


from __future__ import annotations

import collections
import pprint
from pathlib import Path






def 							__lowercase     (				__lowerCAmelCase							:       str     ):
							return "".join(sorted(__lowerCAmelCase     )     )






def 							__lowercase     (				__lowerCAmelCase							:       str     ):
							return word_by_signature[signature(__lowerCAmelCase     )]


snake_case							: str      =   Path(__file__).parent.joinpath('''words.txt''').read_text(encoding='''utf-8''')
snake_case							: List[str]      =   sorted({word.strip().lower() for word in data.splitlines()})

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

if __name__ == "__main__":
						snake_case							: Union[str, Any]      =   {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))








from math import ceil, sqrt






def 							__lowercase     (				__lowerCAmelCase							:       int = 1_0_0_0_0_0_0     ):
							a__    =  0

							for outer_width in range(3      ,					(limit // 4) + 2     ):
														if outer_width**2 > limit:
																					a__    =  max(ceil(sqrt(outer_width**2 - limit     )     )      ,					1     )
														else:
																					a__    =  1
														if (outer_width - hole_width_lower_bound) % 2:
																					hole_width_lower_bound += 1

														answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

							return answer


if __name__ == "__main__":
						print(f"""{solution() = }""")




