_value+std_value # std_value is standard deviation of the metric xgb.cv(param, dtrain, num_round, nfold=5, metrics={'error'}, seed=0, callbacks=[xgb.callback.EvaluationMonitor(show_stdv=True)]) print('running cross validation, disable standard deviation display') # do cross validation, this will print result out as # [iteration] metric_name:mean_value res = xgb.cv(param, dtrain, num_boost_round=10, nfold=5, metrics={'error'}, seed=0, callbacks=[xgb.callback.EvaluationMonitor(show_stdv=False), xgb.callback.EarlyStopping(3)]) print(res) print('running cross validation, with preprocessing function') # define the preprocessing function # used to return the preprocessed training, test data, and parameter # we can use this to do weight rescale, etc. # as a example, we try to set scale_pos_weight def fpreproc(dtrain, dtest, param): label = dtrain.get_label() ratio = float(np.sum(label == 0)) / np.sum(label == 1) param['scale_pos_weight'] = ratio return (dtrain, dtest, param) # do cross validation, for each fold # the dtrain, dtest, param will be passed into fpreproc # then the return value of fpreproc will be used to generate # results of that fold xgb.cv(param, dtrain, num_round, nfold=5, metrics={'auc'}, seed=0, fpreproc=fpreproc) ### # you can also do cross validation with customized loss function # See custom_objective.py ## print('running cross validation, with customized loss function') def logregobj(preds, dtrain): labels = dtrain.get_label() preds = 1.0 / (1.0 + np.exp(-preds)) grad = preds - labels hess = preds * (1.0 - preds) return grad, hess def evalerror(preds, dtrain): labels = dtrain.get_label() return 'error', float(sum(labels != (preds > 0.0))) / len(labels) param = {'max_depth':2, 'eta':1} # train with customized objective xgb.cv(param, dtrain, num_round, nfold=5, seed=0, obj=logregobj, feval=evalerror) xgboost-1.5.2/demo/guide-python/custom_objective.py000066400000000000000000000043061417122711700224700ustar00rootroot00000000000000### # advanced: customized loss function # import os import numpy as np import xgboost as xgb print('start running example to used customized objective function') CURRENT_DIR = os.path.dirname(__file__) dtrain = xgb.DMatrix(os.path.join(CURRENT_DIR, '../data/agaricus.txt.train')) dtest = xgb.DMatrix(os.path.join(CURRENT_DIR, '../data/agaricus.txt.test')) # note: what we are getting is margin value in prediction you must know what # you are doing param = {'max_depth': 2, 'eta': 1, 'objective': 'reg:logistic'} watchlist = [(dtest, 'eval'), (dtrain, 'train')] num_round = 10 # user define objective function, given prediction, return gradient and second # order gradient this is log likelihood loss def logregobj(preds, dtrain): labels = dtrain.get_label() preds = 1.0 / (1.0 + np.exp(-preds)) # transform raw leaf weight grad = preds - labels hess = preds * (1.0 - preds) return grad, hess # user defined evaluation function, return a pair metric_name, result # NOTE: when you do customized loss function, the default prediction value is # margin, which means the prediction is score before logistic transformation. def evalerror(preds, dtrain): labels = dtrain.get_label() preds = 1.0 / (1.0 + np.exp(-preds)) # transform raw leaf weight # return a pair metric_name, result. The metric name must not contain a # colon (:) or a space return 'my-error', float(sum(labels != (preds > 0.5))) / len(labels) py_evals_result = {} # training with customized objective, we can also do step by step training # simply look at training.py's implementation of train py_params = param.copy() py_params.update({'disable_default_eval_metric': True}) py_logreg = xgb.train(py_params, dtrain, num_round, watchlist, obj=logregobj, feval=evalerror, evals_result=py_evals_result) evals_result = {} params = param.copy() params.update({'eval_metric': 'error'}) logreg = xgb.train(params, dtrain, num_boost_round=num_round, evals=watchlist, evals_result=evals_result) for i in range(len(py_evals_result['train']['my-error'])): np.testing.assert_almost_equal(py_evals_result['train']['my-error'], evals_result['train']['error']) xgboost-1.5.2/demo/guide-python/custom_rmsle.py000066400000000000000000000142751417122711700216460ustar00rootroot00000000000000'''Demo for defining customized metric and objective. Notice that for simplicity reason weight is not used in following example. In this script, we implement the Squared Log Error (SLE) objective and RMSLE metric as customized functions, then compare it with native implementation in XGBoost. See doc/tutorials/custom_metric_obj.rst for a step by step walkthrough, with other details. The `SLE` objective reduces impact of outliers in training dataset, hence here we also compare its performance with standard squared error. ''' import numpy as np import xgboost as xgb from typing import Tuple, Dict, List from time import time import argparse import matplotlib from matplotlib import pyplot as plt # shape of generated data. kRows = 4096 kCols = 16 kOutlier = 10000 # mean of generated outliers kNumberOfOutliers = 64 kRatio = 0.7 kSeed = 1994 kBoostRound = 20 np.random.seed(seed=kSeed) def generate_data() -> Tuple[xgb.DMatrix, xgb.DMatrix]: '''Generate data containing outliers.''' x = np.random.randn(kRows, kCols) y = np.random.randn(kRows) y += np.abs(np.min(y)) # Create outliers for i in range(0, kNumberOfOutliers): ind = np.random.randint(0, len(y)-1) y[ind] += np.random.randint(0, kOutlier) train_portion = int(kRows * kRatio) # rmsle requires all label be greater than -1. assert np.all(y > -1.0) train_x: np.ndarray = x[: train_portion] train_y: np.ndarray = y[: train_portion] dtrain = xgb.DMatrix(train_x, label=train_y) test_x = x[train_portion:] test_y = y[train_portion:] dtest = xgb.DMatrix(test_x, label=test_y) return dtrain, dtest def native_rmse(dtrain: xgb.DMatrix, dtest: xgb.DMatrix) -> Dict[str, Dict[str, List[float]]]: '''Train using native implementation of Root Mean Squared Loss.''' print('Squared Error') squared_error = { 'objective': 'reg:squarederror', 'eval_metric': 'rmse', 'tree_method': 'hist', 'seed': kSeed } start = time() results: Dict[str, Dict[str, List[float]]] = {} xgb.train(squared_error, dtrain=dtrain, num_boost_round=kBoostRound, evals=[(dtrain, 'dtrain'), (dtest, 'dtest')], evals_result=results) print('Finished Squared Error in:', time() - start, '\n') return results def native_rmsle(dtrain: xgb.DMatrix, dtest: xgb.DMatrix) -> Dict[str, Dict[str, List[float]]]: '''Train using native implementation of Squared Log Error.''' print('Squared Log Error') results: Dict[str, Dict[str, List[float]]] = {} squared_log_error = { 'objective': 'reg:squaredlogerror', 'eval_metric': 'rmsle', 'tree_method': 'hist', 'seed': kSeed } start = time() xgb.train(squared_log_error, dtrain=dtrain, num_boost_round=kBoostRound, evals=[(dtrain, 'dtrain'), (dtest, 'dtest')], evals_result=results) print('Finished Squared Log Error in:', time() - start) return results def py_rmsle(dtrain: xgb.DMatrix, dtest: xgb.DMatrix) -> Dict: '''Train using Python implementation of Squared Log Error.''' def gradient(predt: np.ndarray, dtrain: xgb.DMatrix) -> np.ndarray: '''Compute the gradient squared log error.''' y = dtrain.get_label() return (np.log1p(predt) - np.log1p(y)) / (predt + 1) def hessian(predt: np.ndarray, dtrain: xgb.DMatrix) -> np.ndarray: '''Compute the hessian for squared log error.''' y = dtrain.get_label() return ((-np.log1p(predt) + np.log1p(y) + 1) / np.power(predt + 1, 2)) def squared_log(predt: np.ndarray, dtrain: xgb.DMatrix) -> Tuple[np.ndarray, np.ndarray]: '''Squared Log Error objective. A simplified version for RMSLE used as objective function. :math:`\frac{1}{2}[log(pred + 1) - log(label + 1)]^2` ''' predt[predt < -1] = -1 + 1e-6 grad = gradient(predt, dtrain) hess = hessian(predt, dtrain) return grad, hess def rmsle(predt: np.ndarray, dtrain: xgb.DMatrix) -> Tuple[str, float]: ''' Root mean squared log error metric. :math:`\sqrt{\frac{1}{N}[log(pred + 1) - log(label + 1)]^2}` ''' y = dtrain.get_label() predt[predt < -1] = -1 + 1e-6 elements = np.power(np.log1p(y) - np.log1p(predt), 2) return 'PyRMSLE', float(np.sqrt(np.sum(elements) / len(y))) results: Dict[str, Dict[str, List[float]]] = {} xgb.train({'tree_method': 'hist', 'seed': kSeed, 'disable_default_eval_metric': 1}, dtrain=dtrain, num_boost_round=kBoostRound, obj=squared_log, feval=rmsle, evals=[(dtrain, 'dtrain'), (dtest, 'dtest')], evals_result=results) return results def plot_history(rmse_evals, rmsle_evals, py_rmsle_evals): fig, axs = plt.subplots(3, 1) ax0: matplotlib.axes.Axes = axs[0] ax1: matplotlib.axes.Axes = axs[1] ax2: matplotlib.axes.Axes = axs[2] x = np.arange(0, kBoostRound, 1) ax0.plot(x, rmse_evals['dtrain']['rmse'], label='train-RMSE') ax0.plot(x, rmse_evals['dtest']['rmse'], label='test-RMSE') ax0.legend() ax1.plot(x, rmsle_evals['dtrain']['rmsle'], label='train-native-RMSLE') ax1.plot(x, rmsle_evals['dtest']['rmsle'], label='test-native-RMSLE') ax1.legend() ax2.plot(x, py_rmsle_evals['dtrain']['PyRMSLE'], label='train-PyRMSLE') ax2.plot(x, py_rmsle_evals['dtest']['PyRMSLE'], label='test-PyRMSLE') ax2.legend() plt.show() plt.close() def main(args): dtrain, dtest = generate_data() rmse_evals = native_rmse(dtrain, dtest) rmsle_evals = native_rmsle(dtrain, dtest) py_rmsle_evals = py_rmsle(dtrain, dtest) if args.plot != 0: plot_history(rmse_evals, rmsle_evals, py_rmsle_evals) if __name__ == '__main__': parser = argparse.ArgumentParser( description='Arguments for custom RMSLE objective function demo.') parser.add_argument( '--plot', type=int, default=1, help='Set to 0 to disable plotting the evaluation history.') args = parser.parse_args() main(args) xgboost-1.5.2/demo/guide-python/custom_softmax.py000066400000000000000000000127061417122711700222020ustar00rootroot00000000000000'''Demo for creating customized multi-class objective function. This demo is only applicable after (excluding) XGBoost 1.0.0, as before this version XGBoost returns transformed prediction for multi-class objective function. More details in comments. ''' import numpy as np import xgboost as xgb from matplotlib import pyplot as plt import argparse np.random.seed(1994) kRows = 100 kCols = 10 kClasses = 4 # number of classes kRounds = 10 # number of boosting rounds. # Generate some random data for demo. X = np.random.randn(kRows, kCols) y = np.random.randint(0, 4, size=kRows) m = xgb.DMatrix(X, y) def softmax(x): '''Softmax function with x as input vector.''' e = np.exp(x) return e / np.sum(e) def softprob_obj(predt: np.ndarray, data: xgb.DMatrix): '''Loss function. Computing the gradient and approximated hessian (diagonal). Reimplements the `multi:softprob` inside XGBoost. ''' labels = data.get_label() if data.get_weight().size == 0: # Use 1 as weight if we don't have custom weight. weights = np.ones((kRows, 1), dtype=float) else: weights = data.get_weight() # The prediction is of shape (rows, classes), each element in a row # represents a raw prediction (leaf weight, hasn't gone through softmax # yet). In XGBoost 1.0.0, the prediction is transformed by a softmax # function, fixed in later versions. assert predt.shape == (kRows, kClasses) grad = np.zeros((kRows, kClasses), dtype=float) hess = np.zeros((kRows, kClasses), dtype=float) eps = 1e-6 # compute the gradient and hessian, slow iterations in Python, only # suitable for demo. Also the one in native XGBoost core is more robust to # numeric overflow as we don't do anything to mitigate the `exp` in # `softmax` here. for r in range(predt.shape[0]): target = labels[r] p = softmax(predt[r, :]) for c in range(predt.shape[1]): assert target >= 0 or target <= kClasses g = p[c] - 1.0 if c == target else p[c] g = g * weights[r] h = max((2.0 * p[c] * (1.0 - p[c]) * weights[r]).item(), eps) grad[r, c] = g hess[r, c] = h # Right now (XGBoost 1.0.0), reshaping is necessary grad = grad.reshape((kRows * kClasses, 1)) hess = hess.reshape((kRows * kClasses, 1)) return grad, hess def predict(booster: xgb.Booster, X): '''A customized prediction function that converts raw prediction to target class. ''' # Output margin means we want to obtain the raw prediction obtained from # tree leaf weight. predt = booster.predict(X, output_margin=True) out = np.zeros(kRows) for r in range(predt.shape[0]): # the class with maximum prob (not strictly prob as it haven't gone # through softmax yet so it doesn't sum to 1, but result is the same # for argmax). i = np.argmax(predt[r]) out[r] = i return out def merror(predt: np.ndarray, dtrain: xgb.DMatrix): y = dtrain.get_label() # Like custom objective, the predt is untransformed leaf weight assert predt.shape == (kRows, kClasses) out = np.zeros(kRows) for r in range(predt.shape[0]): i = np.argmax(predt[r]) out[r] = i assert y.shape == out.shape errors = np.zeros(kRows) errors[y != out] = 1.0 return 'PyMError', np.sum(errors) / kRows def plot_history(custom_results, native_results): fig, axs = plt.subplots(2, 1) ax0 = axs[0] ax1 = axs[1] pymerror = custom_results['train']['PyMError'] merror = native_results['train']['merror'] x = np.arange(0, kRounds, 1) ax0.plot(x, pymerror, label='Custom objective') ax0.legend() ax1.plot(x, merror, label='multi:softmax') ax1.legend() plt.show() def main(args): custom_results = {} # Use our custom objective function booster_custom = xgb.train({'num_class': kClasses, 'disable_default_eval_metric': True}, m, num_boost_round=kRounds, obj=softprob_obj, feval=merror, evals_result=custom_results, evals=[(m, 'train')]) predt_custom = predict(booster_custom, m) native_results = {} # Use the same objective function defined in XGBoost. booster_native = xgb.train({'num_class': kClasses, 'eval_metric': 'merror'}, m, num_boost_round=kRounds, evals_result=native_results, evals=[(m, 'train')]) predt_native = booster_native.predict(m) # We are reimplementing the loss function in XGBoost, so it should # be the same for normal cases. assert np.all(predt_custom == predt_native) np.testing.assert_allclose(custom_results['train']['PyMError'], native_results['train']['merror']) if args.plot != 0: plot_history(custom_results, native_results) if __name__ == '__main__': parser = argparse.ArgumentParser( description='Arguments for custom softmax objective function demo.') parser.add_argument( '--plot', type=int, default=1, help='Set to 0 to disable plotting the evaluation history.') args = parser.parse_args() main(args) xgboost-1.5.2/demo/guide-python/evals_result.py000066400000000000000000000017671417122711700216440ustar00rootroot00000000000000## # This script demonstrate how to access the eval metrics in xgboost ## import os import xgboost as xgb CURRENT_DIR = os.path.dirname(__file__) dtrain = xgb.DMatrix(os.path.join(CURRENT_DIR, '../data/agaricus.txt.train')) dtest = xgb.DMatrix(os.path.join(CURRENT_DIR, '../data/agaricus.txt.test')) param = [('max_depth', 2), ('objective', 'binary:logistic'), ('eval_metric', 'logloss'), ('eval_metric', 'error')] num_round = 2 watchlist = [(dtest,'eval'), (dtrain,'train')] evals_result = {} bst = xgb.train(param, dtrain, num_round, watchlist, evals_result=evals_result) print('Access logloss metric directly from evals_result:') print(evals_result['eval']['logloss']) print('') print('Access metrics through a loop:') for e_name, e_mtrs in evals_result.items(): print('- {}'.format(e_name)) for e_mtr_name, e_mtr_vals in e_mtrs.items(): print(' - {}'.format(e_mtr_name)) print(' - {}'.format(e_mtr_vals)) print('') print('Access complete dictionary:') print(evals_result) xgboost-1.5.2/demo/guide-python/external_memory.py000066400000000000000000000057151417122711700223430ustar00rootroot00000000000000"""Experimental support for external memory. This is similar to the one in `quantile_data_iterator.py`, but for external memory instead of Quantile DMatrix. The feature is not ready for production use yet. .. versionadded:: 1.5.0 """ import os import xgboost from typing import Callable, List, Tuple import tempfile import numpy as np def make_batches( n_samples_per_batch: int, n_features: int, n_batches: int ) -> Tuple[List[np.ndarray], List[np.ndarray]]: """Generate random batches.""" X = [] y = [] rng = np.random.RandomState(1994) for i in range(n_batches): _X = rng.randn(n_samples_per_batch, n_features) _y = rng.randn(n_samples_per_batch) X.append(_X) y.append(_y) return X, y class Iterator(xgboost.DataIter): """A custom iterator for loading files in batches.""" def __init__(self, file_paths: List[Tuple[str, str]]): self._file_paths = file_paths self._it = 0 # XGBoost will generate some cache files under current directory with the prefix # "cache" super().