



def 					__lowerCAmelCase		(  __lowerCamelCase	:    List[Any]				,   __lowerCamelCase	:    List[str]	)  ->						int:
					__lowerCAmelCase	   =1  # To kept the Calculated Value
					# Since C(n, k) = C(n, n-k)
					if k > (n - k):
										__lowerCAmelCase	   =n - k
					# Calculate C(n,k)
					for i in range(__lowerCamelCase	):
										result *= n - i
										result //= i + 1
					return result






def 					__lowerCAmelCase		(  __lowerCamelCase	:    Union[str, Any]	)  ->						int:
					return binomial_coefficient(2 * node_count				,   __lowerCamelCase	) // (node_count + 1)






def 					__lowerCAmelCase		(  __lowerCamelCase	:    str	)  ->						int:



					if n < 0:
										raise ValueError("""factorial() not defined for negative values"""	)
					__lowerCAmelCase	   =1
					for i in range(1				,   n + 1	):
										result *= i
					return result






def 					__lowerCAmelCase		(  __lowerCamelCase	:    Union[str, Any]	)  ->						int:
					return catalan_number(__lowerCamelCase	) * factorial(__lowerCamelCase	)


if __name__ == "__main__":
				lowercase_	       =			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."
				)









from typing import TYPE_CHECKING

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


lowercase_	       =			{
    '''configuration_encodec''': [
        '''ENCODEC_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''EncodecConfig''',
    ],
    '''feature_extraction_encodec''': ['''EncodecFeatureExtractor'''],
}

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				lowercase_	       =			[
				    '''ENCODEC_PRETRAINED_MODEL_ARCHIVE_LIST''',
				    '''EncodecModel''',
				    '''EncodecPreTrainedModel''',
				]

if TYPE_CHECKING:
				from .configuration_encodec import (
				    ENCODEC_PRETRAINED_CONFIG_ARCHIVE_MAP,
				    EncodecConfig,
				)
				from .feature_extraction_encodec import EncodecFeatureExtractor

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_encodec import (
								    ENCODEC_PRETRAINED_MODEL_ARCHIVE_LIST,
								    EncodecModel,
								    EncodecPreTrainedModel,
								)

else:
				import sys

				lowercase_	       =			_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)




