from itertools import product







def  __UpperCamelCase    (						A ,							A							):
     UpperCamelCase__										=      sides_number
     UpperCamelCase__										=      max_face_number * dice_number
     UpperCamelCase__										=      [0] * (max_total + 1)

     UpperCamelCase__										=      1
     UpperCamelCase__										=      range(A ,							max_face_number + 1							)
     for dice_numbers in product(A ,							repeat=A							):
          UpperCamelCase__										=      sum(A							)
          totals_frequencies[total] += 1

     return totals_frequencies







def  __UpperCamelCase    (						):
     UpperCamelCase__										=      total_frequency_distribution(
         sides_number=4 ,							dice_number=9							)
     UpperCamelCase__										=      total_frequency_distribution(
         sides_number=6 ,							dice_number=6							)

     UpperCamelCase__										=      0
     UpperCamelCase__										=      9
     UpperCamelCase__										=      4 * 9
     UpperCamelCase__										=      6
     for peter_total in range(A ,							max_peter_total + 1							):
          peter_wins_count += peter_totals_frequencies[peter_total] * sum(
              colin_totals_frequencies[min_colin_total:peter_total]							)

     UpperCamelCase__										=      (4**9) * (6**6)
     UpperCamelCase__										=      peter_wins_count / total_games_number

     UpperCamelCase__										=      round(A ,							ndigits=7							)

     return rounded_peter_win_probability


if __name__ == "__main__":
     print(f"""{solution() = }""")




# Lint as: python3
# pylint: enable=line-too-long
# pylint: disable=g-import-not-at-top,g-bad-import-order,wrong-import-position

__magic_name__								='''2.13.1'''

import platform

import pyarrow
from packaging import version


if version.parse(platform.python_version()) < version.parse('''3.7'''):
     raise ImportWarning(
         '''To use `datasets`, Python>=3.7 is required, and the current version of Python doesn\'t match this condition.'''
     )

if version.parse(pyarrow.__version__).major < 8:
     raise ImportWarning(
         '''To use `datasets`, the module `pyarrow>=8.0.0` is required, and the current version of `pyarrow` doesn\'t match this condition.\n'''
         '''If you are running this in a Google Colab, you should probably just restart the runtime to use the right version of `pyarrow`.'''
     )

del platform
del pyarrow
del version

from .arrow_dataset import Dataset
from .arrow_reader import ReadInstruction
from .builder import ArrowBasedBuilder, BeamBasedBuilder, BuilderConfig, DatasetBuilder, GeneratorBasedBuilder
from .combine import concatenate_datasets, interleave_datasets
from .dataset_dict import DatasetDict, IterableDatasetDict
from .download import *
from .features import *
from .fingerprint import disable_caching, enable_caching, is_caching_enabled, set_caching_enabled
from .info import DatasetInfo, MetricInfo
from .inspect import (
    get_dataset_config_info,
    get_dataset_config_names,
    get_dataset_infos,
    get_dataset_split_names,
    inspect_dataset,
    inspect_metric,
    list_datasets,
    list_metrics,
)
from .iterable_dataset import IterableDataset
from .load import load_dataset, load_dataset_builder, load_from_disk, load_metric
from .metric import Metric
from .splits import (
    NamedSplit,
    NamedSplitAll,
    Split,
    SplitBase,
    SplitDict,
    SplitGenerator,
    SplitInfo,
    SubSplitInfo,
    percent,
)
from .tasks import *
from .utils import *
from .utils import logging


# deprecated modules
from datasets import arrow_dataset as _arrow_dataset  # isort:skip
from datasets import utils as _utils  # isort:skip
from datasets.utils import download_manager as _deprecated_download_manager  # isort:skip

__magic_name__								=concatenate_datasets
__magic_name__								=DownloadConfig
__magic_name__								=DownloadManager
__magic_name__								=DownloadMode
__magic_name__								=DownloadConfig
__magic_name__								=DownloadMode
__magic_name__								=DownloadManager

del _arrow_dataset, _utils, _deprecated_download_manager



