




from itertools import product




def 		lowerCAmelCase_   (	lowerCamelCase	,     lowerCamelCase   ):
				__magic_name__	:	Dict								=sides_number
				__magic_name__	:	Optional[Any]								=max_face_number * dice_number
				__magic_name__	:	str								=[0] * (max_total + 1)

				__magic_name__	:	Optional[int]								=1
				__magic_name__	:	List[Any]								=range(_lowerCamelCase	,     max_face_number + 1   )
				for dice_numbers in product(_lowerCamelCase	,     repeat=_lowerCamelCase   ):
								__magic_name__	:	List[Any]								=sum(_lowerCamelCase   )
								totals_frequencies[total] += 1

				return totals_frequencies




def 		lowerCAmelCase_   (	):
				__magic_name__	:	Optional[Any]								=total_frequency_distribution(
				    sides_number=4	,     dice_number=9   )
				__magic_name__	:	Optional[int]								=total_frequency_distribution(
				    sides_number=6	,     dice_number=6   )

				__magic_name__	:	Optional[Any]								=0
				__magic_name__	:	Any								=9
				__magic_name__	:	Union[str, Any]								=4 * 9
				__magic_name__	:	Optional[Any]								=6
				for peter_total in range(_lowerCamelCase	,     max_peter_total + 1   ):
								peter_wins_count += peter_totals_frequencies[peter_total] * sum(
								    colin_totals_frequencies[min_colin_total:peter_total]   )

				__magic_name__	:	Union[str, Any]								=(4**9) * (6**6)
				__magic_name__	:	List[str]								=peter_wins_count / total_games_number

				__magic_name__	:	Dict								=round(_lowerCamelCase	,     ndigits=7   )

				return rounded_peter_win_probability


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





# coding=utf-8
# Copyright 2020 The HuggingFace Inc. team.
#
# 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.

# this script dumps information about the environment

import os
import sys

import transformers


UpperCAmelCase_		:				str									=     "3"

print("Python version:", sys.version)
print("transformers version:", transformers.__version__)

try:
							import torch

							print("Torch version:", torch.__version__)
							print("Cuda available:", torch.cuda.is_available())
							print("Cuda version:", torch.version.cuda)
							print("CuDNN version:", torch.backends.cudnn.version())
							print("Number of GPUs available:", torch.cuda.device_count())
							print("NCCL version:", torch.cuda.nccl.version())
except ImportError:
							print("Torch version:", None)

try:
							import deepspeed

							print("DeepSpeed version:", deepspeed.__version__)
except ImportError:
							print("DeepSpeed version:", None)

try:
							import tensorflow as tf

							print("TensorFlow version:", tf.__version__)
							print("TF GPUs available:", bool(tf.config.list_physical_devices("GPU")))
							print("Number of TF GPUs available:", len(tf.config.list_physical_devices("GPU")))
except ImportError:
							print("TensorFlow version:", None)




