"""simple docstring"""







from decimal import Decimal, getcontext
from math import ceil, factorial


def      __lowerCAmelCase(		__UpperCAmelCase			):






	"""simple docstring"""





	if not isinstance(__UpperCAmelCase     ,__UpperCAmelCase			):
		raise TypeError('Undefined for non-integers'			)
	elif precision < 1:
		raise ValueError('Undefined for non-natural numbers'			)

	_lowercase :    Optional[Any]							=							precision
	_lowercase :    Dict							=							ceil(precision / 14			)
	_lowercase :    int							=							426_880 * Decimal(10_005			).sqrt()
	_lowercase :    Optional[Any]							=							1
	_lowercase :    Union[str, Any]							=							13_591_409
	_lowercase :    Optional[int]							=							Decimal(__UpperCAmelCase			)
	for k in range(1     ,__UpperCAmelCase			):
		_lowercase :    List[str]							=							factorial(6 * k			) // (factorial(3 * k			) * factorial(__UpperCAmelCase			) ** 3)
		linear_term += 545_140_134
		exponential_term *= -262_537_412_640_768_000
		partial_sum += Decimal(multinomial_term * linear_term			) / exponential_term
	return str(constant_term / partial_sum			)[:-1]


if __name__ == "__main__":
						SCREAMING_SNAKE_CASE									=						50
						print(f"""The first {n} digits of pi is: {pi(n)}""")




"""simple docstring"""







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			)]


SCREAMING_SNAKE_CASE									=						Path(__file__).parent.joinpath('words.txt').read_text(encoding='utf-8')
SCREAMING_SNAKE_CASE									=						sorted({word.strip().lower() for word in data.splitlines()})

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

if __name__ == "__main__":
						SCREAMING_SNAKE_CASE									=						{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))



