






'''simple docstring'''
from itertools import product

def 							a	(   _UpperCAmelCase = 1_5 ):






					"""simple docstring"""







					a_									=   0.0
					a_									=   4_2
					a_									=   4_2
					a_									=   4_2
					a_									=   4_2
					a_									=   4_2
					a_									=   4_2

					for series in product(range(2 )					,  repeat=_UpperCAmelCase ):
										a_									=   series.count(1 )
										a_									=   num_turns - num_blue
										if num_red >= num_blue:
															continue
										a_									=   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 os
import shutil
import unittest
from unittest.mock import patch

from transformers.testing_utils import CaptureStd, is_pt_tf_cross_test, require_torch


class    _snake_case   (				unittest.TestCase					):

					"""simple docstring"""





					@patch('sys.argv'   , ['fakeprogrampath', 'env']     )
					def  __SCREAMING_SNAKE_CASE (     self     )      ->	Tuple:
										# test transformers-cli env
										import transformers.commands.transformers_cli

										with CaptureStd() as cs:
															transformers.commands.transformers_cli.main()
										self.assertIn('Python version'   , cs.out     )
										self.assertIn('Platform'   , cs.out     )
										self.assertIn('Using distributed or parallel set-up in script?'   , cs.out     )




					@is_pt_tf_cross_test
					@patch(
					    'sys.argv'   , ['fakeprogrampath', 'pt-to-tf', '--model-name', 'hf-internal-testing/tiny-random-gptj', '--no-pr']     )
					def  __SCREAMING_SNAKE_CASE (     self     )      ->	List[str]:
										import transformers.commands.transformers_cli

										shutil.rmtree('/tmp/hf-internal-testing/tiny-random-gptj'   , ignore_errors=UpperCAmelCase__     )  # cleans potential past runs
										transformers.commands.transformers_cli.main()

										# The original repo has no TF weights -- if they exist, they were created by the CLI
										self.assertTrue(os.path.exists('/tmp/hf-internal-testing/tiny-random-gptj/tf_model.h5'     )     )




					@require_torch
					@patch('sys.argv'   , ['fakeprogrampath', 'download', 'hf-internal-testing/tiny-random-gptj', '--cache-dir', '/tmp']     )
					def  __SCREAMING_SNAKE_CASE (     self     )      ->	List[Any]:
										import transformers.commands.transformers_cli

										# # remove any previously downloaded model to start clean
										shutil.rmtree('/tmp/models--hf-internal-testing--tiny-random-gptj'   , ignore_errors=UpperCAmelCase__     )

										# run the command
										transformers.commands.transformers_cli.main()

										# check if the model files are downloaded correctly on /tmp/models--hf-internal-testing--tiny-random-gptj
										self.assertTrue(os.path.exists('/tmp/models--hf-internal-testing--tiny-random-gptj/blobs'     )     )
										self.assertTrue(os.path.exists('/tmp/models--hf-internal-testing--tiny-random-gptj/refs'     )     )
										self.assertTrue(os.path.exists('/tmp/models--hf-internal-testing--tiny-random-gptj/snapshots'     )     )




					@require_torch
					@patch(
					    'sys.argv'   , [
					        'fakeprogrampath',
					        'download',
					        'hf-internal-testing/test_dynamic_model_with_tokenizer',
					        '--trust-remote-code',
					        '--cache-dir',
					        '/tmp',
					    ]   , )
					def  __SCREAMING_SNAKE_CASE (     self     )      ->	int:
										import transformers.commands.transformers_cli

										# # remove any previously downloaded model to start clean
										shutil.rmtree('/tmp/models--hf-internal-testing--test_dynamic_model_with_tokenizer'   , ignore_errors=UpperCAmelCase__     )

										# run the command
										transformers.commands.transformers_cli.main()

										# check if the model files are downloaded correctly on /tmp/models--hf-internal-testing--test_dynamic_model_with_tokenizer
										self.assertTrue(os.path.exists('/tmp/models--hf-internal-testing--test_dynamic_model_with_tokenizer/blobs'     )     )
										self.assertTrue(os.path.exists('/tmp/models--hf-internal-testing--test_dynamic_model_with_tokenizer/refs'     )     )
										self.assertTrue(
										    os.path.exists('/tmp/models--hf-internal-testing--test_dynamic_model_with_tokenizer/snapshots'     )     )

