


from math import pow
def 				__lowerCamelCase						( UpperCAmelCase_						:		int ,  UpperCAmelCase_						:		int ,  UpperCAmelCase_						:		int ,  UpperCAmelCase_						:		int ,  UpperCAmelCase_						:		int ,  ):




      """simple docstring"""





      if current_sum == needed_sum:
            # If the sum of the powers is equal to needed_sum, then we have a solution.
            solutions_count += 1
            return current_sum, solutions_count

      a						:List[Any] 							=       int(pow(UpperCAmelCase_ ,  UpperCAmelCase_						)						)
      if current_sum + i_to_n <= needed_sum:
            # If the sum of the powers is less than needed_sum, then continue adding powers.
            current_sum += i_to_n
            a							,				a						:List[Any] 							=       backtrack(
                UpperCAmelCase_ ,  UpperCAmelCase_ ,  current_number + 1 ,  UpperCAmelCase_ ,  UpperCAmelCase_						)
            current_sum -= i_to_n
      if i_to_n < needed_sum:
            # If the power of i is less than needed_sum, then try with the next power.
            a							,				a						:List[str] 							=       backtrack(
                UpperCAmelCase_ ,  UpperCAmelCase_ ,  current_number + 1 ,  UpperCAmelCase_ ,  UpperCAmelCase_						)
      return current_sum, solutions_count
def 				__lowerCamelCase						( UpperCAmelCase_						:		int ,  UpperCAmelCase_						:		int						):




      """simple docstring"""





      if not (1 <= needed_sum <= 1000 and 2 <= power <= 10):
            raise ValueError(
                '''Invalid input\n'''
                '''needed_sum must be between 1 and 1000, power between 2 and 10.'''						)

      return backtrack(UpperCAmelCase_ ,  UpperCAmelCase_ ,  1 ,  0 ,  0						)[1]  # Return the solutions_count


if __name__ == "__main__":
     import doctest

     doctest.testmod()









from __future__ import annotations

import collections
import pprint
from pathlib import Path
def 				__lowerCamelCase						( UpperCAmelCase_						:		str						):




      """simple docstring"""





      return "".join(sorted(UpperCAmelCase_						)						)
def 				__lowerCamelCase						( UpperCAmelCase_						:		str						):




      """simple docstring"""





      return word_by_signature[signature(UpperCAmelCase_						)]


snake_case				:    str       				=     Path(__file__).parent.joinpath('''words.txt''').read_text(encoding='''utf-8''')
snake_case				:    Optional[int]       				=     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				:    Optional[int]       				=     {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))





