



from itertools import product





def 							A			(  _UpperCAmelCase       :     int							,     _UpperCAmelCase       :     int					)       ->				list[int]:







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

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

			return totals_frequencies





def 							A			(  )       ->				float:







			'''simple docstring'''
			_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(_UpperCAmelCase							,     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(_UpperCAmelCase							,     ndigits=7					)

			return rounded_peter_win_probability


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





import random
import unittest

import torch

from diffusers import IFInpaintingPipeline
from diffusers.utils import floats_tensor
from diffusers.utils.import_utils import is_xformers_available
from diffusers.utils.testing_utils import skip_mps, torch_device

from ..pipeline_params import (
    TEXT_GUIDED_IMAGE_INPAINTING_BATCH_PARAMS,
    TEXT_GUIDED_IMAGE_INPAINTING_PARAMS,
)
from ..test_pipelines_common import PipelineTesterMixin
from . import IFPipelineTesterMixin







@skip_mps
class     __lowerCAmelCase					(    A       ,		A       ,		unittest.TestCase		):
			UpperCamelCase           =  IFInpaintingPipeline
			UpperCamelCase           =  TEXT_GUIDED_IMAGE_INPAINTING_PARAMS - {'''width''', '''height'''}
			UpperCamelCase           =  TEXT_GUIDED_IMAGE_INPAINTING_BATCH_PARAMS
			UpperCamelCase           =  PipelineTesterMixin.required_optional_params - {'''latents'''}



			def 					_lowerCamelCase (		self     :						List[str])     ->					Tuple:



						"""simple docstring"""






						return self._get_dummy_components()



			def 					_lowerCamelCase (		self     :						Any				,	A     :						int				,	A     :						Dict=0)     ->					Tuple:



						"""simple docstring"""






						if str(A).startswith('mps'):
									_UpperCAmelCase	 =     torch.manual_seed(A)
						else:
									_UpperCAmelCase	 =     torch.Generator(device=A).manual_seed(A)

						_UpperCAmelCase	 =     floats_tensor((1, 3, 32, 32)				,	rng=random.Random(A)).to(A)
						_UpperCAmelCase	 =     floats_tensor((1, 3, 32, 32)				,	rng=random.Random(A)).to(A)

						_UpperCAmelCase	 =     {
						    'prompt': 'A painting of a squirrel eating a burger',
						    'image': image,
						    'mask_image': mask_image,
						    'generator': generator,
						    'num_inference_steps': 2,
						    'output_type': 'numpy',
						}

						return inputs



			@unittest.skipIf(
			    torch_device != 'cuda' or not is_xformers_available()				,	reason='XFormers attention is only available with CUDA and `xformers` installed'				,	)
			def 					_lowerCamelCase (		self     :						List[str])     ->					Union[str, Any]:



						"""simple docstring"""






						self._test_xformers_attention_forwardGenerator_pass(expected_max_diff=1E-3)



			def 					_lowerCamelCase (		self     :						Optional[Any])     ->					Optional[int]:



						"""simple docstring"""






						self._test_save_load_optional_components()



			@unittest.skipIf(torch_device != 'cuda'				,	reason='float16 requires CUDA')
			def 					_lowerCamelCase (		self     :						List[str])     ->					Any:



						"""simple docstring"""






						super().test_save_load_floataa(expected_max_diff=1E-1)



			def 					_lowerCamelCase (		self     :						Optional[int])     ->					Tuple:



						"""simple docstring"""






						self._test_attention_slicing_forward_pass(expected_max_diff=1E-2)



			def 					_lowerCamelCase (		self     :						str)     ->					List[str]:



						"""simple docstring"""






						self._test_save_load_local()



			def 					_lowerCamelCase (		self     :						int)     ->					Tuple:



						"""simple docstring"""






						self._test_inference_batch_single_identical(
						    expected_max_diff=1E-2				,	)
