





from itertools import product





def   _lowercase       (    _UpperCAmelCase = 15					)    ->	int:
				lowerCamelCase									=0.0
				lowerCamelCase									=42
				lowerCamelCase									=42
				lowerCamelCase									=42
				lowerCamelCase									=42
				lowerCamelCase									=42
				lowerCamelCase									=42

				for series in product(range(2					)      ,   repeat=_UpperCAmelCase					):
								lowerCamelCase									=series.count(1					)
								lowerCamelCase									=num_turns - num_blue
								if num_red >= num_blue:
												continue
								lowerCamelCase									=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() = }")












from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


UpperCAmelCase__    :      Optional[Any]       					={
    '''configuration_donut_swin''': ['''DONUT_SWIN_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''DonutSwinConfig'''],
    '''processing_donut''': ['''DonutProcessor'''],
}

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCAmelCase__    :      Any       					=[
							    '''DONUT_SWIN_PRETRAINED_MODEL_ARCHIVE_LIST''',
							    '''DonutSwinModel''',
							    '''DonutSwinPreTrainedModel''',
							]

try:
							if not is_vision_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCAmelCase__    :      Tuple       					=['''DonutFeatureExtractor''']
							UpperCAmelCase__    :      List[str]       					=['''DonutImageProcessor''']


if TYPE_CHECKING:
							from .configuration_donut_swin import DONUT_SWIN_PRETRAINED_CONFIG_ARCHIVE_MAP, DonutSwinConfig
							from .processing_donut import DonutProcessor

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_donut_swin import (
														    DONUT_SWIN_PRETRAINED_MODEL_ARCHIVE_LIST,
														    DonutSwinModel,
														    DonutSwinPreTrainedModel,
														)

							try:
														if not is_vision_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .feature_extraction_donut import DonutFeatureExtractor
														from .image_processing_donut import DonutImageProcessor

else:
							import sys

							UpperCAmelCase__    :      int       					=_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)





