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




def        __UpperCamelCase					(    lowerCAmelCase__							:    int  ):
 return binomial_coefficient(2 * node_count  ,       lowerCAmelCase__  ) // (node_count + 1)




def        __UpperCamelCase					(    lowerCAmelCase__							:    int  ):
 if n < 0:
  raise ValueError('''factorial() not defined for negative values'''  )
 __a			:  Any		    =  1
 for i in range(1  ,       n + 1  ):
  result *= i
 return result




def        __UpperCamelCase					(    lowerCAmelCase__							:    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 transformers import BertTokenizerFast

from .custom_tokenization import CustomTokenizer



class 		UpperCamelCase__  (	__lowercase   ):
   _SCREAMING_SNAKE_CASE				:							Union[str, Any]     	=				CustomTokenizer
   pass
