
"""simple docstring"""






def __A						(   a_ :							int		,		a_ :							int     )->							int:




		'''simple docstring'''






		SCREAMING_SNAKE_CASE       :     Dict				= 1  # To kept the Calculated Value
		# Since C(n, k) = C(n, n-k)
		if k > (n - k):
				SCREAMING_SNAKE_CASE       :     Optional[Any]				= n - k
		# Calculate C(n,k)
		for i in range(a_     ):
				result *= n - i
				result //= i + 1
		return result





def __A						(   a_ :							int     )->							int:




		'''simple docstring'''






		return binomial_coefficient(2 * node_count		,		a_     ) // (node_count + 1)





def __A						(   a_ :							int     )->							int:




		'''simple docstring'''






		if n < 0:
				raise ValueError('''factorial() not defined for negative values'''     )
		SCREAMING_SNAKE_CASE       :     Optional[int]				= 1
		for i in range(1		,		n + 1     ):
				result *= i
		return result





def __A						(   a_ :							int     )->							int:




		'''simple docstring'''






		return catalan_number(a_     ) * factorial(a_     )


if __name__ == "__main__":
					lowerCamelCase__ :       List[str]						     =			int(input("Enter the number of nodes: ").strip() or 0)
					if node_count <= 0:
										raise ValueError("We need some nodes to work with.")
					print(
					    f'''Given {node_count} nodes, there are {binary_tree_count(node_count)} '''
					    f'''binary trees and {catalan_number(node_count)} binary search trees.'''
					)







"""simple docstring"""






from typing import TYPE_CHECKING

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


lowerCamelCase__ :       Tuple						     =			{
    "configuration_mctct": ["MCTCT_PRETRAINED_CONFIG_ARCHIVE_MAP", "MCTCTConfig"],
    "feature_extraction_mctct": ["MCTCTFeatureExtractor"],
    "processing_mctct": ["MCTCTProcessor"],
}


try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					lowerCamelCase__ :       Union[str, Any]						     =			[
					    "MCTCT_PRETRAINED_MODEL_ARCHIVE_LIST",
					    "MCTCTForCTC",
					    "MCTCTModel",
					    "MCTCTPreTrainedModel",
					]


if TYPE_CHECKING:
					from .configuration_mctct import MCTCT_PRETRAINED_CONFIG_ARCHIVE_MAP, MCTCTConfig
					from .feature_extraction_mctct import MCTCTFeatureExtractor
					from .processing_mctct import MCTCTProcessor

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_mctct import MCTCT_PRETRAINED_MODEL_ARCHIVE_LIST, MCTCTForCTC, MCTCTModel, MCTCTPreTrainedModel

else:
					import sys

					lowerCamelCase__ :       Tuple						     =			_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)