__init__(cache_prefix=os.path.join(".", "cache")) def load_file(self) -> Tuple[np.ndarray, np.ndarray]: X_path, y_path = self._file_paths[self._it] X = np.loadtxt(X_path) y = np.loadtxt(y_path) assert X.shape[0] == y.shape[0] return X, y def next(self, input_data: Callable) -> int: """Advance the iterator by 1 step and pass the data to XGBoost. This function is called by XGBoost during the construction of ``DMatrix`` """ if self._it == len(self._file_paths): # return 0 to let XGBoost know this is the end of iteration return 0 # input_data is a function passed in by XGBoost who has the similar signature to # the ``DMatrix`` constructor. X, y = self.load_file() input_data(data=X, label=y) self._it += 1 return 1 def reset(self) -> None: """Reset the iterator to its beginning""" self._it = 0 def main(tmpdir: str) -> xgboost.Booster: # generate some random data for demo batches = make_batches(1024, 17, 31) files = [] for i, (X, y) in enumerate(zip(*batches)): X_path = os.path.join(tmpdir, "X-" + str(i) + ".txt") np.savetxt(X_path, X) y_path = os.path.join(tmpdir, "y-" + str(i) + ".txt") np.savetxt(y_path, y) files.append((X_path, y_path)) it = Iterator(files) # For non-data arguments, specify it here once instead of passing them by the `next` # method. missing = np.NaN Xy = xgboost.DMatrix(it, missing=missing, enable_categorical=False) # Other tree methods including ``hist`` and ``gpu_hist`` also work, but has some # caveats. This is still an experimental feature. booster = xgboost.train({"tree_method": "approx"}, Xy) return booster if __name__ == "__main__": with tempfile.TemporaryDirectory() as tmpdir: main(tmpdir) xgboost-1.5.2/demo/guide-python/feature_weights.py000066400000000000000000000022521417122711700223070ustar00rootroot00000000000000'''Using feature weight to change column sampling. .. versionadded:: 1.3.0 ''' import numpy as np import xgboost from matplotlib import pyplot as plt import argparse def main(args): rng = np.random.RandomState(1994) kRows = 1000 kCols = 10 X = rng.randn(kRows, kCols) y = rng.randn(kRows) fw = np.ones(shape=(kCols,)) for i in range(kCols): fw[i] *= float(i) dtrain = xgboost.DMatrix(X, y) dtrain.set_info(feature_weights=fw) bst = xgboost.train({'tree_method': 'hist', 'colsample_bynode': 0.5}, dtrain, num_boost_round=10, evals=[(dtrain, 'd')]) feature_map = bst.get_fscore() # feature zero has 0 weight assert feature_map.get('f0', None) is None assert max(feature_map.values()) == feature_map.get('f9') if args.plot: xgboost.plot_importance(bst) plt.show() if __name__ == '__main__': parser = argparse.ArgumentParser() parser.add_argument( '--plot', type=int, default=1, help='Set to 0 to disable plotting the evaluation history.') args = parser.parse_args() main(args) xgboost-1.5.2/demo/guide-python/gamma_regression.py000066400000000000000000000020151417122711700224410ustar00rootroot00000000000000import xgboost as xgb import numpy as np # this script demonstrates how to fit gamma regression model (with log link function) # in xgboost, before running the demo you need to generate the autoclaims dataset # by running gen_autoclaims.R located in xgboost/demo/data. data = np.genfromtxt('../data/autoclaims.csv', delimiter=',') dtrain = xgb.DMatrix(data[0:4741, 0:34], data[0:4741, 34]) dtest = xgb.DMatrix(data[4741:6773, 0:34], data[4741:6773, 34]) # for gamma regression, we need to set the objective to 'reg:gamma', it also suggests # to set the base_score to a value between 1 to 5 if the number of iteration is small param = {'objective':'reg:gamma', 'booster':'gbtree', 'base_score':3} # the rest of settings are the same watchlist = [(dtest, 'eval'), (dtrain, 'train')] num_round = 30 # training and evaluation bst = xgb.train(param, dtrain, num_round, watchlist) preds = bst.predict(dtest) labels = dtest.get_label() print('test deviance=%f' % (2 * np.sum((labels - preds) / preds - np.log(labels) + np.log(preds)))) xgboost-1.5.2/demo/guide-python/generalized_linear_model.py000066400000000000000000000024311417122711700241240ustar00rootroot00000000000000import os import xgboost as xgb ## # this script demonstrate how to fit generalized linear model in xgboost # basically, we are using linear model, instead of tree for our boosters ## CURRENT_DIR = os.path.dirname(__file__) dtrain = xgb.DMatrix(os.path.join(CURRENT_DIR, '../data/agaricus.txt.train')) dtest = xgb.DMatrix(os.path.join(CURRENT_DIR, '../data/agaricus.txt.test')) # change booster to gblinear, so that we are fitting a linear model # alpha is the L1 regularizer # lambda is the L2 regularizer # you can also set lambda_bias which is L2 regularizer on the bias term param = {'objective':'binary:logistic', 'booster':'gblinear', 'alpha': 0.0001, 'lambda': 1} # normally, you do not need to set eta (step_size) # XGBoost uses a parallel coordinate descent algorithm (shotgun), # there could be affection on convergence with parallelization on certain cases # setting eta to be smaller value, e.g 0.5 can make the optimization more stable # param['eta'] = 1 ## # the rest of settings are the same ## watchlist = [(dtest, 'eval'), (dtrain, 'train')] num_round = 4 bst = xgb.train(param, dtrain, num_round, watchlist) preds = bst.predict(dtest) labels = dtest.get_label() print('error=%f' % (sum(1 for i in range(len(preds)) if int(preds[i] > 0.5) != labels[i]) / float(len(preds)))) xgboost-1.5.2/demo/guide-python/predict_first_ntree.py000066400000000000000000000034531417122711700231640ustar00rootroot00000000000000import os import numpy as np import xgboost as xgb from sklearn.datasets import load_svmlight_file CURRENT_DIR = os.path.dirname(__file__) train = os.path.join(CURRENT_DIR, "../data/agaricus.txt.train") test = os.path.join(CURRENT_DIR, "../data/agaricus.txt.test") def native_interface(): # load data in do training dtrain = xgb.DMatrix(train) dtest = xgb.DMatrix(test) param = {"max_depth": 2, "eta": 1, "objective": "binary:logistic"} watchlist = [(dtest, "eval"), (dtrain, "train")] num_round = 3 bst = xgb.train(param, dtrain, num_round, watchlist) print("start testing prediction from first n trees") # predict using first 1 tree label = dtest.get_label() ypred1 = bst.predict(dtest, iteration_range=(0, 1)) # by default, we predict using all the trees ypred2 = bst.predict(dtest) print("error of ypred1=%f" % (np.sum((ypred1 > 0.5) != label) / float(len(label)))) print("error of ypred2=%f" % (np.sum((ypred2 > 0.5) != label) / float(len(label)))) def sklearn_interface(): X_train, y_train = load_svmlight_file(train) X_test, y_test = load_svmlight_file(test) clf = xgb.XGBClassifier(n_estimators=3, max_depth=2, eta=1, use_label_encoder=False) clf.fit(X_train, y_train, eval_set=[(X_test, y_test)]) assert clf.n_classes_ == 2 print("start testing prediction from first n trees") # predict using first 1 tree ypred1 = clf.predict(X_test, iteration_range=(0, 1)) # by default, we predict using all the trees ypred2 = clf.predict(X_test) print( "error of ypred1=%f" % (np.sum((ypred1 > 0.5) != y_test) / float(len(y_test))) ) print( "error of ypred2=%f" % (np.sum((ypred2 > 0.5) != y_test) / float(len(y_test))) ) if __name__ == "__main__": native_interface() sklearn_interface() xgboost-1.5.2/demo/guide-python/predict_leaf_indices.py000066400000000000000000000013031417122711700232350ustar00rootroot00000000000000import os import xgboost as xgb # load data in do training CURRENT_DIR = os.path.dirname(__file__) dtrain = xgb.DMatrix(os.path.join(CURRENT_DIR, '../data/agaricus.txt.train')) dtest = xgb.DMatrix(os.path.join(CURRENT_DIR, '../data/agaricus.txt.test')) param = {'max_depth': 2, 'eta': 1, 'objective': 'binary:logistic'} watchlist = [(dtest, 'eval'), (dtrain, 'train')] num_round = 3 bst = xgb.train(param, dtrain, num_round, watchlist) print('start testing predict the leaf indices') # predict using first 2 tree leafindex = bst.predict(dtest, ntree_limit=2, pred_leaf=True) print(leafindex.shape) print(leafindex) # predict all trees leafindex = bst.predict(dtest, pred_leaf=True) print(leafindex.shape) xgboost-1.5.2/demo/guide-python/quantile_data_iterator.py000066400000000000000000000064331417122711700236530ustar00rootroot00000000000000'''A demo for defining data iterator. .. versionadded:: 1.2.0 The demo that defines a customized iterator for passing batches of data into `xgboost.DeviceQuantileDMatrix` and use this `DeviceQuantileDMatrix` for training. The feature is used primarily designed to reduce the required GPU memory for training on distributed environment. Aftering going through the demo, one might ask why don't we use more native Python iterator? That's because XGBoost requires a `reset` function, while using `itertools.tee` might incur significant memory usage according to: https://docs.python.org/3/library/itertools.html#itertools.tee. ''' import xgboost import cupy import numpy COLS = 64 ROWS_PER_BATCH = 1000 # data is splited by rows BATCHES = 32 class IterForDMatrixDemo(xgboost.core.DataIter): '''A data iterator for XGBoost DMatrix. `reset` and `next` are required for any data iterator, other functions here are utilites for demonstration's purpose. ''' def __init__(self): '''Generate some random data for demostration. Actual data can be anything that is currently supported by XGBoost. ''' self.rows = ROWS_PER_BATCH self.cols = COLS rng = cupy.random.RandomState(1994) self._data = [rng.randn(self.rows, self.cols)] * BATCHES self._labels = [rng.randn(self.rows)] * BATCHES self._weights = [rng.uniform(size=self.rows)] * BATCHES self.it = 0 # set iterator to 0 super().__init__() def as_array(self): return cupy.concatenate(self._data) def as_array_labels(self): return cupy.concatenate(self._labels) def as_array_weights(self): return cupy.concatenate(self._weights) def data(self): '''Utility function for obtaining current batch of data.''' return self._data[self.it] def labels(self): '''Utility function for obtaining current batch of label.''' return self._labels[self.it] def weights(self): return self._weights[self.it] def reset(self): '''Reset the iterator''' self.it = 0 def next(self, input_data): '''Yield next batch of data.''' if self.it == len(self._data): # Return 0 when there's no more batch. return 0 input_data(data=self.data(), label=self.labels(), weight=self.weights()) self.it += 1 return 1 def main(): rounds = 100 it = IterForDMatrixDemo() # Use iterator, must be `DeviceQuantileDMatrix` for quantile DMatrix. m_with_it = xgboost.DeviceQuantileDMatrix(it) # Use regular DMatrix. m = xgboost.DMatrix(it.as_array(), it.as_array_labels(), weight=it.as_array_weights()) assert m_with_it.num_col() == m.num_col() assert m_with_it.num_row() == m.num_row() reg_with_it = xgboost.train({'tree_method': 'gpu_hist'}, m_with_it, num_boost_round=rounds) predict_with_it = reg_with_it.predict(m_with_it) reg = xgboost.train({'tree_method': 'gpu_hist'}, m, num_boost_round=rounds) predict = reg.predict(m) numpy.testing.assert_allclose(predict_with_it, predict, rtol=1e6) if __name__ == '__main__': main() xgboost-1.5.2/demo/guide-python/sklearn_evals_result.py000066400000000000000000000023001417122711700233430ustar00rootroot00000000000000## # This script demonstrate how to access the xgboost eval metrics by using sklearn ## import xgboost as xgb import numpy as np from sklearn.datasets import make_hastie_10_2 X, y = make_hastie_10_2(n_samples=2000, random_state=42) # Map labels from {-1, 1} to {0, 1} labels, y = np.unique(y, return_inverse=True) X_train, X_test = X[:1600], X[1600:] y_train, y_test = y[:1600], y[1600:] param_dist = {'objective':'binary:logistic', 'n_estimators':2} clf = xgb.XGBModel(**param_dist) # Or you can use: clf = xgb.XGBClassifier(**param_dist) clf.fit(X_train, y_train, eval_set=[(X_train, y_train), (X_test, y_test)], eval_metric='logloss', verbose=True) # Load evals result by calling the evals_result() function evals_result = clf.evals_result() print('Access logloss metric directly from validation_0:') print(evals_result['validation_0']['logloss']) print('') print('Access metrics through a loop:') for e_name, e_mtrs in evals_result.items(): print('- {}'.format(e_name)) for e_mtr_name, e_mtr_vals in e_mtrs.items(): print(' - {}'.format(e_mtr_name)) print(' - {}'.format(e_mtr_vals)) print('') print('Access complete dict:') print(evals_result) xgboost-1.5.2/demo/guide-python/sklearn_examples.py000066400000000000000000000046531417122711700224660ustar00rootroot00000000000000''' Created on 1 Apr 2015 @author: Jamie Hall ''' import pickle import xgboost as xgb import numpy as np from sklearn.model_selection import KFold, train_test_split, GridSearchCV from sklearn.metrics import confusion_matrix, mean_squared_error from sklearn.datasets import load_iris, load_digits, load_boston rng = np.random.RandomState(31337) print("Zeros and Ones from the Digits dataset: binary classification") digits = load_digits(n_class=2) y = digits['target'] X = digits['data'] kf = KFold(n_splits=2, shuffle=True, random_state=rng) for train_index, test_index in kf.split(X): xgb_model = xgb.XGBClassifier(n_jobs=1).fit(X[train_index], y[train_index]) predictions = xgb_model.predict(X[test_index]) actuals = y[test_index] print(confusion_matrix(actuals, predictions)) print("Iris: multiclass classification") iris = load_iris() y = iris['target'] X = iris['data'] kf = KFold(n_splits=2, shuffle=True, random_state=rng) for train_index, test_index in kf.split(X): xgb_model = xgb.XGBClassifier(n_jobs=1).fit(X[train_index], y[train_index]) predictions = xgb_model.predict(X[test_index]) actuals = y[test_index] print(confusion_matrix(actuals, predictions)) print("Boston Housing: regression") boston = load_boston() y = boston['target'] X = boston['data'] kf = KFold(n_splits=2, shuffle=True, random_state=rng) for train_index, test_index in kf.split(X): xgb_model = xgb.XGBRegressor(n_jobs=1).fit(X[train_index], y[train_index]) predictions = xgb_model.predict(X[test_index]) actuals = y[test_index] print(mean_squared_error(actuals, predictions)) print("Parameter optimization") y = boston['target'] X = boston['data'] xgb_model = xgb.XGBRegressor(n_jobs=1) clf = GridSearchCV(xgb_model, {'max_depth': [2, 4, 6], 'n_estimators': [50, 100, 200]}, verbose=1, n_jobs=1) clf.fit(X, y) print(clf.best_score_) print(clf.best_params_) # The sklearn API models are picklable print("Pickling sklearn API models") # must open in binary format to pickle pickle.dump(clf, open("best_boston.pkl", "wb")) clf2 = pickle.load(open("best_boston.pkl", "rb")) print(np.allclose(clf.predict(X), clf2.predict(X))) # Early-stopping X = digits['data'] y = digits['target'] X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0) clf = xgb.XGBClassifier(n_jobs=1) clf.fit(X_train, y_train, early_stopping_rounds=10, eval_metric="auc", eval_set=[(X_test, y_test)]) xgboost-1.5.2/demo/guide-python/sklearn_parallel.py000066400000000000000000000011321417122711700224310ustar00rootroot00000000000000from sklearn.model_selection import GridSearchCV from sklearn.datasets import load_boston import xgboost as xgb import multiprocessing if __name__ == "__main__": print("Parallel Parameter optimization") boston = load_boston() y = boston['target'] X = boston['data'] xgb_model = xgb.XGBRegressor(n_jobs=multiprocessing.cpu_count() // 2) clf = GridSearchCV(xgb_model, {'max_depth': [2, 4, 6], 'n_estimators': [50, 100, 200]}, verbose=1, n_jobs=2) clf.fit(X, y) print(clf.best_score_) print(clf.best_params_) xgboost-1.5.2/demo/guide-python/update_process.py000066400000000000000000000061121417122711700221410ustar00rootroot00000000000000"""Demo for using `process_type` with `prune` and `refresh`. Modifying existing trees is not a well established use for XGBoost, so feel free to experiment. """ import xgboost as xgb from sklearn.datasets import load_boston import numpy as np def main(): n_rounds = 32 X, y = load_boston(return_X_y=True) # Train a model first X_train = X[: X.shape[0] // 2] y_train = y[: y.shape[0] // 2] Xy = xgb.DMatrix(X_train, y_train) evals_result: xgb.callback.EvaluationMonitor.EvalsLog = {} booster = xgb.train( {"tree_method": "gpu_hist", "max_depth": 6}, Xy, num_boost_round=n_rounds, evals=[(Xy, "Train")], evals_result=evals_result, ) SHAP = booster.predict(Xy, pred_contribs=True) # Refresh the leaf value and tree statistic X_refresh = X[X.shape[0] // 2:] y_refresh = y[y.shape[0] // 2:] Xy_refresh = xgb.DMatrix(X_refresh, y_refresh) # The model will adapt to other half of the data by changing leaf value (no change in # split condition) with refresh_leaf set to True. refresh_result: xgb.callback.EvaluationMonitor.EvalsLog = {} refreshed = xgb.train( {"process_type": "update", "updater": "refresh", "refresh_leaf": True}, Xy_refresh, num_boost_round=n_rounds, xgb_model=booster, evals=[(Xy, "Original"), (Xy_refresh, "Train")], evals_result=refresh_result, ) # Refresh the model without changing the leaf value, but tree statistic including # cover and weight are refreshed. refresh_result: xgb.callback.EvaluationMonitor.EvalsLog = {} refreshed = xgb.train( {"process_type": "update", "updater": "refresh", "refresh_leaf": False}, Xy_refresh, num_boost_round=n_rounds, xgb_model=booster, evals=[(Xy, "Original"), (Xy_refresh, "Train")], evals_result=refresh_result, ) # Without refreshing the leaf value, resulting trees should be the same with original # model except for accumulated statistic. The rtol is for floating point error in # prediction. np.testing.assert_allclose( refresh_result["Original"]["rmse"], evals_result["Train"]["rmse"], rtol=1e-5 ) # But SHAP value is changed as cover in tree nodes are changed. refreshed_SHAP = refreshed.predict(Xy, pred_contribs=True) assert not np.allclose(SHAP, refreshed_SHAP, rtol=1e-3) # Prune the trees with smaller max_depth X_update = X_train y_update = y_train Xy_update = xgb.DMatrix(X_update, y_update) prune_result: xgb.callback.EvaluationMonitor.EvalsLog = {} pruned = xgb.train( {"process_type": "update", "updater": "prune", "max_depth": 2}, Xy_update, num_boost_round=n_rounds, xgb_model=booster, evals=[(Xy, "Original"), (Xy_update, "Train")], evals_result=prune_result, ) # Have a smaller model, but similar accuracy. np.testing.assert_allclose( np.array(prune_result["Original"]["rmse"]), np.array(prune_result["Train"]["rmse"]), atol=1e-5 ) if __name__ == "__main__": main() xgboost-1.5.2/demo/json-model/000077500000000000000000000000001417122711700162025ustar00rootroot00000000000000xgboost-1.5.2/demo/json-model/README.md000066400000000000000000000004621417122711700174630ustar00rootroot00000000000000We introduced initial support for saving XGBoost model in JSON format in 1.0.0. Note that it's still experimental and under development, output schema is subject to change due to bug fixes or further refactoring. For an overview, see https://xgboost.readthedocs.io/en/latest/tutorials/saving_model.html .xgboost-1.5.2/demo/json-model/json_parser.py000066400000000000000000000131231417122711700211010ustar00rootroot00000000000000'''Demonstration for parsing JSON tree model file generated by XGBoost. The support is experimental, output schema is subject to change in the future. ''' import json import argparse class Tree: '''A tree built by XGBoost.''' # Index into node array _left = 0 _right = 1 _parent = 2 _ind = 3 _cond = 4 _default_left = 5 # Index into stat array _loss_chg = 0 _sum_hess = 1 _base_weight = 2 def __init__(self, tree_id: int, nodes, stats): self.tree_id = tree_id self.nodes = nodes self.stats = stats def loss_change(self, node_id: int): '''Loss gain of a node.''' return self.stats[node_id][self._loss_chg] def sum_hessian(self, node_id: int): '''Sum Hessian of a node.''' return self.stats[node_id][self._sum_hess] def base_weight(self, node_id: int): '''Base weight of a node.''' return self.stats[node_id][self._base_weight] def split_index(self, node_id: int): '''Split feature index of node.''' return self.nodes[node_id][self._ind] def split_condition(self, node_id: int): '''Split value of a node.''' return self.nodes[node_id][self._cond] def parent(self, node_id: int): '''Parent ID of a node.''' return self.nodes[node_id][self._parent] def left_child(self, node_id: int): '''Left child ID of a node.''' return self.nodes[node_id][self._left] def right_child(self, node_id: int): '''Right child ID of a node.''' return self.nodes[node_id][self._right] def is_leaf(self, node_id: int): '''Whether a node is leaf.''' return self.nodes[node_id][self._left] == -1 def is_deleted(self, node_id: int): '''Whether a node is deleted.''' # std::numeric_limits::max() return self.nodes[node_id][self._ind] == 4294967295 def __str__(self): stacks = [0] nodes = [] while stacks: node = {} nid = stacks.pop() node['node id'] = nid node['gain'] = self.loss_change(nid) node['cover'] = self.sum_hessian(nid) nodes.append(node) if not self.is_leaf(nid) and not self.is_deleted(nid): left = self.left_child(nid) right = self.right_child(nid) stacks.append(left) stacks.append(right) string = '\n'.join(map(lambda x: ' ' + str(x), nodes)) return string class Model: '''Gradient boosted tree model.''' def __init__(self, model: dict): '''Construct the Model from JSON object. parameters ---------- m: A dictionary loaded by json ''' # Basic property of a model self.learner_model_shape = model['learner']['learner_model_param'] self.num_output_group = int(self.learner_model_shape['num_class']) self.num_feature = int(self.learner_model_shape['num_feature']) self.base_score = float(self.learner_model_shape['base_score']) # A field encoding which output group a tree belongs self.tree_info = model['learner']['gradient_booster']['model'][ 'tree_info'] model_shape = model['learner']['gradient_booster']['model'][ 'gbtree_model_param'] # JSON representation of trees j_trees = model['learner']['gradient_booster']['model']['trees'] # Load the trees self.num_trees = int(model_shape['num_trees']) self.leaf_size = int(model_shape['size_leaf_vector']) # Right now XGBoost doesn't support vector leaf yet assert self.leaf_size == 0, str(self.leaf_size) trees = [] for i in range(self.num_trees): tree = j_trees[i] tree_id = int(tree['id']) assert tree_id == i, (tree_id, i) # properties left_children = tree['left_children'] right_children = tree['right_children'] parents = tree['parents'] split_conditions = tree['split_conditions'] split_indices = tree['split_indices'] default_left = tree['default_left'] # stats base_weights = tree['base_weights'] loss_changes = tree['loss_changes'] sum_hessian = tree['sum_hessian'] stats = [] nodes = [] # We resemble the structure used inside XGBoost, which is similar # to adjacency list. for node_id in range(len(left_children)): nodes.append([ left_children[node_id], right_children[node_id], parents[node_id], split_indices[node_id], split_conditions[node_id], default_left[node_id] ]) stats.append([ loss_changes[node_id], sum_hessian[node_id], base_weights[node_id] ]) tree = Tree(tree_id, nodes, stats) trees.append(tree) self.trees = trees def print_model(self): for i, tree in enumerate(self.trees): print('tree_id:', i) print(tree) if __name__ == '__main__': parser = argparse.ArgumentParser( description='Demonstration for loading and printing XGBoost model.') parser.add_argument('--model', type=str, required=True, help='Path to JSON model file.') args = parser.parse_args() with open(args.model, 'r') as fd: model = json.load(fd) model = Model(model) model.print_model() xgboost-1.5.2/demo/kaggle-higgs/000077500000000000000000000000001417122711700164645ustar00rootroot00000000000000xgboost-1.5.2/demo/kaggle-higgs/README.md000066400000000000000000000020161417122711700177420ustar00rootroot00000000000000Highlights ===== Higgs challenge ends recently, xgboost is being used by many users. This list highlights the xgboost solutions of players * Blogpost by phunther: [Winning solution of Kaggle Higgs competition: what a single model can do](http://no2147483647.wordpress.com/2014/09/17/winning-solution-of-kaggle-higgs-competition-what-a-single-model-can-do/) * The solution by Tianqi Chen and Tong He [Link](https://github.com/hetong007/higgsml) Guide for Kaggle Higgs Challenge ===== This is the folder giving example of how to use XGBoost Python Module to run Kaggle Higgs competition This script will achieve about 3.600 AMS score in public leaderboard. To get start, you need do following step: 1. Compile the XGBoost python lib ```bash cd ../.. make ``` 2. Put training.csv test.csv on folder './data' (you can create a symbolic link) 3. Run ./run.sh Speed ===== speedtest.py compares xgboost's speed on this dataset with sklearn.GBM Using R module ===== * Alternatively, you can run using R, higgs-train.R and higgs-pred.R. xgboost-1.5.2/demo/kaggle-higgs/higgs-cv.py000077500000000000000000000026331417122711700205540ustar00rootroot00000000000000#!/usr/bin/python import numpy as np import xgboost as xgb ### load data in do training train = np.loadtxt('./data/training.csv', delimiter=',', skiprows=1, converters={32: lambda x:int(x=='s'.encode('utf-8')) } ) label = train[:,32] data = train[:,1:31] weight = train[:,31] dtrain = xgb.DMatrix( data, label=label, missing = -999.0, weight=weight ) param = {'max_depth':6, 'eta':0.1, 'objective':'binary:logitraw', 'nthread':4} num_round = 120 print ('running cross validation, with preprocessing function') # define the preprocessing function # used to return the preprocessed training, test data, and parameter # we can use this to do weight rescale, etc. # as a example, we try to set scale_pos_weight def fpreproc(dtrain, dtest, param): label = dtrain.get_label() ratio = float(np.sum(label == 0)) / np.sum(label==1) param['scale_pos_weight'] = ratio wtrain = dtrain.get_weight() wtest = dtest.get_weight() sum_weight = sum(wtrain) + sum(wtest) wtrain *= sum_weight / sum(wtrain) wtest *= sum_weight / sum(wtest) dtrain.set_weight(wtrain) dtest.set_weight(wtest) return (dtrain, dtest, param) # do cross validation, for each fold # the dtrain, dtest, param will be passed into fpreproc # then the return value of fpreproc will be used to generate # results of that fold xgb.cv(param, dtrain, num_round, nfold=5, metrics={'ams@0.15', 'auc'}, seed = 0, fpreproc = fpreproc) xgboost-1.5.2/demo/kaggle-higgs/higgs-numpy.py000077500000000000000000000032621417122711700213130ustar00rootroot00000000000000#!/usr/bin/python # this is the example script to use xgboost to train import numpy as np import xgboost as xgb test_size = 550000 # path to where the data lies dpath = 'data' # load in training data, directly use numpy dtrain = np.loadtxt( dpath+'/training.csv', delimiter=',', skiprows=1, converters={32: lambda x:int(x=='s'.encode('utf-8')) } ) print ('finish loading from csv ') label = dtrain[:,32] data = dtrain[:,1:31] # rescale weight to make it same as test set weight = dtrain[:,31] * float(test_size) / len(label) sum_wpos = sum( weight[i] for i in range(len(label)) if label[i] == 1.0 ) sum_wneg = sum( weight[i] for i in range(len(label)) if label[i] == 0.0 ) # print weight statistics print ('weight statistics: wpos=%g, wneg=%g, ratio=%g' % ( sum_wpos, sum_wneg, sum_wneg/sum_wpos )) # construct xgboost.DMatrix from numpy array, treat -999.0 as missing value xgmat = xgb.DMatrix( data, label=label, missing = -999.0, weight=weight ) # setup parameters for xgboost param = {} # use logistic regression loss, use raw prediction before logistic transformation # since we only need the rank param['objective'] = 'binary:logitraw' # scale weight of positive examples param['scale_pos_weight'] = sum_wneg/sum_wpos param['eta'] = 0.1 param['max_depth'] = 6 param['eval_metric'] = 'auc' param['nthread'] = 16 # you can directly throw param in, though we want to watch multiple metrics here plst = list(param.items())+[('eval_metric', 'ams@0.15')] watchlist = [ (xgmat,'train') ] # boost 120 trees num_round = 120 print ('loading data end, start to boost trees') bst = xgb.train( plst, xgmat, num_round, watchlist ); # save out model bst.save_model('higgs.model') print ('finish training') xgboost-1.5.2/demo/kaggle-higgs/higgs-pred.R000066400000000000000000000013061417122711700206400ustar00rootroot00000000000000# install xgboost package, see R-package in root folder require(xgboost) require(methods) modelfile <- "higgs.model" outfile <- "higgs.pred.csv" dtest <- read.csv("data/test.csv", header=TRUE) data <- as.matrix(dtest[2:31]) idx <- dtest[[1]] xgmat <- xgb.DMatrix(data, missing = -999.0) bst <- xgb.load(modelfile=modelfile) ypred <- predict(bst, xgmat) rorder <- rank(ypred, ties.method="first") threshold <- 0.15 # to be completed ntop <- length(rorder) - as.integer(threshold*length(rorder)) plabel <- ifelse(rorder > ntop, "s", "b") outdata <- list("EventId" = idx, "RankOrder" = rorder, "Class" = plabel) write.csv(outdata, file = outfile, quote=FALSE, row.names=FALSE) xgboost-1.5.2/demo/kaggle-higgs/higgs-pred.py000077500000000000000000000022131417122711700210700ustar00rootroot00000000000000#!/usr/bin/python # make prediction import numpy as np import xgboost as xgb # path to where the data lies dpath = 'data' modelfile = 'higgs.model' outfile = 'higgs.pred.csv' # make top 15% as positive threshold_ratio = 0.15 # load in training data, directly use numpy dtest = np.loadtxt( dpath+'/test.csv', delimiter=',', skiprows=1 ) data = dtest[:,1:31] idx = dtest[:,0] print ('finish loading from csv ') xgmat = xgb.DMatrix( data, missing = -999.0 ) bst = xgb.Booster({'nthread':16}, model_file = modelfile) ypred = bst.predict( xgmat ) res = [ ( int(idx[i]), ypred[i] ) for i in range(len(ypred)) ] rorder = {} for k, v in sorted( res, key = lambda x:-x[1] ): rorder[ k ] = len(rorder) + 1 # write out predictions ntop = int( threshold_ratio * len(rorder ) ) fo = open(outfile, 'w') nhit = 0 ntot = 0 fo.write('EventId,RankOrder,Class\n') for k, v in res: if rorder[k] <= ntop: lb = 's' nhit += 1 else: lb = 'b' # change output rank order to follow Kaggle convention fo.write('%s,%d,%s\n' % ( k, len(rorder)+1-rorder[k], lb ) ) ntot += 1 fo.close() print ('finished writing into prediction file') xgboost-1.5.2/demo/kaggle-higgs/higgs-train.R000066400000000000000000000020621417122711700210230ustar00rootroot00000000000000# install xgboost package, see R-package in root folder require(xgboost) require(methods) testsize <- 550000 dtrain <- read.csv("data/training.csv", header=TRUE) dtrain[33] <- dtrain[33] == "s" label <- as.numeric(dtrain[[33]]) data <- as.matrix(dtrain[2:31]) weight <- as.numeric(dtrain[[32]]) * testsize / length(label) sumwpos <- sum(weight * (label==1.0)) sumwneg <- sum(weight * (label==0.0)) print(paste("weight statistics: wpos=", sumwpos, "wneg=", sumwneg, "ratio=", sumwneg / sumwpos)) xgmat <- xgb.DMatrix(data, label = label, weight = weight, missing = -999.0) param <- list("objective" = "binary:logitraw", "scale_pos_weight" = sumwneg / sumwpos, "bst:eta" = 0.1, "bst:max_depth" = 6, "eval_metric" = "auc", "eval_metric" = "ams@0.15", "nthread" = 16) watchlist <- list("train" = xgmat) nrounds = 120 print ("loading data end, start to boost trees") bst = xgb.train(param, xgmat, nrounds, watchlist ); # save out model xgb.save(bst, "higgs.model") print ('finish training') xgboost-1.5.2/demo/kaggle-higgs/run.sh000077500000000000000000000003451417122711700176310ustar00rootroot00000000000000#!/bin/bash python -u higgs-numpy.py ret=$? if [[ $ret != 0 ]]; then echo "ERROR in higgs-numpy.py" exit $ret fi python -u higgs-pred.py ret=$? if [[ $ret != 0 ]]; then echo "ERROR in higgs-pred.py" exit $ret fi xgboost-1.5.2/demo/kaggle-higgs/speedtest.R000066400000000000000000000036311417122711700206120ustar00rootroot00000000000000# install xgboost package, see R-package in root folder require(xgboost) require(gbm) require(methods) testsize <- 550000 dtrain <- read.csv("data/training.csv", header=TRUE, nrows=350001) dtrain$Label = as.numeric(dtrain$Label=='s') # gbm.time = system.time({ # gbm.model <- gbm(Label ~ ., data = dtrain[, -c(1,32)], n.trees = 120, # interaction.depth = 6, shrinkage = 0.1, bag.fraction = 1, # verbose = TRUE) # }) # print(gbm.time) # Test result: 761.48 secs # dtrain[33] <- dtrain[33] == "s" # label <- as.numeric(dtrain[[33]]) data <- as.matrix(dtrain[2:31]) weight <- as.numeric(dtrain[[32]]) * testsize / length(label) sumwpos <- sum(weight * (label==1.0)) sumwneg <- sum(weight * (label==0.0)) print(paste("weight statistics: wpos=", sumwpos, "wneg=", sumwneg, "ratio=", sumwneg / sumwpos)) xgboost.time = list() threads = c(1,2,4,8,16) for (i in 1:length(threads)){ thread = threads[i] xgboost.time[[i]] = system.time({ xgmat <- xgb.DMatrix(data, label = label, weight = weight, missing = -999.0) param <- list("objective" = "binary:logitraw", "scale_pos_weight" = sumwneg / sumwpos, "bst:eta" = 0.1, "bst:max_depth" = 6, "eval_metric" = "auc", "eval_metric" = "ams@0.15", "nthread" = thread) watchlist <- list("train" = xgmat) nrounds = 120 print ("loading data end, start to boost trees") bst = xgb.train(param, xgmat, nrounds, watchlist ); # save out model xgb.save(bst, "higgs.model") print ('finish training') }) } xgboost.time # [[1]] # user system elapsed # 99.015 0.051 98.982 # # [[2]] # user system elapsed # 100.268 0.317 55.473 # # [[3]] # user system elapsed # 111.682 0.777 35.963 # # [[4]] # user system elapsed # 149.396 1.851 32.661 # # [[5]] # user system elapsed # 157.390 5.988 40.949 xgboost-1.5.2/demo/kaggle-higgs/speedtest.py000077500000000000000000000040001417122711700210330ustar00rootroot00000000000000#!/usr/bin/python # this is the example script to use xgboost to train import numpy as np import xgboost as xgb from sklearn.ensemble import GradientBoostingClassifier import time test_size = 550000 # path to where the data lies dpath = 'data' # load in training data, directly use numpy dtrain = np.loadtxt( dpath+'/training.csv', delimiter=',', skiprows=1, converters={32: lambda x:int(x=='s') } ) print ('finish loading from csv ') label = dtrain[:,32] data = dtrain[:,1:31] # rescale weight to make it same as test set weight = dtrain[:,31] * float(test_size) / len(label) sum_wpos = sum( weight[i] for i in range(len(label)) if label[i] == 1.0 ) sum_wneg = sum( weight[i] for i in range(len(label)) if label[i] == 0.0 ) # print weight statistics print ('weight statistics: wpos=%g, wneg=%g, ratio=%g' % ( sum_wpos, sum_wneg, sum_wneg/sum_wpos )) # construct xgboost.DMatrix from numpy array, treat -999.0 as missing value xgmat = xgb.DMatrix( data, label=label, missing = -999.0, weight=weight ) # setup parameters for xgboost param = {} # use logistic regression loss param['objective'] = 'binary:logitraw' # scale weight of positive examples param['scale_pos_weight'] = sum_wneg/sum_wpos param['bst:eta'] = 0.1 param['bst:max_depth'] = 6 param['eval_metric'] = 'auc' param['nthread'] = 4 plst = param.items()+[('eval_metric', 'ams@0.15')] watchlist = [ (xgmat,'train') ] # boost 10 trees num_round = 10 print ('loading data end, start to boost trees') print ("training GBM from sklearn") tmp = time.time() gbm = GradientBoostingClassifier(n_estimators=num_round, max_depth=6, verbose=2) gbm.fit(data, label) print ("sklearn.GBM costs: %s seconds" % str(time.time() - tmp)) #raw_input() print ("training xgboost") threads = [1, 2, 4, 16] for i in threads: param['nthread'] = i tmp = time.time() plst = param.items()+[('eval_metric', 'ams@0.15')] bst = xgb.train( plst, xgmat, num_round, watchlist ); print ("XGBoost with %d thread costs: %s seconds" % (i, str(time.time() - tmp))) print ('finish training') xgboost-1.5.2/demo/kaggle-otto/000077500000000000000000000000001417122711700163505ustar00rootroot00000000000000xgboost-1.5.2/demo/kaggle-otto/README.MD000066400000000000000000000012311417122711700175240ustar00rootroot00000000000000Benchmark for Otto Group Competition ========= This is a folder containing the benchmark for the [Otto Group Competition on Kaggle](http://www.kaggle.com/c/otto-group-product-classification-challenge). ## Getting started 1. Put `train.csv` and `test.csv` under the `data` folder 2. Run the script 3. Submit the `submission.csv` The parameter `nthread` controls the number of cores to run on, please set it to suit your machine. ## R-package To install the R-package of xgboost, please run ```r devtools::install_github('tqchen/xgboost',subdir='R-package') ``` Windows users may need to install [RTools](http://cran.r-project.org/bin/windows/Rtools/) first. xgboost-1.5.2/demo/kaggle-otto/otto_train_pred.R000066400000000000000000000023351417122711700216720ustar00rootroot00000000000000require(xgboost) require(methods) train = read.csv('data/train.csv',header=TRUE,stringsAsFactors = FALSE) test = read.csv('data/test.csv',header=TRUE,stringsAsFactors = FALSE) train = train[,-1] test = test[,-1] y = train[,ncol(train)] y = gsub('Class_','',y) y = as.integer(y)-1 # xgboost take features in [0,numOfClass) x = rbind(train[,-ncol(train)],test) x = as.matrix(x) x = matrix(as.numeric(x),nrow(x),ncol(x)) trind = 1:length(y) teind = (nrow(train)+1):nrow(x) # Set necessary parameter param <- list("objective" = "multi:softprob", "eval_metric" = "mlogloss", "num_class" = 9, "nthread" = 8) # Run Cross Validation cv.nrounds = 50 bst.cv = xgb.cv(param=param, data = x[trind,], label = y, nfold = 3, nrounds=cv.nrounds) # Train the model nrounds = 50 bst = xgboost(param=param, data = x[trind,], label = y, nrounds=nrounds) # Make prediction pred = predict(bst,x[teind,]) pred = matrix(pred,9,length(pred)/9) pred = t(pred) # Output submission pred = format(pred, digits=2,scientific=F) # shrink the size of submission pred = data.frame(1:nrow(pred),pred) names(pred) = c('id', paste0('Class_',1:9)) write.csv(pred,file='submission.csv', quote=FALSE,row.names=FALSE) xgboost-1.5.2/demo/kaggle-otto/understandingXGBoostModel.Rmd000066400000000000000000000232171417122711700241150ustar00rootroot00000000000000--- title: "Understanding XGBoost Model on Otto Dataset" author: "Michaël Benesty" output: rmarkdown::html_vignette: css: ../../R-package/vignettes/vignette.css number_sections: yes toc: yes --- Introduction ============ **XGBoost** is an implementation of the famous gradient boosting algorithm. This model is often described as a *blackbox*, meaning it works well but it is not trivial to understand how. Indeed, the model is made of hundreds (thousands?) of decision trees. You may wonder how possible a human would be able to have a general view of the model? While XGBoost is known for its fast speed and accurate predictive power, it also comes with various functions to help you understand the model. The purpose of this RMarkdown document is to demonstrate how easily we can leverage the functions already implemented in **XGBoost R** package. Of course, everything showed below can be applied to the dataset you may have to manipulate at work or wherever! First we will prepare the **Otto** dataset and train a model, then we will generate two visualisations to get a clue of what is important to the model, finally, we will see how we can leverage these information. Preparation of the data ======================= This part is based on the **R** tutorial example by [Tong He](https://github.com/dmlc/xgboost/blob/master/demo/kaggle-otto/otto_train_pred.R) First, let's load the packages and the dataset. ```{r loading} require(xgboost) require(methods) require(data.table) require(magrittr) train <- fread('data/train.csv', header = T, stringsAsFactors = FALSE) test <- fread('data/test.csv', header=TRUE, stringsAsFactors = FALSE) ``` > `magrittr` and `data.table` are here to make the code cleaner and much more rapid. Let's explore the dataset. ```{r explore} # Train dataset dimensions dim(train) # Training content train[1:6,1:5, with =FALSE] # Test dataset dimensions dim(test) # Test content test[1:6,1:5, with =FALSE] ``` > We only display the 6 first rows and 5 first columns for convenience Each *column* represents a feature measured by an `integer`. Each *row* is an **Otto** product. Obviously the first column (`ID`) doesn't contain any useful information. To let the algorithm focus on real stuff, we will delete it. ```{r clean, results='hide'} # Delete ID column in training dataset train[, id := NULL] # Delete ID column in testing dataset test[, id := NULL] ``` According to its description, the **Otto** challenge is a multi class classification challenge. We need to extract the labels (here the name of the different classes) from the dataset. We only have two files (test and training), it seems logical that the training file contains the class we are looking for. Usually the labels is in the first or the last column. We already know what is in the first column, let's check the content of the last one. ```{r searchLabel} # Check the content of the last column train[1:6, ncol(train), with = FALSE] # Save the