"""simple docstring"""







from itertools import product


def 					a__ (						UpperCAmelCase__    :     int = 1_5     )->		int:
						UpperCAmelCase__   		=						0.0
						UpperCAmelCase__   		=						4_2
						UpperCAmelCase__   		=						4_2
						UpperCAmelCase__   		=						4_2
						UpperCAmelCase__   		=						4_2
						UpperCAmelCase__   		=						4_2
						UpperCAmelCase__   		=						4_2

						for series in product(range(2     )						,     repeat=UpperCAmelCase__     ):
												UpperCAmelCase__   		=						series.count(1     )
												UpperCAmelCase__   		=						num_turns - num_blue
												if num_red >= num_blue:
																		continue
												UpperCAmelCase__   		=						1.0
												for ind, col in enumerate(UpperCAmelCase__						,     2     ):
																		if col == 0:
																								prob *= (ind - 1) / ind
																		else:
																								prob *= 1 / ind

												total_prob += prob

						return int(1 / total_prob     )


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


"""simple docstring"""







import random
import unittest

import numpy as np
import torch

from diffusers import DDIMScheduler, LDMSuperResolutionPipeline, UNetaDModel, VQModel
from diffusers.utils import PIL_INTERPOLATION, floats_tensor, load_image, slow, torch_device
from diffusers.utils.testing_utils import enable_full_determinism, require_torch


enable_full_determinism()


class      _lowercase						(				unittest.TestCase					):

				@property
				def     A	(       self    :      Any       ):


										'''simple docstring'''
										UpperCAmelCase__   		=						1
										UpperCAmelCase__   		=						3
										UpperCAmelCase__   		=						(3_2, 3_2)

										UpperCAmelCase__   		=						floats_tensor((batch_size, num_channels) + sizes    ,      rng=random.Random(0       )       ).to(_lowercase       )
										return image

				@property
				def     A	(       self    :      List[str]       ):


										'''simple docstring'''
										torch.manual_seed(0       )
										UpperCAmelCase__   		=						UNetaDModel(
										    block_out_channels=(3_2, 6_4)    ,      layers_per_block=2    ,      sample_size=3_2    ,      in_channels=6    ,      out_channels=3    ,      down_block_types=("""DownBlock2D""", """AttnDownBlock2D""")    ,      up_block_types=("""AttnUpBlock2D""", """UpBlock2D""")    ,      )
										return model

				@property
				def     A	(       self    :      Tuple       ):


										'''simple docstring'''
										torch.manual_seed(0       )
										UpperCAmelCase__   		=						VQModel(
										    block_out_channels=[3_2, 6_4]    ,      in_channels=3    ,      out_channels=3    ,      down_block_types=["""DownEncoderBlock2D""", """DownEncoderBlock2D"""]    ,      up_block_types=["""UpDecoderBlock2D""", """UpDecoderBlock2D"""]    ,      latent_channels=3    ,      )
										return model

				def     A	(       self    :      Any       ):


										'''simple docstring'''
										UpperCAmelCase__   		=						"""cpu"""
										UpperCAmelCase__   		=						self.dummy_uncond_unet
										UpperCAmelCase__   		=						DDIMScheduler()
										UpperCAmelCase__   		=						self.dummy_vq_model

										UpperCAmelCase__   		=						LDMSuperResolutionPipeline(unet=_lowercase    ,      vqvae=_lowercase    ,      scheduler=_lowercase       )
										ldm.to(_lowercase       )
										ldm.set_progress_bar_config(disable=_lowercase       )

										UpperCAmelCase__   		=						self.dummy_image.to(_lowercase       )

										UpperCAmelCase__   		=						torch.Generator(device=_lowercase       ).manual_seed(0       )
										UpperCAmelCase__   		=						ldm(image=_lowercase    ,      generator=_lowercase    ,      num_inference_steps=2    ,      output_type="""numpy"""       ).images

										UpperCAmelCase__   		=						image[0, -3:, -3:, -1]

										assert image.shape == (1, 6_4, 6_4, 3)
										UpperCAmelCase__   		=						np.array([0.8678, 0.8245, 0.6381, 0.6830, 0.4385, 0.5599, 0.4641, 0.6201, 0.5150]       )

										assert np.abs(image_slice.flatten() - expected_slice       ).max() < 1e-2

				@unittest.skipIf(torch_device != """cuda"""    ,      """This test requires a GPU"""       )
				def     A	(       self    :      Dict       ):


										'''simple docstring'''
										UpperCAmelCase__   		=						self.dummy_uncond_unet
										UpperCAmelCase__   		=						DDIMScheduler()
										UpperCAmelCase__   		=						self.dummy_vq_model

										# put models in fp16
										UpperCAmelCase__   		=						unet.half()
										UpperCAmelCase__   		=						vqvae.half()

										UpperCAmelCase__   		=						LDMSuperResolutionPipeline(unet=_lowercase    ,      vqvae=_lowercase    ,      scheduler=_lowercase       )
										ldm.to(_lowercase       )
										ldm.set_progress_bar_config(disable=_lowercase       )

										UpperCAmelCase__   		=						self.dummy_image.to(_lowercase       )

										UpperCAmelCase__   		=						ldm(_lowercase    ,      num_inference_steps=2    ,      output_type="""numpy"""       ).images

										assert image.shape == (1, 6_4, 6_4, 3)


@slow
@require_torch
class      _lowercase						(				unittest.TestCase					):

				def     A	(       self    :      List[Any]       ):


										'''simple docstring'''
										UpperCAmelCase__   		=						load_image(
										    """https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main"""
										    """/vq_diffusion/teddy_bear_pool.png"""       )
										UpperCAmelCase__   		=						init_image.resize((6_4, 6_4)    ,      resample=PIL_INTERPOLATION["""lanczos"""]       )

										UpperCAmelCase__   		=						LDMSuperResolutionPipeline.from_pretrained("""duongna/ldm-super-resolution"""    ,      device_map="""auto"""       )
										ldm.set_progress_bar_config(disable=_lowercase       )

										UpperCAmelCase__   		=						torch.manual_seed(0       )
										UpperCAmelCase__   		=						ldm(image=_lowercase    ,      generator=_lowercase    ,      num_inference_steps=2_0    ,      output_type="""numpy"""       ).images

										UpperCAmelCase__   		=						image[0, -3:, -3:, -1]

										assert image.shape == (1, 2_5_6, 2_5_6, 3)
										UpperCAmelCase__   		=						np.array([0.7644, 0.7679, 0.7642, 0.7633, 0.7666, 0.7560, 0.7425, 0.7257, 0.6907]       )

										assert np.abs(image_slice.flatten() - expected_slice       ).max() < 1e-2

