

def 					__lowerCamelCase	( UpperCamelCase__   ,							UpperCamelCase__      ):







							'''simple docstring'''






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





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






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





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






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





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






							return catalan_number(UpperCamelCase__      ) * factorial(UpperCamelCase__      )


if __name__ == "__main__":
					_UpperCAmelCase		:   List[Any]										=       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 __future__ import annotations

import collections
import pprint
from pathlib import Path





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






							return "".join(sorted(UpperCamelCase__      )      )





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






							return word_by_signature[signature(UpperCamelCase__      )]


_UpperCAmelCase		:   str										=       Path(__file__).parent.joinpath("""words.txt""").read_text(encoding="""utf-8""")
_UpperCAmelCase		:   Dict										=       sorted({word.strip().lower() for word in data.splitlines()})

_UpperCAmelCase		:   List[str]										=       collections.defaultdict(list)
for word in word_list:
					word_by_signature[signature(word)].append(word)

if __name__ == "__main__":
					_UpperCAmelCase		:   Dict										=       {word: anagram(word) for word in word_list if len(anagram(word)) > 1}

					with open("""anagrams.txt""", """w""") as file:
										file.write("""all_anagrams = \n """)
										file.write(pprint.pformat(all_anagrams))