name of the last column nameLastCol <- names(train)[ncol(train)] ``` The classes are provided as character string in the `r ncol(train)`th column called `r nameLastCol`. As you may know, **XGBoost** doesn't support anything else than numbers. So we will convert classes to `integer`. Moreover, according to the documentation, it should start at `0`. For that purpose, we will: * extract the target column * remove `Class_` from each class name * convert to `integer` * remove `1` to the new value ```{r classToIntegers} # Convert from classes to numbers y <- train[, nameLastCol, with = FALSE][[1]] %>% gsub('Class_','',.) %>% {as.integer(.) -1} # Display the first 5 levels y[1:5] ``` We remove label column from training dataset, otherwise **XGBoost** would use it to guess the labels! ```{r deleteCols, results='hide'} train[, nameLastCol:=NULL, with = FALSE] ``` `data.table` is an awesome implementation of data.frame, unfortunately it is not a format supported natively by **XGBoost**. We need to convert both datasets (training and test) in `numeric` Matrix format. ```{r convertToNumericMatrix} trainMatrix <- train[,lapply(.SD,as.numeric)] %>% as.matrix testMatrix <- test[,lapply(.SD,as.numeric)] %>% as.matrix ``` Model training ============== Before the learning we will use the cross validation to evaluate the our error rate. Basically **XGBoost** will divide the training data in `nfold` parts, then **XGBoost** will retain the first part to use it as the test data and perform a training. Then it will reintegrate the first part and retain the second part, do a training and so on... You can look at the function documentation for more information. ```{r crossValidation} numberOfClasses <- max(y) + 1 param <- list("objective" = "multi:softprob", "eval_metric" = "mlogloss", "num_class" = numberOfClasses) cv.nrounds <- 5 cv.nfold <- 3 bst.cv = xgb.cv(param=param, data = trainMatrix, label = y, nfold = cv.nfold, nrounds = cv.nrounds) ``` > As we can see the error rate is low on the test dataset (for a 5mn trained model). Finally, we are ready to train the real model!!! ```{r modelTraining} nrounds = 50 bst = xgboost(param=param, data = trainMatrix, label = y, nrounds=nrounds) ``` Model understanding =================== Feature importance ------------------ So far, we have built a model made of **`r nrounds`** trees. To build a tree, the dataset is divided recursively several times. At the end of the process, you get groups of observations (here, these observations are properties regarding **Otto** products). Each division operation is called a *split*. Each group at each division level is called a branch and the deepest level is called a *leaf*. In the final model, these *leafs* are supposed to be as pure as possible for each tree, meaning in our case that each *leaf* should be made of one class of **Otto** product only (of course it is not true, but that's what we try to achieve in a minimum of splits). **Not all *splits* are equally important**. Basically the first *split* of a tree will have more impact on the purity that, for instance, the deepest *split*. Intuitively, we understand that the first *split* makes most of the work, and the following *splits* focus on smaller parts of the dataset which have been misclassified by the first *tree*. In the same way, in Boosting we try to optimize the misclassification at each round (it is called the *loss*). So the first *tree* will do the big work and the following trees will focus on the remaining, on the parts not correctly learned by the previous *trees*. The improvement brought by each *split* can be measured, it is the *gain*. Each *split* is done on one feature only at one value. Let's see what the model looks like. ```{r modelDump} model <- xgb.dump(bst, with.stats = TRUE) model[1:10] ``` > For convenience, we are displaying the first 10 lines of the model only. Clearly, it is not easy to understand what it means. Basically each line represents a *branch*, there is the *tree* ID, the feature ID, the point where it *splits*, and information regarding the next *branches* (left, right, when the row for this feature is N/A). Hopefully, **XGBoost** offers a better representation: **feature importance**. Feature importance is about averaging the *gain* of each feature for all *split* and all *trees*. Then we can use the function `xgb.plot.importance`. ```{r importanceFeature, fig.align='center', fig.height=5, fig.width=10} # Get the feature real names names <- dimnames(trainMatrix)[[2]] # Compute feature importance matrix importance_matrix <- xgb.importance(names, model = bst) # Nice graph xgb.plot.importance(importance_matrix[1:10,]) ``` > To make it understandable we first extract the column names from the `Matrix`. Interpretation -------------- In the feature importance above, we can see the first 10 most important features. This function gives a color to each bar. These colors represent groups of features. Basically a K-means clustering is applied to group each feature by importance. From here you can take several actions. For instance you can remove the less important feature (feature selection process), or go deeper in the interaction between the most important features and labels. Or you can just reason about why these features are so important (in **Otto** challenge we can't go this way because there is not enough information). Tree graph ---------- Feature importance gives you feature weight information but not interaction between features. **XGBoost R** package have another useful function for that. Please, scroll on the right to see the tree. ```{r treeGraph, dpi=1500, fig.align='left'} xgb.plot.tree(feature_names = names, model = bst, n_first_tree = 2) ``` We are just displaying the first two trees here. On simple models the first two trees may be enough. Here, it might not be the case. We can see from the size of the trees that the interaction between features is complicated. Besides, **XGBoost** generate `k` trees at each round for a `k`-classification problem. Therefore the two trees illustrated here are trying to classify data into different classes. Going deeper ============ There are 4 documents you may also be interested in: * [xgboostPresentation.Rmd](https://github.com/dmlc/xgboost/blob/master/R-package/vignettes/xgboostPresentation.Rmd): general presentation * [discoverYourData.Rmd](https://github.com/dmlc/xgboost/blob/master/R-package/vignettes/discoverYourData.Rmd): explaining feature analysis * [Feature Importance Analysis with XGBoost in Tax audit](http://fr.slideshare.net/MichaelBENESTY/feature-importance-analysis-with-xgboost-in-tax-audit): use case * [The Elements of Statistical Learning](http://statweb.stanford.edu/~tibs/ElemStatLearn/): very good book to have a good understanding of the model xgboost-1.5.2/demo/multiclass_classification/000077500000000000000000000000001417122711700213665ustar00rootroot00000000000000xgboost-1.5.2/demo/multiclass_classification/README.md000066400000000000000000000004531417122711700226470ustar00rootroot00000000000000Demonstrating how to use XGBoost accomplish Multi-Class classification task on [UCI Dermatology dataset](https://archive.ics.uci.edu/ml/datasets/Dermatology) Make sure you make xgboost python module in ../../python 1. Run runexp.sh ```bash ./runexp.sh ``` **R version** please see the `train.R`. xgboost-1.5.2/demo/multiclass_classification/runexp.sh000077500000000000000000000004551417122711700232520ustar00rootroot00000000000000#!/bin/bash if [ -f dermatology.data ] then echo "use existing data to run multi class classification" else echo "getting data from uci, make sure you are connected to internet" wget https://archive.ics.uci.edu/ml/machine-learning-databases/dermatology/dermatology.data fi python train.py xgboost-1.5.2/demo/multiclass_classification/train.R000066400000000000000000000030161417122711700226260ustar00rootroot00000000000000library(data.table) library(xgboost) if (!file.exists("./dermatology.data")) { download.file( "https://archive.ics.uci.edu/ml/machine-learning-databases/dermatology/dermatology.data", "dermatology.data", method = "curl" ) } df <- fread("dermatology.data", sep = ",", header = FALSE) df[, `:=`(V34 = as.integer(ifelse(V34 == "?", 0L, V34)), V35 = V35 - 1L)] idx <- sample(nrow(df), size = round(0.7 * nrow(df)), replace = FALSE) train <- df[idx,] test <- df[-idx,] train_x <- train[, 1:34] train_y <- train[, V35] test_x <- test[, 1:34] test_y <- test[, V35] xg_train <- xgb.DMatrix(data = as.matrix(train_x), label = train_y) xg_test = xgb.DMatrix(as.matrix(test_x), label = test_y) params <- list( objective = 'multi:softmax', num_class = 6, max_depth = 6, nthread = 4, eta = 0.1 ) watchlist = list(train = xg_train, test = xg_test) bst <- xgb.train( params = params, data = xg_train, watchlist = watchlist, nrounds = 5 ) pred <- predict(bst, xg_test) error_rate <- sum(pred != test_y) / length(test_y) print(paste("Test error using softmax =", error_rate)) # do the same thing again, but output probabilities params$objective <- 'multi:softprob' bst <- xgb.train(params, xg_train, nrounds = 5, watchlist) pred_prob <- predict(bst, xg_test) pred_mat <- matrix(pred_prob, ncol = 6, byrow = TRUE) # validation # rowSums(pred_mat) pred_label <- apply(pred_mat, 1, which.max) - 1L error_rate = sum(pred_label != test_y) / length(test_y) print(paste("Test error using softprob =", error_rate)) xgboost-1.5.2/demo/multiclass_classification/train.py000077500000000000000000000030201417122711700230530ustar00rootroot00000000000000#!/usr/bin/python from __future__ import division import numpy as np import xgboost as xgb # label need to be 0 to num_class -1 data = np.loadtxt('./dermatology.data', delimiter=',', converters={33: lambda x:int(x == '?'), 34: lambda x:int(x) - 1}) sz = data.shape train = data[:int(sz[0] * 0.7), :] test = data[int(sz[0] * 0.7):, :] train_X = train[:, :33] train_Y = train[:, 34] test_X = test[:, :33] test_Y = test[:, 34] xg_train = xgb.DMatrix(train_X, label=train_Y) xg_test = xgb.DMatrix(test_X, label=test_Y) # setup parameters for xgboost param = {} # use softmax multi-class classification param['objective'] = 'multi:softmax' # scale weight of positive examples param['eta'] = 0.1 param['max_depth'] = 6 param['nthread'] = 4 param['num_class'] = 6 watchlist = [(xg_train, 'train'), (xg_test, 'test')] num_round = 5 bst = xgb.train(param, xg_train, num_round, watchlist) # get prediction pred = bst.predict(xg_test) error_rate = np.sum(pred != test_Y) / test_Y.shape[0] print('Test error using softmax = {}'.format(error_rate)) # do the same thing again, but output probabilities param['objective'] = 'multi:softprob' bst = xgb.train(param, xg_train, num_round, watchlist) # Note: this convention has been changed since xgboost-unity # get prediction, this is in 1D array, need reshape to (ndata, nclass) pred_prob = bst.predict(xg_test).reshape(test_Y.shape[0], 6) pred_label = np.argmax(pred_prob, axis=1) error_rate = np.sum(pred_label != test_Y) / test_Y.shape[0] print('Test error using softprob = {}'.format(error_rate)) xgboost-1.5.2/demo/rank/000077500000000000000000000000001417122711700150665ustar00rootroot00000000000000xgboost-1.5.2/demo/rank/README.md000066400000000000000000000020451417122711700163460ustar00rootroot00000000000000Learning to rank ==== XGBoost supports accomplishing ranking tasks. In ranking scenario, data are often grouped and we need the [group information file](../../doc/tutorials/input_format.rst#group-input-format) to specify ranking tasks. The model used in XGBoost for ranking is the LambdaRank. See [parameters](../../doc/parameter.rst) for supported metrics. ### Parameters The configuration setting is similar to the regression and binary classification setting, except user need to specify the objectives: ``` ... objective="rank:pairwise" ... ``` For more usage details please refer to the [binary classification demo](../binary_classification), Instructions ==== The dataset for ranking demo is from LETOR04 MQ2008 fold1. Before running the examples, you need to get the data by running: ``` ./wgetdata.sh ``` ### Command Line Run the example: ``` ./runexp.sh ``` ### Python There are two ways of doing ranking in python. Run the example using `xgboost.train`: ``` python rank.py ``` Run the example using `XGBRanker`: ``` python rank_sklearn.py ``` xgboost-1.5.2/demo/rank/mq2008.conf000066400000000000000000000013441417122711700166660ustar00rootroot00000000000000# General Parameters, see comment for each definition # specify objective objective="rank:pairwise" # Tree Booster Parameters # step size shrinkage eta = 0.1 # minimum loss reduction required to make a further partition gamma = 1.0 # minimum sum of instance weight(hessian) needed in a child min_child_weight = 0.1 # maximum depth of a tree max_depth = 6 # Task parameters # the number of round to do boosting num_round = 4 # 0 means do not save any model except the final round model save_period = 0 # The path of training data data = "mq2008.train" # The path of validation data, used to monitor training process, here [test] sets name of the validation set eval[test] = "mq2008.vali" # The path of test data test:data = "mq2008.test" xgboost-1.5.2/demo/rank/rank.py000066400000000000000000000024101417122711700163700ustar00rootroot00000000000000#!/usr/bin/python import xgboost as xgb from xgboost import DMatrix from sklearn.datasets import load_svmlight_file # This script demonstrate how to do ranking with xgboost.train x_train, y_train = load_svmlight_file("mq2008.train") x_valid, y_valid = load_svmlight_file("mq2008.vali") x_test, y_test = load_svmlight_file("mq2008.test") group_train = [] with open("mq2008.train.group", "r") as f: data = f.readlines() for line in data: group_train.append(int(line.split("\n")[0])) group_valid = [] with open("mq2008.vali.group", "r") as f: data = f.readlines() for line in data: group_valid.append(int(line.split("\n")[0])) group_test = [] with open("mq2008.test.group", "r") as f: data = f.readlines() for line in data: group_test.append(int(line.split("\n")[0])) train_dmatrix = DMatrix(x_train, y_train) valid_dmatrix = DMatrix(x_valid, y_valid) test_dmatrix = DMatrix(x_test) train_dmatrix.set_group(group_train) valid_dmatrix.set_group(group_valid) params = {'objective': 'rank:ndcg', 'eta': 0.1, 'gamma': 1.0, 'min_child_weight': 0.1, 'max_depth': 6} xgb_model = xgb.train(params, train_dmatrix, num_boost_round=4, evals=[(valid_dmatrix, 'validation')]) pred = xgb_model.predict(test_dmatrix) xgboost-1.5.2/demo/rank/rank_sklearn.py000066400000000000000000000021521417122711700201120ustar00rootroot00000000000000#!/usr/bin/python import xgboost as xgb from sklearn.datasets import load_svmlight_file # This script demonstrate how to do ranking with XGBRanker x_train, y_train = load_svmlight_file("mq2008.train") x_valid, y_valid = load_svmlight_file("mq2008.vali") x_test, y_test = load_svmlight_file("mq2008.test") group_train = [] with open("mq2008.train.group", "r") as f: data = f.readlines() for line in data: group_train.append(int(line.split("\n")[0])) group_valid = [] with open("mq2008.vali.group", "r") as f: data = f.readlines() for line in data: group_valid.append(int(line.split("\n")[0])) group_test = [] with open("mq2008.test.group", "r") as f: data = f.readlines() for line in data: group_test.append(int(line.split("\n")[0])) params = {'objective': 'rank:ndcg', 'learning_rate': 0.1, 'gamma': 1.0, 'min_child_weight': 0.1, 'max_depth': 6, 'n_estimators': 4} model = xgb.sklearn.XGBRanker(**params) model.fit(x_train, y_train, group_train, verbose=True, eval_set=[(x_valid, y_valid)], eval_group=[group_valid]) pred = model.predict(x_test) xgboost-1.5.2/demo/rank/runexp.sh000077500000000000000000000001371417122711700167470ustar00rootroot00000000000000#!/bin/bash ../../xgboost mq2008.conf ../../xgboost mq2008.conf task=pred model_in=0004.model xgboost-1.5.2/demo/rank/trans_data.py000066400000000000000000000022301417122711700175550ustar00rootroot00000000000000import sys def save_data(group_data,output_feature,output_group): if len(group_data) == 0: return output_group.write(str(len(group_data))+"\n") for data in group_data: # only include nonzero features feats = [ p for p in data[2:] if float(p.split(':')[1]) != 0.0 ] output_feature.write(data[0] + " " + " ".join(feats) + "\n") if __name__ == "__main__": if len(sys.argv) != 4: print ("Usage: python trans_data.py [Ranksvm Format Input] [Output Feature File] [Output Group File]") sys.exit(0) fi = open(sys.argv[1]) output_feature = open(sys.argv[2],"w") output_group = open(sys.argv[3],"w") group_data = [] group = "" for line in fi: if not line: break if "#" in line: line = line[:line.index("#")] splits = line.strip().split(" ") if splits[1] != group: save_data(group_data,output_feature,output_group) group_data = [] group = splits[1] group_data.append(splits) save_data(group_data,output_feature,output_group) fi.close() output_feature.close() output_group.close() xgboost-1.5.2/demo/rank/wgetdata.sh000077500000000000000000000006651417122711700172340ustar00rootroot00000000000000#!