

from itertools import product





def a(lowercase__      ,			lowercase__						):





	'''simple docstring'''
	snake_case_   		=			sides_number
	snake_case_   		=			max_face_number * dice_number
	snake_case_   		=			[0] * (max_total + 1)

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

	return totals_frequencies





def a():





	'''simple docstring'''
	snake_case_   		=			total_frequency_distribution(
	    sides_number=4      ,			dice_number=9						)
	snake_case_   		=			total_frequency_distribution(
	    sides_number=6      ,			dice_number=6						)

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

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

	snake_case_   		=			round(lowercase__      ,			ndigits=7						)

	return rounded_peter_win_probability


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



import json
import logging
import os
import sys
from pathlib import Path

import finetune_rag

from transformers.file_utils import is_apex_available
from transformers.testing_utils import (
    TestCasePlus,
    execute_subprocess_async,
    require_ray,
    require_torch_gpu,
    require_torch_multi_gpu,
)


logging.basicConfig(level=logging.DEBUG)
A									=  logging.getLogger()

A									=  logging.StreamHandler(sys.stdout)
logger.addHandler(stream_handler)


class SCREAMING_SNAKE_CASE	(		__snake_case				):






			"""simple docstring"""




			def       __lowerCAmelCase			(     self			,					__UpperCamelCase				):

				"""simple docstring"""


				os.makedirs(__UpperCamelCase			,					exist_ok=__UpperCamelCase				)
				snake_case_   		=			{'source': 'What is love ?', 'target': 'life'}
				snake_case_   		=			{'train': 12, 'val': 2, 'test': 2}
				for split in ["train", "test", "val"]:
					for field in ["source", "target"]:
						snake_case_   		=			'\n'.join([contents[field]] * n_lines[split]				)
						with open(os.path.join(__UpperCamelCase			,					f"""{split}.{field}"""				)			,					'w'				) as f:
							f.write(__UpperCamelCase				)


			def       __lowerCAmelCase			(     self			,					__UpperCamelCase			,					__UpperCamelCase = "pytorch"				):

				"""simple docstring"""


				snake_case_   		=			self.get_auto_remove_tmp_dir()
				snake_case_   		=			os.path.join(__UpperCamelCase			,					'output'				)
				snake_case_   		=			os.path.join(__UpperCamelCase			,					'data'				)
				self._create_dummy_data(data_dir=__UpperCamelCase				)

				snake_case_   		=			f"""
                --data_dir {data_dir} \
                --output_dir {output_dir} \
                --model_name_or_path facebook/rag-sequence-base \
                --model_type rag_sequence \
                --do_train \
                --do_predict \
                --n_val -1 \
                --val_check_interval 1.0 \
                --train_batch_size 2 \
                --eval_batch_size 1 \
                --max_source_length 25 \
                --max_target_length 25 \
                --val_max_target_length 25 \
                --test_max_target_length 25 \
                --label_smoothing 0.1 \
                --dropout 0.1 \
                --attention_dropout 0.1 \
                --weight_decay 0.001 \
                --adam_epsilon 1e-08 \
                --max_grad_norm 0.1 \
                --lr_scheduler polynomial \
                --learning_rate 3e-04 \
                --num_train_epochs 1 \
                --warmup_steps 4 \
                --gradient_accumulation_steps 1 \
                --distributed-port 8787 \
                --use_dummy_dataset 1 \
                --distributed_retriever {distributed_retriever} \
            """.split()

				if gpus > 0:
					testargs.append(f"""--gpus={gpus}"""				)
					if is_apex_available():
						testargs.append('--fp16'				)
				else:
					testargs.append('--gpus=0'				)
					testargs.append('--distributed_backend=ddp_cpu'				)
					testargs.append('--num_processes=2'				)

				snake_case_   		=			[sys.executable, str(Path(finetune_rag.__file__				).resolve()				)] + testargs
				execute_subprocess_async(__UpperCamelCase			,					env=self.get_env()				)

				snake_case_   		=			os.path.join(__UpperCamelCase			,					'metrics.json'				)
				with open(__UpperCamelCase				) as f:
					snake_case_   		=			json.load(__UpperCamelCase				)
				return result


			@require_torch_gpu
			def       __lowerCAmelCase			(     self				):

				"""simple docstring"""


				snake_case_   		=			self._run_finetune(gpus=1				)
				self.assertGreaterEqual(result['test'][0]['test_avg_em']			,					0.2				)


			@require_torch_multi_gpu
			def       __lowerCAmelCase			(     self				):

				"""simple docstring"""


				snake_case_   		=			self._run_finetune(gpus=2				)
				self.assertGreaterEqual(result['test'][0]['test_avg_em']			,					0.2				)


			@require_torch_gpu
			@require_ray
			def       __lowerCAmelCase			(     self				):

				"""simple docstring"""


				snake_case_   		=			self._run_finetune(gpus=1			,					distributed_retriever='ray'				)
				self.assertGreaterEqual(result['test'][0]['test_avg_em']			,					0.2				)







			@require_torch_multi_gpu
			@require_ray
			def       __lowerCAmelCase			(     self				):

				"""simple docstring"""


				snake_case_   		=			self._run_finetune(gpus=1			,					distributed_retriever='ray'				)
				self.assertGreaterEqual(result['test'][0]['test_avg_em']			,					0.2				)
