


'''simple docstring'''
def       a_				(	UpperCamelCase_						,  UpperCamelCase_ ):
							A_			    =		1  # To kept the Calculated Value
							# Since C(n, k) = C(n, n-k)
							if k > (n - k):
														A_			    =		n - k
							# Calculate C(n,k)
							for i in range(UpperCamelCase_ ):
														result *= n - i
														result //= i + 1
							return result







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







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







def       a_				(	UpperCamelCase_ ):
							return catalan_number(UpperCamelCase_ ) * factorial(UpperCamelCase_ )


if __name__ == "__main__":
							__SCREAMING_SNAKE_CASE					:				Optional[int]									=		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'''
import string
from math import logaa







def       a_				(	UpperCamelCase_						,  UpperCamelCase_ ):
							A_			    =		document.translate(
							    str.maketrans(""						,  ""						,  string.punctuation ) ).replace("\n"						,  "" )
							A_			    =		document_without_punctuation.split(" " )  # word tokenization
							return len([word for word in tokenize_document if word.lower() == term.lower()] )







def       a_				(	UpperCamelCase_						,  UpperCamelCase_ ):
							A_			    =		corpus.lower().translate(
							    str.maketrans(""						,  ""						,  string.punctuation ) )  # strip all punctuation and replace it with ''
							A_			    =		corpus_without_punctuation.split("\n" )
							A_			    =		term.lower()
							return (len([doc for doc in docs if term in doc] ), len(UpperCamelCase_ ))







def       a_				(	UpperCamelCase_						,  UpperCamelCase_						,  UpperCamelCase_=False ):
							if smoothing:
														if n == 0:
																					raise ValueError("log10(0) is undefined." )
														return round(1 + logaa(n / (1 + df) )						,  3 )

							if df == 0:
														raise ZeroDivisionError("df must be > 0" )
							elif n == 0:
														raise ValueError("log10(0) is undefined." )
							return round(logaa(n / df )						,  3 )







def       a_				(	UpperCamelCase_						,  UpperCamelCase_ ):
							return round(tf * idf						,  3 )