/bin/bash if [ -f MQ2008.rar ] then echo "Use downloaded data to run experiment." else echo "Downloading data." wget https://s3-us-west-2.amazonaws.com/xgboost-examples/MQ2008.rar unrar x MQ2008.rar mv -f MQ2008/Fold1/*.txt . fi python trans_data.py train.txt mq2008.train mq2008.train.group python trans_data.py test.txt mq2008.test mq2008.test.group python trans_data.py vali.txt mq2008.vali mq2008.vali.group xgboost-1.5.2/demo/rmm_plugin/000077500000000000000000000000001417122711700163045ustar00rootroot00000000000000xgboost-1.5.2/demo/rmm_plugin/README.md000066400000000000000000000045371417122711700175740ustar00rootroot00000000000000Using XGBoost with RAPIDS Memory Manager (RMM) plugin (EXPERIMENTAL) ==================================================================== [RAPIDS Memory Manager (RMM)](https://github.com/rapidsai/rmm) library provides a collection of efficient memory allocators for NVIDIA GPUs. It is now possible to use XGBoost with memory allocators provided by RMM, by enabling the RMM integration plugin. The demos in this directory highlights one RMM allocator in particular: **the pool sub-allocator**. This allocator addresses the slow speed of `cudaMalloc()` by allocating a large chunk of memory upfront. Subsequent allocations will draw from the pool of already allocated memory and thus avoid the overhead of calling `cudaMalloc()` directly. See [this GTC talk slides](https://on-demand.gputechconf.com/gtc/2015/presentation/S5530-Stephen-Jones.pdf) for more details. Before running the demos, ensure that XGBoost is compiled with the RMM plugin enabled. To do this, run CMake with option `-DPLUGIN_RMM=ON` (`-DUSE_CUDA=ON` also required): ``` cmake .. -DUSE_CUDA=ON -DUSE_NCCL=ON -DPLUGIN_RMM=ON make -j4 ``` CMake will attempt to locate the RMM library in your build environment. You may choose to build RMM from the source, or install it using the Conda package manager. If CMake cannot find RMM, you should specify the location of RMM with the CMake prefix: ``` # If using Conda: cmake .. -DUSE_CUDA=ON -DUSE_NCCL=ON -DPLUGIN_RMM=ON -DCMAKE_PREFIX_PATH=$CONDA_PREFIX # If using RMM installed with a custom location cmake .. -DUSE_CUDA=ON -DUSE_NCCL=ON -DPLUGIN_RMM=ON -DCMAKE_PREFIX_PATH=/path/to/rmm ``` # Informing XGBoost about RMM pool When XGBoost is compiled with RMM, most of the large size allocation will go through RMM allocators, but some small allocations in performance critical areas are using a different caching allocator so that we can have better control over memory allocation behavior. Users can override this behavior and force the use of rmm for all allocations by setting the global configuration ``use_rmm``: ``` python with xgb.config_context(use_rmm=True): clf = xgb.XGBClassifier(tree_method="gpu_hist") ``` Depending on the choice of memory pool size or type of allocator, this may have negative performance impact. * [Using RMM with a single GPU](./rmm_singlegpu.py) * [Using RMM with a local Dask cluster consisting of multiple GPUs](./rmm_mgpu_with_dask.py) xgboost-1.5.2/demo/rmm_plugin/rmm_mgpu_with_dask.py000066400000000000000000000024651417122711700225450ustar00rootroot00000000000000import xgboost as xgb from sklearn.datasets import make_classification import dask from dask.distributed import Client from dask_cuda import LocalCUDACluster def main(client): # Optionally force XGBoost to use RMM for all GPU memory allocation, see ./README.md # xgb.set_config(use_rmm=True) X, y = make_classification(n_samples=10000, n_informative=5, n_classes=3) # In pratice one should prefer loading the data with dask collections instead of using # `from_array`. X = dask.array.from_array(X) y = dask.array.from_array(y) dtrain = xgb.dask.DaskDMatrix(client, X, label=y) params = {'max_depth': 8, 'eta': 0.01, 'objective': 'multi:softprob', 'num_class': 3, 'tree_method': 'gpu_hist', 'eval_metric': 'merror'} output = xgb.dask.train(client, params, dtrain, num_boost_round=100, evals=[(dtrain, 'train')]) bst = output['booster'] history = output['history'] for i, e in enumerate(history['train']['merror']): print(f'[{i}] train-merror: {e}') if __name__ == '__main__': # To use RMM pool allocator with a GPU Dask cluster, just add rmm_pool_size option to # LocalCUDACluster constructor. with LocalCUDACluster(rmm_pool_size='2GB') as cluster: with Client(cluster) as client: main(client) xgboost-1.5.2/demo/rmm_plugin/rmm_singlegpu.py000066400000000000000000000012121417122711700215220ustar00rootroot00000000000000import xgboost as xgb import rmm from sklearn.datasets import make_classification # Initialize RMM pool allocator rmm.reinitialize(pool_allocator=True) # Optionally force XGBoost to use RMM for all GPU memory allocation, see ./README.md # xgb.set_config(use_rmm=True) X, y = make_classification(n_samples=10000, n_informative=5, n_classes=3) dtrain = xgb.DMatrix(X, label=y) params = { "max_depth": 8, "eta": 0.01, "objective": "multi:softprob", "num_class": 3, "tree_method": "gpu_hist", } # XGBoost will automatically use the RMM pool allocator bst = xgb.train(params, dtrain, num_boost_round=100, evals=[(dtrain, "train")]) xgboost-1.5.2/dev/000077500000000000000000000000001417122711700137655ustar00rootroot00000000000000xgboost-1.5.2/dev/query_contributors.py000066400000000000000000000055301417122711700203240ustar00rootroot00000000000000"""Query list of all contributors and reviewers in a release""" from sh.contrib import git import sys import re import requests import json if len(sys.argv) != 5: print(f'Usage: {sys.argv[0]} [starting commit/tag] [ending commit/tag] [GitHub username] ' + '[GitHub password]') sys.exit(1) from_commit = sys.argv[1] to_commit = sys.argv[2] username = sys.argv[3] password = sys.argv[4] contributors = set() reviewers = set() def paginate_request(url, callback): r = requests.get(url, auth=(username, password)) assert r.status_code == requests.codes.ok, f'Code: {r.status_code}, Text: {r.text}' callback(json.loads(r.text)) while 'next' in r.links: r = requests.get(r.links['next']['url'], auth=(username, password)) callback(json.loads(r.text)) for line in git.log(f'{from_commit}..{to_commit}', '--pretty=format:%s', '--reverse', '--first-parent'): m = re.search('\(#([0-9]+)\)$', line.rstrip()) if m: pr_id = m.group(1) print(f'PR #{pr_id}') def process_commit_list(commit_list): try: contributors.update([commit['author']['login'] for commit in commit_list]) except TypeError: prompt = (f'Error fetching contributors for PR #{pr_id}. Enter it manually, ' + 'as a space-separated list: ') contributors.update(str(input(prompt)).split(' ')) def process_review_list(review_list): reviewers.update([x['user']['login'] for x in review_list]) def process_comment_list(comment_list): reviewers.update([x['user']['login'] for x in comment_list]) paginate_request(f'https://api.github.com/repos/dmlc/xgboost/pulls/{pr_id}/commits', process_commit_list) paginate_request(f'https://api.github.com/repos/dmlc/xgboost/pulls/{pr_id}/reviews', process_review_list) paginate_request(f'https://api.github.com/repos/dmlc/xgboost/issues/{pr_id}/comments', process_comment_list) print('Contributors: ', end='') for x in sorted(contributors): r = requests.get(f'https://api.github.com/users/{x}', auth=(username, password)) assert r.status_code == requests.codes.ok, f'Code: {r.status_code}, Text: {r.text}' user_info = json.loads(r.text) if user_info['name'] is None: print(f"@{x}, ", end='') else: print(f"{user_info['name']} (@{x}), ", end='') print('\nReviewers: ', end='') for x in sorted(reviewers): r = requests.get(f'https://api.github.com/users/{x}', auth=(username, password)) assert r.status_code == requests.codes.ok, f'Code: {r.status_code}, Text: {r.text}' user_info = json.loads(r.text) if user_info['name'] is None: print(f"@{x}, ", end='') else: print(f"{user_info['name']} (@{x}), ", end='') print('') xgboost-1.5.2/dev/release-pypi.py000066400000000000000000000076351417122711700167510ustar00rootroot00000000000000"""Simple script for downloading and checking pypi release wheels. tqdm, sh are required to run this script. """ from urllib.request import urlretrieve import argparse from typing import List from sh.contrib import git from distutils import version import subprocess import tqdm import os # The package building is managed by Jenkins CI. PREFIX = "https://s3-us-west-2.amazonaws.com/xgboost-nightly-builds/release_" DIST = os.path.join(os.path.curdir, "python-package", "dist") pbar = None def show_progress(block_num, block_size, total_size): "Show file download progress." global pbar if pbar is None: pbar = tqdm.tqdm(total=total_size / 1024, unit="kB") downloaded = block_num * block_size if downloaded < total_size: pbar.update(block_size / 1024) else: pbar.close() pbar = None def retrieve(url, filename=None): return urlretrieve(url, filename, reporthook=show_progress) def latest_hash() -> str: "Get latest commit hash." ret = subprocess.run(["git", "rev-parse", "HEAD"], capture_output=True) assert ret.returncode == 0, "Failed to get latest commit hash." commit_hash = ret.stdout.decode("utf-8").strip() return commit_hash def download_wheels( platforms: List[str], dir_URL: str, src_filename_prefix: str, target_filename_prefix: str, ) -> List: """Download all binary wheels. dir_URL is the URL for remote directory storing the release wheels """ filenames = [] for platform in platforms: src_wheel = src_filename_prefix + platform + ".whl" url = dir_URL + src_wheel target_wheel = target_filename_prefix + platform + ".whl" filename = os.path.join(DIST, target_wheel) filenames.append(filename) print("Downloading from:", url, "to:", filename) retrieve(url=url, filename=filename) ret = subprocess.run(["twine", "check", filename], capture_output=True) assert ret.returncode == 0, "Failed twine check" stderr = ret.stderr.decode("utf-8") stdout = ret.stdout.decode("utf-8") assert stderr.find("warning") == -1, "Unresolved warnings:\n" + stderr assert stdout.find("warning") == -1, "Unresolved warnings:\n" + stdout return filenames def check_path(): root = os.path.abspath(os.path.curdir) assert os.path.basename(root) == "xgboost", "Must be run on project root." def main(args: argparse.Namespace) -> None: check_path() rel = version.StrictVersion(args.release) platforms = [ "win_amd64", "manylinux2014_x86_64", "manylinux2014_aarch64", "macosx_10_14_x86_64.macosx_10_15_x86_64.macosx_11_0_x86_64", ] print("Release:", rel) major, minor, patch = rel.version branch = "release_" + str(major) + "." + str(minor) + ".0" git.clean("-xdf") git.checkout(branch) git.pull("origin", branch) git.submodule("update") commit_hash = latest_hash() dir_URL = PREFIX + str(major) + "." + str(minor) + ".0" + "/" src_filename_prefix = "xgboost-" + args.release + "%2B" + commit_hash + "-py3-none-" target_filename_prefix = "xgboost-" + args.release + "-py3-none-" if not os.path.exists(DIST): os.mkdir(DIST) filenames = download_wheels( platforms, dir_URL, src_filename_prefix, target_filename_prefix ) print("List of downloaded wheels:", filenames) print( """ Following steps should be done manually: - Generate source package by running `python setup.py sdist`. - Upload pypi package by `python3 -m twine upload dist/` for all wheels. - Check the uploaded files on `https://pypi.org/project/xgboost//#files` and `pip install xgboost==` """ ) if __name__ == "__main__": parser = argparse.ArgumentParser() parser.add_argument( "--release", type=str, required=True, help="Version tag, e.g. '1.3.2'." ) args = parser.parse_args() main(args) xgboost-1.5.2/dev/release-tarball.sh000077500000000000000000000034041417122711700173640ustar00rootroot00000000000000#!/usr/bin/env bash # Helper script for creating release tarball. print_usage() { printf "Script for making release source tarball.\n" printf "Usage:\n\trelease-tarball.sh \n\n" } print_error() { local msg=$1 printf "\u001b[31mError\u001b[0m: $msg\n\n" print_usage } check_input() { local TAG=$1 if [ -z $TAG ]; then print_error "Empty tag argument" exit -1 fi } check_curdir() { local CUR_ABS=$1 printf "Current directory: ${CUR_ABS}\n" local CUR=$(basename $CUR_ABS) if [ $CUR == "dev" ]; then cd .. CUR=$(basename $(pwd)) fi if [ $CUR != "xgboost" ]; then print_error "Must be in project root or xgboost/dev. Current directory: ${CUR}" exit -1; fi } # Remove all submodules. cleanup_git() { local TAG=$1 check_input $TAG git checkout $TAG || exit -1 local SUBMODULES=$(grep "path = " ./.gitmodules | cut -f 3 --delimiter=' ' -) for module in $SUBMODULES; do rm -rf ${module}/.git done rm -rf .git } make_tarball() { local SRCDIR=$1 local CUR_ABS=$2 tar -czf xgboost.tar.gz xgboost printf "Copying ${SRCDIR}/xgboost.tar.gz back to ${CUR_ABS}/xgboost.tar.gz .\n" cp xgboost.tar.gz ${CUR_ABS}/xgboost.tar.gz printf "Writing hash to ${CUR_ABS}/hash .\n" sha256sum -z ${CUR_ABS}/xgboost.tar.gz | cut -f 1 --delimiter=' ' > ${CUR_ABS}/hash } main() { local TAG=$1 check_input $TAG local CUR_ABS=$(pwd) check_curdir $CUR_ABS local TMPDIR=$(mktemp -d) printf "tmpdir: ${TMPDIR}\n" git clean -xdf || exit -1 cp -R . $TMPDIR/xgboost pushd . cd $TMPDIR/xgboost cleanup_git $TAG cd .. make_tarball $TMPDIR $CUR_ABS popd rm -rf $TMPDIR } main $1 xgboost-1.5.2/dmlc-core/000077500000000000000000000000001417122711700150545ustar00rootroot00000000000000xgboost-1.5.2/doc/000077500000000000000000000000001417122711700137545ustar00rootroot00000000000000xgboost-1.5.2/doc/.gitignore000066400000000000000000000000641417122711700157440ustar00rootroot00000000000000html latex *.sh _* doxygen parser.py *.pyc web-data xgboost-1.5.2/doc/Doxyfile.in000066400000000000000000003107751417122711700161040ustar00rootroot00000000000000# Doxyfile 1.8.8 # This file describes the settings to be used by the documentation system # doxygen (www.doxygen.org) for a project. # # All text after a double hash (##) is considered a comment and is placed in # front of the TAG it is preceding. # # All text after a single hash (#) is considered a comment and will be ignored. # The format is: # TAG = value [value, ...] # For lists, items can also be appended using: # TAG += value [value, ...] # Values that contain spaces should be placed between quotes (\" \"). #--------------------------------------------------------------------------- # Project related configuration options #--------------------------------------------------------------------------- # This tag specifies the encoding used for all characters in the config file # that follow. The default is UTF-8 which is also the encoding used for all text # before the first occurrence of this tag. Doxygen uses libiconv (or the iconv # built into libc) for the transcoding. See http://www.gnu.org/software/libiconv # for the list of possible encodings. # The default value is: UTF-8. DOXYFILE_ENCODING = UTF-8 # The PROJECT_NAME tag is a single word (or a sequence of words surrounded by # double-quotes, unless you are using Doxywizard) that should identify the # project for which the documentation is generated. This name is used in the # title of most generated pages and in a few other places. # The default value is: My Project. PROJECT_NAME = "xgboost" # The PROJECT_NUMBER tag can be used to enter a project or revision number. This # could be handy for archiving the generated documentation or if some version # control system is used. PROJECT_NUMBER = @XGBOOST_VERSION@ # Using the PROJECT_BRIEF tag one can provide an optional one line description # for a project that appears at the top of each page and should give viewer a # quick idea about the purpose of the project. Keep the description short. PROJECT_BRIEF = # With the PROJECT_LOGO tag one can specify an logo or icon that is included in # the documentation. The maximum height of the logo should not exceed 55 pixels # and the maximum width should not exceed 200 pixels. Doxygen will copy the logo # to the output directory. PROJECT_LOGO = # The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute) path # into which the generated documentation will be written. If a relative path is # entered, it will be relative to the location where doxygen was started. If # left blank the current directory will be used. OUTPUT_DIRECTORY = @PROJECT_BINARY_DIR@/doc_doxygen # If the CREATE_SUBDIRS tag is set to YES, then doxygen will create 4096 sub- # directories (in 2 levels) under the output directory of each output format and # will distribute the generated files over these directories. Enabling this # option can be useful when feeding doxygen a huge amount of source files, where # putting all generated files in the same directory would otherwise causes # performance problems for the file system. # The default value is: NO. CREATE_SUBDIRS = NO # If the ALLOW_UNICODE_NAMES tag is set to YES, doxygen will allow non-ASCII # characters to appear in the names of generated files. If set to NO, non-ASCII # characters will be escaped, for example _xE3_x81_x84 will be used for Unicode # U+3044. # The default value is: NO. #ALLOW_UNICODE_NAMES = NO # The OUTPUT_LANGUAGE tag is used to specify the language in which all # documentation generated by doxygen is written. Doxygen will use this # information to generate all constant output in the proper language. # Possible values are: Afrikaans, Arabic, Armenian, Brazilian, Catalan, Chinese, # Chinese-Traditional, Croatian, Czech, Danish, Dutch, English (United States), # Esperanto, Farsi (Persian), Finnish, French, German, Greek, Hungarian, # Indonesian, Italian, Japanese, Japanese-en (Japanese with English messages), # Korean, Korean-en (Korean with English messages), Latvian, Lithuanian, # Macedonian, Norwegian, Persian (Farsi), Polish, Portuguese, Romanian, Russian, # Serbian, Serbian-Cyrillic, Slovak, Slovene, Spanish, Swedish, Turkish, # Ukrainian and Vietnamese. # The default value is: English. OUTPUT_LANGUAGE = English # If the BRIEF_MEMBER_DESC tag is set to YES doxygen will include brief member # descriptions after the members that are listed in the file and class # documentation (similar to Javadoc). Set to NO to disable this. # The default value is: YES. BRIEF_MEMBER_DESC = YES # If the REPEAT_BRIEF tag is set to YES doxygen will prepend the brief # description of a member or function before the detailed description # # Note: If both HIDE_UNDOC_MEMBERS and BRIEF_MEMBER_DESC are set to NO, the # brief descriptions will be completely suppressed. # The default value is: YES. REPEAT_BRIEF = YES # This tag implements a quasi-intelligent brief description abbreviator that is # used to form the text in various listings. Each string in this list, if found # as the leading text of the brief description, will be stripped from the text # and the result, after processing the whole list, is used as the annotated # text. Otherwise, the brief description is used as-is. If left blank, the # following values are used ($name is automatically replaced with the name of # the entity):The $name class, The $name widget, The $name file, is, provides, # specifies, contains, represents, a, an and the. ABBREVIATE_BRIEF = # If the ALWAYS_DETAILED_SEC and REPEAT_BRIEF tags are both set to YES then # doxygen will generate a detailed section even if there is only a brief # description. # The default value is: NO. ALWAYS_DETAILED_SEC = NO # If the INLINE_INHERITED_MEMB tag is set to YES, doxygen will show all # inherited members of a class in the documentation of that class as if those # members were ordinary class members. Constructors, destructors and assignment # operators of the base classes will not be shown. # The default value is: NO. INLINE_INHERITED_MEMB = NO # If the FULL_PATH_NAMES tag is set to YES doxygen will prepend the full path # before files name in the file list and in the header files. If set to NO the # shortest path that makes the file name unique will be used # The default value is: YES. FULL_PATH_NAMES = YES # The STRIP_FROM_PATH tag can be used to strip a user-defined part of the path. # Stripping is only done if one of the specified strings matches the left-hand # part of the path. The tag can be used to show relative paths in the file list. # If left blank the directory from which doxygen is run is used as the path to # strip. # # Note that you can specify absolute paths here, but also relative paths, which # will be relative from the directory where doxygen is started. # This tag requires that the tag FULL_PATH_NAMES is set to YES. STRIP_FROM_PATH = # The STRIP_FROM_INC_PATH tag can be used to strip a user-defined part of the # path mentioned in the documentation of a class, which tells the reader which # header file to include in order to use a class. If left blank only the name of # the header file containing the class definition is used. Otherwise one should # specify the list of include paths that are normally passed to the compiler # using the -I flag. STRIP_FROM_INC_PATH = # If the SHORT_NAMES tag is set to YES, doxygen will generate much shorter (but # less readable) file names. This can be useful is your file systems doesn't # support long names like on DOS, Mac, or CD-ROM. # The default value is: NO. SHORT_NAMES = NO # If the JAVADOC_AUTOBRIEF tag is set to YES then doxygen will interpret the # first line (until the first dot) of a Javadoc-style comment as the brief # description. If set to NO, the Javadoc-style will behave just like regular Qt- # style comments (thus requiring an explicit @brief command for a brief # description.) # The default value is: NO. JAVADOC_AUTOBRIEF = NO # If the QT_AUTOBRIEF tag is set to YES then doxygen will interpret the first # line (until the first dot) of a Qt-style comment as the brief description. If # set to NO, the Qt-style will behave just like regular Qt-style comments (thus # requiring an explicit \brief command for a brief description.) # The default value is: NO. QT_AUTOBRIEF = NO # The MULTILINE_CPP_IS_BRIEF tag can be set to YES to make doxygen treat a # multi-line C++ special comment block (i.e. a block of //! or /// comments) as # a brief description. This used to be the default behavior. The new default is # to treat a multi-line C++ comment block as a detailed description. Set this # tag to YES if you prefer the old behavior instead. # # Note that setting this tag to YES also means that rational rose comments are # not recognized any more. # The default value is: NO. MULTILINE_CPP_IS_BRIEF = NO # If the INHERIT_DOCS tag is set to YES then an undocumented member inherits the # documentation from any documented member that it re-implements. # The default value is: YES. INHERIT_DOCS = YES # If the SEPARATE_MEMBER_PAGES tag is set to YES, then doxygen will produce a # new page for each member. If set to NO, the documentation of a member will be # part of the file/class/namespace that contains it. # The default value is: NO. SEPARATE_MEMBER_PAGES = NO # The TAB_SIZE tag can be used to set the number of spaces in a tab. Doxygen # uses this value to replace tabs by spaces in code fragments. # Minimum value: 1, maximum value: 16, default value: 4. TAB_SIZE = 8 # This tag can be used to specify a number of aliases that act as commands in # the documentation. An alias has the form: # name=value # For example adding # "sideeffect=@par Side Effects:\n" # will allow you to put the command \sideeffect (or @sideeffect) in the # documentation, which will result in a user-defined paragraph with heading # "Side Effects:". You can put \n's in the value part of an alias to insert # newlines. ALIASES = # This tag can be used to specify a number of word-keyword mappings (TCL only). # A mapping has the form "name=value". For example adding "class=itcl::class" # will allow you to use the command class in the itcl::class meaning. TCL_SUBST = # Set the OPTIMIZE_OUTPUT_FOR_C tag to YES if your project consists of C sources # only. Doxygen will then generate output that is more tailored for C. For # instance, some of the names that are used will be different. The list of all # members will be omitted, etc. # The default value is: NO. OPTIMIZE_OUTPUT_FOR_C = NO # Set the OPTIMIZE_OUTPUT_JAVA tag to YES if your project consists of Java or # Python sources only. Doxygen will then generate output that is more tailored # for that language. For instance, namespaces will be presented as packages, # qualified scopes will look different, etc. # The default value is: NO. OPTIMIZE_OUTPUT_JAVA = NO # Set the OPTIMIZE_FOR_FORTRAN tag to YES if your project consists of Fortran # sources. Doxygen will then generate output that is tailored for Fortran. # The default value is: NO. OPTIMIZE_FOR_FORTRAN = NO # Set the OPTIMIZE_OUTPUT_VHDL tag to YES if your project consists of VHDL # sources. Doxygen will then generate output that is tailored for VHDL. # The default value is: NO. OPTIMIZE_OUTPUT_VHDL = NO # Doxygen selects the parser to use depending on the extension of the files it # parses. With this tag you can assign which parser to use for a given # extension. Doxygen has a built-in mapping, but you can override or extend it # using this tag. The format is ext=language, where ext is a file extension, and # language is one of the parsers supported by doxygen: IDL, Java, Javascript, # C#, C, C++, D, PHP, Objective-C, Python, Fortran (fixed format Fortran: # FortranFixed, free formatted Fortran: FortranFree, unknown formatted Fortran: # Fortran. In the later case the parser tries to guess whether the code is fixed # or free formatted code, this is the default for Fortran type files), VHDL. For # instance to make doxygen treat .inc files as Fortran files (default is PHP), # and .f files as C (default is Fortran), use: inc=Fortran f=C. # # Note For files without extension you can use no_extension as a placeholder. # # Note that for custom extensions you also need to set FILE_PATTERNS otherwise # the files are not read by doxygen. EXTENSION_MAPPING = # If the MARKDOWN_SUPPORT tag is enabled then doxygen pre-processes all comments # according to the Markdown format, which allows for more readable # documentation. See http://daringfireball.net/projects/markdown/ for details. # The output of markdown processing is further processed by doxygen, so you can # mix doxygen, HTML, and XML commands with Markdown formatting. Disable only in # case of backward compatibilities issues. # The default value is: YES. #MARKDOWN_SUPPORT = YES # When enabled doxygen tries to link words that correspond to documented # classes, or namespaces to their corresponding documentation. Such a link can # be prevented in individual cases by by putting a % sign in front of the word # or globally by setting AUTOLINK_SUPPORT to NO. # The default value is: YES. #AUTOLINK_SUPPORT = YES # If you use STL classes (i.e. std::string, std::vector, etc.) but do not want # to include (a tag file for) the STL sources as input, then you should set this # tag to YES in order to let doxygen match functions declarations and # definitions whose arguments contain STL classes (e.g. func(std::string); # versus func(std::string) {}). This also make the inheritance and collaboration # diagrams that involve STL classes more complete and accurate. # The default value is: NO. BUILTIN_STL_SUPPORT = NO # If you use Microsoft's C++/CLI language, you should set this option to YES to # enable parsing support. # The default value is: NO. CPP_CLI_SUPPORT = NO # Set the SIP_SUPPORT tag to YES if your project consists of sip (see: # http://www.riverbankcomputing.co.uk/software/sip/intro) sources only. Doxygen # will parse them like normal C++ but will assume all classes use public instead # of private inheritance when no explicit protection keyword is present. # The default value is: NO. SIP_SUPPORT = NO # For Microsoft's IDL there are propget and propput attributes to indicate # getter and setter methods for a property. Setting this option to YES will make # doxygen to replace the get and set methods by a property in the documentation. # This will only work if the methods are indeed getting or setting a simple # type. If this is not the case, or you want to show the methods anyway, you # should set this option to NO. # The default value is: YES. IDL_PROPERTY_SUPPORT = YES # If member grouping is used in the documentation and the DISTRIBUTE_GROUP_DOC # tag is set to YES, then doxygen will reuse the documentation of the first # member in the group (if any) for the other members of the group. By default # all members of a group must be documented explicitly. # The default value is: NO. DISTRIBUTE_GROUP_DOC = NO # Set the SUBGROUPING tag to YES to allow class member groups of the same type # (for instance a group of public functions) to be put as a subgroup of that # type (e.g. under the Public Functions section). Set it to NO to prevent # subgrouping. Alternatively, this can be done per class using the # \nosubgrouping command. # The default value is: YES. SUBGROUPING = YES # When the INLINE_GROUPED_CLASSES tag is set to YES, classes, structs and unions # are shown inside the group in which they are included (e.g. using \ingroup) # instead of on a separate page (for HTML and Man pages) or section (for LaTeX # and RTF). # # Note that this feature does not work in combination with # SEPARATE_MEMBER_PAGES. # The default value is: NO. INLINE_GROUPED_CLASSES = NO # When the INLINE_SIMPLE_STRUCTS tag is set to YES, structs, classes, and unions # with only public data fields or simple typedef fields will be shown inline in # the documentation of the scope in which they are defined (i.e. file, # namespace, or group documentation), provided this scope is documented. If set # to NO, structs, classes, and unions are shown on a separate page (for HTML and # Man pages) or section (for LaTeX and RTF). # The default value is: NO. INLINE_SIMPLE_STRUCTS = NO # When TYPEDEF_HIDES_STRUCT tag is enabled, a typedef of a struct, union, or # enum is documented as struct, union, or enum with the name of the typedef. So # typedef struct TypeS {} TypeT, will appear in the documentation as a struct # with name TypeT. When disabled the typedef will appear as a member of a file, # namespace, or class. And the struct will be named TypeS. This can typically be # useful for C code in case the coding convention dictates that all compound # types are typedef'ed and only the typedef is referenced, never the tag name. # The default value is: NO. TYPEDEF_HIDES_STRUCT = NO # The size of the symbol lookup cache can be set using LOOKUP_CACHE_SIZE. This # cache is used to resolve symbols given their name and scope. Since this can be # an expensive process and often the same symbol appears multiple times in the # code, doxygen keeps a cache of pre-resolved symbols. If the cache is too small # doxygen will become slower. If the cache is too large, memory is wasted. The # cache size is given by this formula: 2^(16+LOOKUP_CACHE_SIZE). The valid range # is 0..9, the default is 0, corresponding to a cache size of 2^16=65536 # symbols. At the end of a run doxygen will report the cache usage and suggest # the optimal cache size from a speed point of view. # Minimum value: 0, maximum value: 9, default value: 0. LOOKUP_CACHE_SIZE = 0 #--------------------------------------------------------------------------- # Build related configuration options #--------------------------------------------------------------------------- # If the EXTRACT_ALL tag is set to YES doxygen will assume all entities in # documentation are documented, even if no documentation was available. Private # class members and static file members will be hidden unless the # EXTRACT_PRIVATE respectively EXTRACT_STATIC tags are set to YES. # Note: This will also disable the warnings about undocumented members that are # normally produced when WARNINGS is set to YES. # The default value is: NO. EXTRACT_ALL = YES # If the EXTRACT_PRIVATE tag is set to YES all private members of a class will # be included in the documentation. # The default value is: NO. EXTRACT_PRIVATE = NO # If the EXTRACT_PACKAGE tag is set to YES all members with package or internal # scope will be included in the documentation. # The default value is: NO. #EXTRACT_PACKAGE = NO # If the EXTRACT_STATIC tag is set to YES all static members of a file will be # included in the documentation. # The default value is: NO. EXTRACT_STATIC = NO # If the EXTRACT_LOCAL_CLASSES tag is set to YES classes (and structs) defined # locally in source files will be included in the documentation. If set to NO # only classes defined in header files are included. Does not have any effect # for Java sources. # The default value is: YES. EXTRACT_LOCAL_CLASSES = YES # This flag is only useful for Objective-C code. When set to YES local methods, # which are defined in the implementation section but not in the interface are # included in the documentation. If set to NO only methods in the interface are # included. # The default value is: NO. EXTRACT_LOCAL_METHODS = NO # If this flag is set to YES, the members of anonymous namespaces will be # extracted and appear in the documentation as a namespace called # 'anonymous_namespace{file}', where file will be replaced with the base name of # the file that contains the anonymous namespace. By default anonymous namespace # are hidden. # The default value is: NO. EXTRACT_ANON_NSPACES = NO # If the HIDE_UNDOC_MEMBERS tag is set to YES, doxygen will hide all # undocumented members inside documented classes or files. If set to NO these # members will be included in the various overviews, but no documentation # section is generated. This option has no effect if EXTRACT_ALL is enabled. # The default value is: NO. HIDE_UNDOC_MEMBERS = NO # If the HIDE_UNDOC_CLASSES tag is set to YES, doxygen will hide all # undocumented classes that are normally visible in the class hierarchy. If set # to NO these classes will be included in the various overviews. This option has # no effect if EXTRACT_ALL is enabled. # The default value is: NO. HIDE_UNDOC_CLASSES = NO # If the HIDE_FRIEND_COMPOUNDS tag is set to YES, doxygen will hide all friend # (class|struct|union) declarations. If set to NO these declarations will be # included in the documentation. # The default value is: NO. HIDE_FRIEND_COMPOUNDS = NO # If the HIDE_IN_BODY_DOCS tag is set to YES, doxygen will hide any # documentation blocks found inside the body of a function. If set to NO these # blocks will be appended to the function's detailed documentation block. # The default value is: NO. HIDE_IN_BODY_DOCS = NO # The INTERNAL_DOCS tag determines if documentation that is typed after a # \internal command is included. If the tag is set to NO then the documentation # will be excluded. Set it to YES to include the internal documentation. # The default value is: NO. INTERNAL_DOCS = NO # If the CASE_SENSE_NAMES tag is set to NO then doxygen will only generate file # names in lower-case letters. If set to YES upper-case letters are also # allowed. This is useful if you have classes or files whose names only differ # in case and if your file system supports case sensitive file names. Windows # and Mac users are advised to set this option to NO. # The default value is: system dependent. CASE_SENSE_NAMES = YES # If the HIDE_SCOPE_NAMES tag is set to NO then doxygen will show members with # their full class and namespace scopes in the documentation. If set to YES the # scope will be hidden. # The default value is: NO. HIDE_SCOPE_NAMES = NO # If the SHOW_INCLUDE_FILES tag is set to YES then doxygen will put a list of # the files that are included by a file in the documentation of that file. # The default value is: YES. SHOW_INCLUDE_FILES = YES # If the SHOW_GROUPED_MEMB_INC tag is set to YES then Doxygen will add for each # grouped member an include statement to the documentation, telling the reader # which file to include in order to use the member. # The default value is: NO. #SHOW_GROUPED_MEMB_INC = NO # If the FORCE_LOCAL_INCLUDES tag is set to YES then doxygen will list include # files with double quotes in the documentation rather than with sharp brackets. # The default value is: NO. FORCE_LOCAL_INCLUDES = NO # If the INLINE_INFO tag is set to YES then a tag [inline] is inserted in the # documentation for inline members. # The default value is: YES. INLINE_INFO = YES # If the SORT_MEMBER_DOCS tag is set to YES then doxygen will sort the # (detailed) documentation of file and class members alphabetically by member # name. If set to NO the members will appear in declaration order. # The default value is: YES. SORT_MEMBER_DOCS = YES # If the SORT_BRIEF_DOCS tag is set to YES then doxygen will sort the brief # descriptions of file, namespace and class members alphabetically by member # name. If set to NO the members will appear in declaration order. Note that # this will also influence the order of the classes in the class list. # The default value is: NO. SORT_BRIEF_DOCS = NO # If the SORT_MEMBERS_CTORS_1ST tag is set to YES then doxygen will sort the # (brief and detailed) documentation of class members so that constructors and # destructors are listed first. If set to NO the constructors will appear in the # respective orders defined by SORT_BRIEF_DOCS and SORT_MEMBER_DOCS. # Note: If SORT_BRIEF_DOCS is set to NO this option is ignored for sorting brief # member documentation. # Note: If SORT_MEMBER_DOCS is set to NO this option is ignored for sorting # detailed member documentation. # The default value is: NO. SORT_MEMBERS_CTORS_1ST = NO # If the SORT_GROUP_NAMES tag is set to YES then doxygen will sort the hierarchy # of group names into alphabetical order. If set to NO the group names will # appear in their defined order. # The default value is: NO. SORT_GROUP_NAMES = NO # If the SORT_BY_SCOPE_NAME tag is set to YES, the class list will be sorted by # fully-qualified names, including namespaces. If set to NO, the class list will # be sorted only by class name, not including the namespace part. # Note: This option is not very useful if HIDE_SCOPE_NAMES is set to YES. # Note: This option applies only to the class list, not to the alphabetical # list. # The default value is: NO. SORT_BY_SCOPE_NAME = NO # If the STRICT_PROTO_MATCHING option is enabled and doxygen fails to do proper # type resolution of all parameters of a function it will reject a match between # the prototype and the implementation of a member function even if there is # only one candidate or it is obvious which candidate to choose by doing a # simple string match. By disabling STRICT_PROTO_MATCHING doxygen will still # accept a match between prototype and implementation in such cases. # The default value is: NO. STRICT_PROTO_MATCHING = NO # The GENERATE_TODOLIST tag can be used to enable ( YES) or disable ( NO) the # todo list. This list is created by putting \todo commands in the # documentation. # The default value is: YES. GENERATE_TODOLIST = YES # The GENERATE_TESTLIST tag can be used to enable ( YES) or disable ( NO) the # test list. This list is created by putting \test commands in the # documentation. # The default value is: YES. GENERATE_TESTLIST = YES # The GENERATE_BUGLIST tag can be used to enable ( YES) or disable ( NO) the bug # list. This list is created by putting \bug commands in the documentation. # The default value is: YES. GENERATE_BUGLIST = YES # The GENERATE_DEPRECATEDLIST tag can be used to enable ( YES) or disable ( NO) # the deprecated list. This list is created by putting \deprecated commands in # the documentation. # The default value is: YES. GENERATE_DEPRECATEDLIST= YES # The ENABLED_SECTIONS tag can be used to enable conditional documentation # sections, marked by \if ... \endif and \cond # ... \endcond blocks. ENABLED_SECTIONS = # The MAX_INITIALIZER_LINES tag determines the maximum number of lines that the # initial value of a variable or macro / define can have for it to appear in the # documentation. If the initializer consists of more lines than specified here # it will be hidden. Use a value of 0 to hide initializers completely. The # appearance of the value of individual variables and macros / defines can be # controlled using \showinitializer or \hideinitializer command in the # documentation regardless of this setting. # Minimum