"""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))




"""simple docstring"""







import math


def      __lowerCAmelCase(		__UpperCAmelCase			):






	"""simple docstring"""





	if not isinstance(__UpperCAmelCase     ,__UpperCAmelCase			):
		_lowercase :    List[Any]							=							F'''Input value of [number={number}] must be an integer'''
		raise TypeError(__UpperCAmelCase			)

	if number < 1:
		_lowercase :    List[Any]							=							F'''Input value of [number={number}] must be > 0'''
		raise ValueError(__UpperCAmelCase			)
	elif number == 1:
		return 3
	elif number == 2:
		return 5
	else:
		_lowercase :    str							=							int(math.log(number // 3     ,2			)			) + 2

		_lowercase :    Union[str, Any]							=							[3, 5]
		_lowercase :    Optional[int]							=							2
		_lowercase :    List[Any]							=							3
		for block in range(1     ,__UpperCAmelCase			):
			for _ in range(__UpperCAmelCase			):
				proth_list.append(2 ** (block + 1) + proth_list[proth_index - 1]			)
				proth_index += 1
			increment *= 2

	return proth_list[number - 1]


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						for number in range(11):
												SCREAMING_SNAKE_CASE									=						0
												try:
																		SCREAMING_SNAKE_CASE									=						proth(number)
												except ValueError:
																		print(f"""ValueError: there is no {number}th Proth number""")
																		continue

												print(f"""The {number}th Proth number: {value}""")



