

'''simple docstring'''
def 	_lowerCAmelCase (						_UpperCamelCase						:					int							,			_UpperCamelCase						:					int    )				->      int:
					"""simple docstring"""




					_SCREAMING_SNAKE_CASE							   =1  # To kept the Calculated Value
					# Since C(n, k) = C(n, n-k)
					if k > (n - k):
										_SCREAMING_SNAKE_CASE							   =n - k
					# Calculate C(n,k)
					for i in range(_UpperCamelCase    ):
										result *= n - i
										result //= i + 1
					return result


def 	_lowerCAmelCase (						_UpperCamelCase						:					int    )				->      int:
					"""simple docstring"""




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


def 	_lowerCAmelCase (						_UpperCamelCase						:					int    )				->      int:
					"""simple docstring"""




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


def 	_lowerCAmelCase (						_UpperCamelCase						:					int    )				->      int:
					"""simple docstring"""




					return catalan_number(_UpperCamelCase    ) * factorial(_UpperCamelCase    )


if __name__ == "__main__":
					lowerCamelCase			:				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 ...utils import logging
from ..ta.modeling_tf_ta import TFTaEncoderModel, TFTaForConditionalGeneration, TFTaModel
from .configuration_mta import MTaConfig


lowerCamelCase			:				Optional[Any] 			=					logging.get_logger(__name__)

lowerCamelCase			:				Optional[Any] 			=					"T5Config"







class 							A__   (	A__  ):
  A__					=    'mt5'
  A__					=    MTaConfig







class 							A__   (	A__  ):
  A__					=    'mt5'
  A__					=    MTaConfig







class 							A__   (	A__  ):
  A__					=    'mt5'
  A__					=    MTaConfig