value: 0, maximum value: 10000, default value: 30. MAX_INITIALIZER_LINES = 30 # Set the SHOW_USED_FILES tag to NO to disable the list of files generated at # the bottom of the documentation of classes and structs. If set to YES the list # will mention the files that were used to generate the documentation. # The default value is: YES. SHOW_USED_FILES = YES # Set the SHOW_FILES tag to NO to disable the generation of the Files page. This # will remove the Files entry from the Quick Index and from the Folder Tree View # (if specified). # The default value is: YES. SHOW_FILES = YES # Set the SHOW_NAMESPACES tag to NO to disable the generation of the Namespaces # page. This will remove the Namespaces entry from the Quick Index and from the # Folder Tree View (if specified). # The default value is: YES. SHOW_NAMESPACES = YES # The FILE_VERSION_FILTER tag can be used to specify a program or script that # doxygen should invoke to get the current version for each file (typically from # the version control system). Doxygen will invoke the program by executing (via # popen()) the command command input-file, where command is the value of the # FILE_VERSION_FILTER tag, and input-file is the name of an input file provided # by doxygen. Whatever the program writes to standard output is used as the file # version. For an example see the documentation. FILE_VERSION_FILTER = # The LAYOUT_FILE tag can be used to specify a layout file which will be parsed # by doxygen. The layout file controls the global structure of the generated # output files in an output format independent way. To create the layout file # that represents doxygen's defaults, run doxygen with the -l option. You can # optionally specify a file name after the option, if omitted DoxygenLayout.xml # will be used as the name of the layout file. # # Note that if you run doxygen from a directory containing a file called # DoxygenLayout.xml, doxygen will parse it automatically even if the LAYOUT_FILE # tag is left empty. LAYOUT_FILE = # The CITE_BIB_FILES tag can be used to specify one or more bib files containing # the reference definitions. This must be a list of .bib files. The .bib # extension is automatically appended if omitted. This requires the bibtex tool # to be installed. See also http://en.wikipedia.org/wiki/BibTeX for more info. # For LaTeX the style of the bibliography can be controlled using # LATEX_BIB_STYLE. To use this feature you need bibtex and perl available in the # search path. See also \cite for info how to create references. CITE_BIB_FILES = #--------------------------------------------------------------------------- # Configuration options related to warning and progress messages #--------------------------------------------------------------------------- # The QUIET tag can be used to turn on/off the messages that are generated to # standard output by doxygen. If QUIET is set to YES this implies that the # messages are off. # The default value is: NO. QUIET = NO # The WARNINGS tag can be used to turn on/off the warning messages that are # generated to standard error ( stderr) by doxygen. If WARNINGS is set to YES # this implies that the warnings are on. # # Tip: Turn warnings on while writing the documentation. # The default value is: YES. WARNINGS = YES # If the WARN_IF_UNDOCUMENTED tag is set to YES, then doxygen will generate # warnings for undocumented members. If EXTRACT_ALL is set to YES then this flag # will automatically be disabled. # The default value is: YES. WARN_IF_UNDOCUMENTED = YES # If the WARN_IF_DOC_ERROR tag is set to YES, doxygen will generate warnings for # potential errors in the documentation, such as not documenting some parameters # in a documented function, or documenting parameters that don't exist or using # markup commands wrongly. # The default value is: YES. WARN_IF_DOC_ERROR = YES # This WARN_NO_PARAMDOC option can be enabled to get warnings for functions that # are documented, but have no documentation for their parameters or return # value. If set to NO doxygen will only warn about wrong or incomplete parameter # documentation, but not about the absence of documentation. # The default value is: NO. WARN_NO_PARAMDOC = YES # The WARN_FORMAT tag determines the format of the warning messages that doxygen # can produce. The string should contain the $file, $line, and $text tags, which # will be replaced by the file and line number from which the warning originated # and the warning text. Optionally the format may contain $version, which will # be replaced by the version of the file (if it could be obtained via # FILE_VERSION_FILTER) # The default value is: $file:$line: $text. WARN_FORMAT = "$file:$line: $text" # The WARN_LOGFILE tag can be used to specify a file to which warning and error # messages should be written. If left blank the output is written to standard # error (stderr). WARN_LOGFILE = #--------------------------------------------------------------------------- # Configuration options related to the input files #--------------------------------------------------------------------------- # The INPUT tag is used to specify the files and/or directories that contain # documented source files. You may enter file names like myfile.cpp or # directories like /usr/src/myproject. Separate the files or directories with # spaces. # Note: If this tag is empty the current directory is searched. INPUT = @PROJECT_SOURCE_DIR@/include @PROJECT_SOURCE_DIR@/src/common # This tag can be used to specify the character encoding of the source files # that doxygen parses. Internally doxygen uses the UTF-8 encoding. Doxygen uses # libiconv (or the iconv built into libc) for the transcoding. See the libiconv # documentation (see: http://www.gnu.org/software/libiconv) for the list of # possible encodings. # The default value is: UTF-8. INPUT_ENCODING = UTF-8 # If the value of the INPUT tag contains directories, you can use the # FILE_PATTERNS tag to specify one or more wildcard patterns (like *.cpp and # *.h) to filter out the source-files in the directories. If left blank the # following patterns are tested:*.c, *.cc, *.cxx, *.cpp, *.c++, *.java, *.ii, # *.ixx, *.ipp, *.i++, *.inl, *.idl, *.ddl, *.odl, *.h, *.hh, *.hxx, *.hpp, # *.h++, *.cs, *.d, *.php, *.php4, *.php5, *.phtml, *.inc, *.m, *.markdown, # *.md, *.mm, *.dox, *.py, *.f90, *.f, *.for, *.tcl, *.vhd, *.vhdl, *.ucf, # *.qsf, *.as and *.js. FILE_PATTERNS = *.h # The RECURSIVE tag can be used to specify whether or not subdirectories should # be searched for input files as well. # The default value is: NO. RECURSIVE = YES # The EXCLUDE tag can be used to specify files and/or directories that should be # excluded from the INPUT source files. This way you can easily exclude a # subdirectory from a directory tree whose root is specified with the INPUT tag. # # Note that relative paths are relative to the directory from which doxygen is # run. EXCLUDE = # The EXCLUDE_SYMLINKS tag can be used to select whether or not files or # directories that are symbolic links (a Unix file system feature) are excluded # from the input. # The default value is: NO. EXCLUDE_SYMLINKS = NO # If the value of the INPUT tag contains directories, you can use the # EXCLUDE_PATTERNS tag to specify one or more wildcard patterns to exclude # certain files from those directories. # # Note that the wildcards are matched against the file with absolute path, so to # exclude all test directories for example use the pattern */test/* EXCLUDE_PATTERNS = */test/* \ logging.h # The EXCLUDE_SYMBOLS tag can be used to specify one or more symbol names # (namespaces, classes, functions, etc.) that should be excluded from the # output. The symbol name can be a fully qualified name, a word, or if the # wildcard * is used, a substring. Examples: ANamespace, AClass, # AClass::ANamespace, ANamespace::*Test # # Note that the wildcards are matched against the file with absolute path, so to # exclude all test directories use the pattern */test/* EXCLUDE_SYMBOLS = # The EXAMPLE_PATH tag can be used to specify one or more files or directories # that contain example code fragments that are included (see the \include # command). EXAMPLE_PATH = # If the value of the EXAMPLE_PATH tag contains directories, you can use the # EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp and # *.h) to filter out the source-files in the directories. If left blank all # files are included. EXAMPLE_PATTERNS = # If the EXAMPLE_RECURSIVE tag is set to YES then subdirectories will be # searched for input files to be used with the \include or \dontinclude commands # irrespective of the value of the RECURSIVE tag. # The default value is: NO. EXAMPLE_RECURSIVE = NO # The IMAGE_PATH tag can be used to specify one or more files or directories # that contain images that are to be included in the documentation (see the # \image command). IMAGE_PATH = # The INPUT_FILTER tag can be used to specify a program that doxygen should # invoke to filter for each input file. Doxygen will invoke the filter program # by executing (via popen()) the command: # # # # where is the value of the INPUT_FILTER tag, and is the # name of an input file. Doxygen will then use the output that the filter # program writes to standard output. If FILTER_PATTERNS is specified, this tag # will be ignored. # # Note that the filter must not add or remove lines; it is applied before the # code is scanned, but not when the output code is generated. If lines are added # or removed, the anchors will not be placed correctly. INPUT_FILTER = # The FILTER_PATTERNS tag can be used to specify filters on a per file pattern # basis. Doxygen will compare the file name with each pattern and apply the # filter if there is a match. The filters are a list of the form: pattern=filter # (like *.cpp=my_cpp_filter). See INPUT_FILTER for further information on how # filters are used. If the FILTER_PATTERNS tag is empty or if none of the # patterns match the file name, INPUT_FILTER is applied. FILTER_PATTERNS = # If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using # INPUT_FILTER ) will also be used to filter the input files that are used for # producing the source files to browse (i.e. when SOURCE_BROWSER is set to YES). # The default value is: NO. FILTER_SOURCE_FILES = NO # The FILTER_SOURCE_PATTERNS tag can be used to specify source filters per file # pattern. A pattern will override the setting for FILTER_PATTERN (if any) and # it is also possible to disable source filtering for a specific pattern using # *.ext= (so without naming a filter). # This tag requires that the tag FILTER_SOURCE_FILES is set to YES. FILTER_SOURCE_PATTERNS = # If the USE_MDFILE_AS_MAINPAGE tag refers to the name of a markdown file that # is part of the input, its contents will be placed on the main page # (index.html). This can be useful if you have a project on for instance GitHub # and want to reuse the introduction page also for the doxygen output. #USE_MDFILE_AS_MAINPAGE = #--------------------------------------------------------------------------- # Configuration options related to source browsing #--------------------------------------------------------------------------- # If the SOURCE_BROWSER tag is set to YES then a list of source files will be # generated. Documented entities will be cross-referenced with these sources. # # Note: To get rid of all source code in the generated output, make sure that # also VERBATIM_HEADERS is set to NO. # The default value is: NO. SOURCE_BROWSER = NO # Setting the INLINE_SOURCES tag to YES will include the body of functions, # classes and enums directly into the documentation. # The default value is: NO. INLINE_SOURCES = NO # Setting the STRIP_CODE_COMMENTS tag to YES will instruct doxygen to hide any # special comment blocks from generated source code fragments. Normal C, C++ and # Fortran comments will always remain visible. # The default value is: YES. STRIP_CODE_COMMENTS = YES # If the REFERENCED_BY_RELATION tag is set to YES then for each documented # function all documented functions referencing it will be listed. # The default value is: NO. REFERENCED_BY_RELATION = NO # If the REFERENCES_RELATION tag is set to YES then for each documented function # all documented entities called/used by that function will be listed. # The default value is: NO. REFERENCES_RELATION = NO # If the REFERENCES_LINK_SOURCE tag is set to YES and SOURCE_BROWSER tag is set # to YES, then the hyperlinks from functions in REFERENCES_RELATION and # REFERENCED_BY_RELATION lists will link to the source code. Otherwise they will # link to the documentation. # The default value is: YES. REFERENCES_LINK_SOURCE = YES # If SOURCE_TOOLTIPS is enabled (the default) then hovering a hyperlink in the # source code will show a tooltip with additional information such as prototype, # brief description and links to the definition and documentation. Since this # will make the HTML file larger and loading of large files a bit slower, you # can opt to disable this feature. # The default value is: YES. # This tag requires that the tag SOURCE_BROWSER is set to YES. #SOURCE_TOOLTIPS = YES # If the USE_HTAGS tag is set to YES then the references to source code will # point to the HTML generated by the htags(1) tool instead of doxygen built-in # source browser. The htags tool is part of GNU's global source tagging system # (see http://www.gnu.org/software/global/global.html). You will need version # 4.8.6 or higher. # # To use it do the following: # - Install the latest version of global # - Enable SOURCE_BROWSER and USE_HTAGS in the config file # - Make sure the INPUT points to the root of the source tree # - Run doxygen as normal # # Doxygen will invoke htags (and that will in turn invoke gtags), so these # tools must be available from the command line (i.e. in the search path). # # The result: instead of the source browser generated by doxygen, the links to # source code will now point to the output of htags. # The default value is: NO. # This tag requires that the tag SOURCE_BROWSER is set to YES. USE_HTAGS = NO # If the VERBATIM_HEADERS tag is set the YES then doxygen will generate a # verbatim copy of the header file for each class for which an include is # specified. Set to NO to disable this. # See also: Section \class. # The default value is: YES. VERBATIM_HEADERS = YES # If the CLANG_ASSISTED_PARSING tag is set to YES, then doxygen will use the # clang parser (see: http://clang.llvm.org/) for more accurate parsing at the # cost of reduced performance. This can be particularly helpful with template # rich C++ code for which doxygen's built-in parser lacks the necessary type # information. # Note: The availability of this option depends on whether or not doxygen was # compiled with the --with-libclang option. # The default value is: NO. #CLANG_ASSISTED_PARSING = NO # If clang assisted parsing is enabled you can provide the compiler with command # line options that you would normally use when invoking the compiler. Note that # the include paths will already be set by doxygen for the files and directories # specified with INPUT and INCLUDE_PATH. # This tag requires that the tag CLANG_ASSISTED_PARSING is set to YES. #CLANG_OPTIONS = #--------------------------------------------------------------------------- # Configuration options related to the alphabetical class index #--------------------------------------------------------------------------- # If the ALPHABETICAL_INDEX tag is set to YES, an alphabetical index of all # compounds will be generated. Enable this if the project contains a lot of # classes, structs, unions or interfaces. # The default value is: YES. ALPHABETICAL_INDEX = YES # The COLS_IN_ALPHA_INDEX tag can be used to specify the number of columns in # which the alphabetical index list will be split. # Minimum value: 1, maximum value: 20, default value: 5. # This tag requires that the tag ALPHABETICAL_INDEX is set to YES. COLS_IN_ALPHA_INDEX = 5 # In case all classes in a project start with a common prefix, all classes will # be put under the same header in the alphabetical index. The IGNORE_PREFIX tag # can be used to specify a prefix (or a list of prefixes) that should be ignored # while generating the index headers. # This tag requires that the tag ALPHABETICAL_INDEX is set to YES. IGNORE_PREFIX = #--------------------------------------------------------------------------- # Configuration options related to the HTML output #--------------------------------------------------------------------------- # If the GENERATE_HTML tag is set to YES doxygen will generate HTML output # The default value is: YES. GENERATE_HTML = YES # The HTML_OUTPUT tag is used to specify where the HTML docs will be put. If a # relative path is entered the value of OUTPUT_DIRECTORY will be put in front of # it. # The default directory is: html. # This tag requires that the tag GENERATE_HTML is set to YES. HTML_OUTPUT = html # The HTML_FILE_EXTENSION tag can be used to specify the file extension for each # generated HTML page (for example: .htm, .php, .asp). # The default value is: .html. # This tag requires that the tag GENERATE_HTML is set to YES. HTML_FILE_EXTENSION = .html # The HTML_HEADER tag can be used to specify a user-defined HTML header file for # each generated HTML page. If the tag is left blank doxygen will generate a # standard header. # # To get valid HTML the header file that includes any scripts and style sheets # that doxygen needs, which is dependent on the configuration options used (e.g. # the setting GENERATE_TREEVIEW). It is highly recommended to start with a # default header using # doxygen -w html new_header.html new_footer.html new_stylesheet.css # YourConfigFile # and then modify the file new_header.html. See also section "Doxygen usage" # for information on how to generate the default header that doxygen normally # uses. # Note: The header is subject to change so you typically have to regenerate the # default header when upgrading to a newer version of doxygen. For a description # of the possible markers and block names see the documentation. # This tag requires that the tag GENERATE_HTML is set to YES. HTML_HEADER = # The HTML_FOOTER tag can be used to specify a user-defined HTML footer for each # generated HTML page. If the tag is left blank doxygen will generate a standard # footer. See HTML_HEADER for more information on how to generate a default # footer and what special commands can be used inside the footer. See also # section "Doxygen usage" for information on how to generate the default footer # that doxygen normally uses. # This tag requires that the tag GENERATE_HTML is set to YES. HTML_FOOTER = # The HTML_STYLESHEET tag can be used to specify a user-defined cascading style # sheet that is used by each HTML page. It can be used to fine-tune the look of # the HTML output. If left blank doxygen will generate a default style sheet. # See also section "Doxygen usage" for information on how to generate the style # sheet that doxygen normally uses. # Note: It is recommended to use HTML_EXTRA_STYLESHEET instead of this tag, as # it is more robust and this tag (HTML_STYLESHEET) will in the future become # obsolete. # This tag requires that the tag GENERATE_HTML is set to YES. HTML_STYLESHEET = # The HTML_EXTRA_STYLESHEET tag can be used to specify additional user-defined # cascading style sheets that are included after the standard style sheets # created by doxygen. Using this option one can overrule certain style aspects. # This is preferred over using HTML_STYLESHEET since it does not replace the # standard style sheet and is therefor more robust against future updates. # Doxygen will copy the style sheet files to the output directory. # Note: The order of the extra stylesheet files is of importance (e.g. the last # stylesheet in the list overrules the setting of the previous ones in the # list). For an example see the documentation. # This tag requires that the tag GENERATE_HTML is set to YES. #HTML_EXTRA_STYLESHEET = # The HTML_EXTRA_FILES tag can be used to specify one or more extra images or # other source files which should be copied to the HTML output directory. Note # that these files will be copied to the base HTML output directory. Use the # $relpath^ marker in the HTML_HEADER and/or HTML_FOOTER files to load these # files. In the HTML_STYLESHEET file, use the file name only. Also note that the # files will be copied as-is; there are no commands or markers available. # This tag requires that the tag GENERATE_HTML is set to YES. HTML_EXTRA_FILES = # The HTML_COLORSTYLE_HUE tag controls the color of the HTML output. Doxygen # will adjust the colors in the stylesheet and background images according to # this color. Hue is specified as an angle on a colorwheel, see # http://en.wikipedia.org/wiki/Hue for more information. For instance the value # 0 represents red, 60 is yellow, 120 is green, 180 is cyan, 240 is blue, 300 # purple, and 360 is red again. # Minimum value: 0, maximum value: 359, default value: 220. # This tag requires that the tag GENERATE_HTML is set to YES. HTML_COLORSTYLE_HUE = 220 # The HTML_COLORSTYLE_SAT tag controls the purity (or saturation) of the colors # in the HTML output. For a value of 0 the output will use grayscales only. A # value of 255 will produce the most vivid colors. # Minimum value: 0, maximum value: 255, default value: 100. # This tag requires that the tag GENERATE_HTML is set to YES. HTML_COLORSTYLE_SAT = 100 # The HTML_COLORSTYLE_GAMMA tag controls the gamma correction applied to the # luminance component of the colors in the HTML output. Values below 100 # gradually make the output lighter, whereas values above 100 make the output # darker. The value divided by 100 is the actual gamma applied, so 80 represents # a gamma of 0.8, The value 220 represents a gamma of 2.2, and 100 does not # change the gamma. # Minimum value: 40, maximum value: 240, default value: 80. # This tag requires that the tag GENERATE_HTML is set to YES. HTML_COLORSTYLE_GAMMA = 80 # If the HTML_TIMESTAMP tag is set to YES then the footer of each generated HTML # page will contain the date and time when the page was generated. Setting this # to NO can help when comparing the output of multiple runs. # The default value is: YES. # This tag requires that the tag GENERATE_HTML is set to YES. HTML_TIMESTAMP = YES # If the HTML_DYNAMIC_SECTIONS tag is set to YES then the generated HTML # documentation will contain sections that can be hidden and shown after the # page has loaded. # The default value is: NO. # This tag requires that the tag GENERATE_HTML is set to YES. HTML_DYNAMIC_SECTIONS = NO # With HTML_INDEX_NUM_ENTRIES one can control the preferred number of entries # shown in the various tree structured indices initially; the user can expand # and collapse entries dynamically later on. Doxygen will expand the tree to # such a level that at most the specified number of entries are visible (unless # a fully collapsed tree already exceeds this amount). So setting the number of # entries 1 will produce a full collapsed tree by default. 0 is a special value # representing an infinite number of entries and will result in a full expanded # tree by default. # Minimum value: 0, maximum value: 9999, default value: 100. # This tag requires that the tag GENERATE_HTML is set to YES. #HTML_INDEX_NUM_ENTRIES = 100 # If the GENERATE_DOCSET tag is set to YES, additional index files will be # generated that can be used as input for Apple's Xcode 3 integrated development # environment (see: http://developer.apple.com/tools/xcode/), introduced with # OSX 10.5 (Leopard). To create a documentation set, doxygen will generate a # Makefile in the HTML output directory. Running make will produce the docset in # that directory and running make install will install the docset in # ~/Library/Developer/Shared/Documentation/DocSets so that Xcode will find it at # startup. See http://developer.apple.com/tools/creatingdocsetswithdoxygen.html # for more information. # The default value is: NO. # This tag requires that the tag GENERATE_HTML is set to YES. GENERATE_DOCSET = NO # This tag determines the name of the docset feed. A documentation feed provides # an umbrella under which multiple documentation sets from a single provider # (such as a company or product suite) can be grouped. # The default value is: Doxygen generated docs. # This tag requires that the tag GENERATE_DOCSET is set to YES. DOCSET_FEEDNAME = "Doxygen generated docs" # This tag specifies a string that should uniquely identify the documentation # set bundle. This should be a reverse domain-name style string, e.g. # com.mycompany.MyDocSet. Doxygen will append .docset to the name. # The default value is: org.doxygen.Project. # This tag requires that the tag GENERATE_DOCSET is set to YES. DOCSET_BUNDLE_ID = org.doxygen.Project # The DOCSET_PUBLISHER_ID tag specifies a string that should uniquely identify # the documentation publisher. This should be a reverse domain-name style # string, e.g. com.mycompany.MyDocSet.documentation. # The default value is: org.doxygen.Publisher. # This tag requires that the tag GENERATE_DOCSET is set to YES. DOCSET_PUBLISHER_ID = org.doxygen.Publisher # The DOCSET_PUBLISHER_NAME tag identifies the documentation publisher. # The default value is: Publisher. # This tag requires that the tag GENERATE_DOCSET is set to YES. DOCSET_PUBLISHER_NAME = Publisher # If the GENERATE_HTMLHELP tag is set to YES then doxygen generates three # additional HTML index files: index.hhp, index.hhc, and index.hhk. The # index.hhp is a project file that can be read by Microsoft's HTML Help Workshop # (see: http://www.microsoft.com/en-us/download/details.aspx?id=21138) on # Windows. # # The HTML Help Workshop contains a compiler that can convert all HTML output # generated by doxygen into a single compiled HTML file (.chm). Compiled HTML # files are now used as the Windows 98 help format, and will replace the old # Windows help format (.hlp) on all Windows platforms in the future. Compressed # HTML files also contain an index, a table of contents, and you can search for # words in the documentation. The HTML workshop also contains a viewer for # compressed HTML files. # The default value is: NO. # This tag requires that the tag GENERATE_HTML is set to YES. GENERATE_HTMLHELP = NO # The CHM_FILE tag can be used to specify the file name of the resulting .chm # file. You can add a path in front of the file if the result should not be # written to the html output directory. # This tag requires that the tag GENERATE_HTMLHELP is set to YES. CHM_FILE = # The HHC_LOCATION tag can be used to specify the location (absolute path # including file name) of the HTML help compiler ( hhc.exe). If non-empty # doxygen will try to run the HTML help compiler on the generated index.hhp. # The file has to be specified with full path. # This tag requires that the tag GENERATE_HTMLHELP is set to YES. HHC_LOCATION = # The GENERATE_CHI flag controls if a separate .chi index file is generated ( # YES) or that it should be included in the master .chm file ( NO). # The default value is: NO. # This tag requires that the tag GENERATE_HTMLHELP is set to YES. GENERATE_CHI = NO # The CHM_INDEX_ENCODING is used to encode HtmlHelp index ( hhk), content ( hhc) # and project file content. # This tag requires that the tag GENERATE_HTMLHELP is set to YES. CHM_INDEX_ENCODING = # The BINARY_TOC flag controls whether a binary table of contents is generated ( # YES) or a normal table of contents ( NO) in the .chm file. Furthermore it # enables the Previous and Next buttons. # The default value is: NO. # This tag requires that the tag GENERATE_HTMLHELP is set to YES. BINARY_TOC = NO # The TOC_EXPAND flag can be set to YES to add extra items for group members to # the table of contents of the HTML help documentation and to the tree view. # The default value is: NO. # This tag requires that the tag GENERATE_HTMLHELP is set to YES. TOC_EXPAND = NO # If the GENERATE_QHP tag is set to YES and both QHP_NAMESPACE and # QHP_VIRTUAL_FOLDER are set, an additional index file will be generated that # can be used as input for Qt's qhelpgenerator to generate a Qt Compressed Help # (.qch) of the generated HTML documentation. # The default value is: NO. # This tag requires that the tag GENERATE_HTML is set to YES. GENERATE_QHP = NO # If the QHG_LOCATION tag is specified, the QCH_FILE tag can be used to specify # the file name of the resulting .qch file. The path specified is relative to # the HTML output folder. # This tag requires that the tag GENERATE_QHP is set to YES. QCH_FILE = # The QHP_NAMESPACE tag specifies the namespace to use when generating Qt Help # Project output. For more information please see Qt Help Project / Namespace # (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#namespace). # The default value is: org.doxygen.Project. # This tag requires that the tag GENERATE_QHP is set to YES. QHP_NAMESPACE = org.doxygen.Project # The QHP_VIRTUAL_FOLDER tag specifies the namespace to use when generating Qt # Help Project output. For more information please see Qt Help Project / Virtual # Folders (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#virtual- # folders). # The default value is: doc. # This tag requires that the tag GENERATE_QHP is set to YES. QHP_VIRTUAL_FOLDER = doc # If the QHP_CUST_FILTER_NAME tag is set, it specifies the name of a custom # filter to add. For more information please see Qt Help Project / Custom # Filters (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#custom- # filters). # This tag requires that the tag GENERATE_QHP is set to YES. QHP_CUST_FILTER_NAME = # The QHP_CUST_FILTER_ATTRS tag specifies the list of the attributes of the # custom filter to add. For more information please see Qt Help Project / Custom # Filters (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#custom- # filters). # This tag requires that the tag GENERATE_QHP is set to YES. QHP_CUST_FILTER_ATTRS = # The QHP_SECT_FILTER_ATTRS tag specifies the list of the attributes this # project's filter section matches. Qt Help Project / Filter Attributes (see: # http://qt-project.org/doc/qt-4.8/qthelpproject.html#filter-attributes). # This tag requires that the tag GENERATE_QHP is set to YES. QHP_SECT_FILTER_ATTRS = # The QHG_LOCATION tag can be used to specify the location of Qt's # qhelpgenerator. If non-empty doxygen will try to run qhelpgenerator on the # generated .qhp file. # This tag requires that the tag GENERATE_QHP is set to YES. QHG_LOCATION = # If the GENERATE_ECLIPSEHELP tag is set to YES, additional index files will be # generated, together with the HTML files, they form an Eclipse help plugin. To # install this plugin and make it available under the help contents menu in # Eclipse, the contents of the directory containing the HTML and XML files needs # to be copied into the plugins directory of eclipse. The name of the directory # within the plugins directory should be the same as the ECLIPSE_DOC_ID value. # After copying Eclipse needs to be restarted before the help appears. # The default value is: NO. # This tag requires that the tag GENERATE_HTML is set to YES. GENERATE_ECLIPSEHELP = NO # A unique identifier for the Eclipse help plugin. When installing the plugin # the directory name containing the HTML and XML files should also have this # name. Each documentation set should have its own identifier. # The default value is: org.doxygen.Project. # This tag requires that the tag GENERATE_ECLIPSEHELP is set to YES. ECLIPSE_DOC_ID = org.doxygen.Project # If you want full control over the layout of the generated HTML pages it might # be necessary to disable the index and replace it with your own. The # DISABLE_INDEX tag can be used to turn on/off the condensed index (tabs) at top # of each HTML page. A value of NO enables the index and the value YES disables # it. Since the tabs in the index contain the same information as the navigation # tree, you can set this option to YES if you also set GENERATE_TREEVIEW to YES. # The default value is: NO. # This tag requires that the tag GENERATE_HTML is set to YES. DISABLE_INDEX = NO # The GENERATE_TREEVIEW tag is used to specify whether a tree-like index # structure should be generated to display hierarchical information. If the tag # value is set to YES, a side panel will be generated containing a tree-like # index structure (just like the one that is generated for HTML Help). For this # to work a browser that supports JavaScript, DHTML, CSS and frames is required # (i.e. any modern browser). Windows users are probably better off using the # HTML help feature. Via custom stylesheets (see HTML_EXTRA_STYLESHEET) one can # further fine-tune the look of the index. As an example, the default style # sheet generated by doxygen has an example that shows how to put an image at # the root of the tree instead of the PROJECT_NAME. Since the tree basically has # the same information as the tab index, you could consider setting # DISABLE_INDEX to YES when enabling this option. # The default value is: NO. # This tag requires that the tag GENERATE_HTML is set to YES. GENERATE_TREEVIEW = NO # The ENUM_VALUES_PER_LINE tag can be used to set the number of enum values that # doxygen will group on one line in the generated HTML documentation. # # Note that a value of 0 will completely suppress the enum values from appearing # in the overview section. # Minimum value: 0, maximum value: 20, default value: 4. # This tag requires that the tag GENERATE_HTML is set to YES. ENUM_VALUES_PER_LINE = 4 # If the treeview is enabled (see GENERATE_TREEVIEW) then this tag can be used # to set the initial width (in pixels) of the frame in which the tree is shown. # Minimum value: 0, maximum value: 1500, default value: 250. # This tag requires that the tag GENERATE_HTML is set to YES. TREEVIEW_WIDTH = 250 # When the EXT_LINKS_IN_WINDOW option is set to YES doxygen will open links to # external symbols imported via tag files in a separate window. # The default value is: NO. # This tag requires that the tag GENERATE_HTML is set to YES. EXT_LINKS_IN_WINDOW = NO # Use this tag to change the font size of LaTeX formulas included as images in # the HTML documentation. When you change the font size after a successful # doxygen run you need to manually remove any form_*.png images from the HTML # output directory to force them to be regenerated. # Minimum value: 8, maximum value: 50, default value: 10. # This tag requires that the tag GENERATE_HTML is set to YES. FORMULA_FONTSIZE = 10 # Use the FORMULA_TRANPARENT tag to determine whether or not the images # generated for formulas are transparent PNGs. Transparent PNGs are not # supported properly for IE 6.0, but are supported on all modern browsers. # # Note that when changing this option you need to delete any form_*.png files in # the HTML output directory before the changes have effect. # The default value is: YES. # This tag requires that the tag GENERATE_HTML is set to YES. FORMULA_TRANSPARENT = YES # Enable the USE_MATHJAX option to render LaTeX formulas using MathJax (see # http://www.mathjax.org) which uses client side Javascript for the rendering # instead of using prerendered bitmaps. Use this if you do not have LaTeX # installed or if you want to formulas look prettier in the HTML output. When # enabled you may also need to install MathJax separately and configure the path # to it using the MATHJAX_RELPATH option. # The default value is: NO. # This tag requires that the tag GENERATE_HTML is set to YES. USE_MATHJAX = NO # When MathJax is enabled you can set the default output format to be used for # the MathJax output. See the MathJax site (see: # http://docs.mathjax.org/en/latest/output.html) for more details. # Possible values are: HTML-CSS (which is slower, but has the best # compatibility), NativeMML (i.e. MathML) and SVG. # The default value is: HTML-CSS. # This tag requires that the tag USE_MATHJAX is set to YES. #MATHJAX_FORMAT = HTML-CSS # When MathJax is enabled you need to specify the location relative to the HTML # output directory using the MATHJAX_RELPATH option. The destination directory # should contain the MathJax.js script. For instance, if the mathjax directory # is located at the same level as the HTML output directory, then # MATHJAX_RELPATH should be ../mathjax. The default value points to the MathJax # Content Delivery Network so you can quickly see the result without installing # MathJax. However, it is strongly recommended to install a local copy of # MathJax from http://www.mathjax.org before deployment. # The default value is: http://cdn.mathjax.org/mathjax/latest. # This tag requires that the tag USE_MATHJAX is set to YES. MATHJAX_RELPATH = http://www.mathjax.org/mathjax # The MATHJAX_EXTENSIONS tag can be used to specify one or more MathJax # extension names that should be enabled during MathJax rendering. For example # MATHJAX_EXTENSIONS = TeX/AMSmath TeX/AMSsymbols # This tag requires that the tag USE_MATHJAX is set to YES. MATHJAX_EXTENSIONS = # The MATHJAX_CODEFILE tag can be used to specify a file with javascript pieces # of code that will be used on startup of the MathJax code. See the MathJax site # (see: http://docs.mathjax.org/en/latest/output.html) for more details. For an # example see the documentation. # This tag requires that the tag USE_MATHJAX is set to YES. #MATHJAX_CODEFILE = # When the SEARCHENGINE tag is enabled doxygen will generate a search box for # the HTML output. The underlying search engine uses javascript and DHTML and # should work on any modern browser. Note that when using HTML help # (GENERATE_HTMLHELP), Qt help (GENERATE_QHP), or docsets (GENERATE_DOCSET) # there is already a search function so this one should typically be disabled. # For large projects the javascript based search engine can be slow, then # enabling SERVER_BASED_SEARCH may provide a better solution. It is possible to # search using the keyboard; to jump to the search box use + S # (what the is depends on the OS and browser, but it is typically # , /