def   lowerCAmelCase_ (				)->  List[Any]:






      '''simple docstring'''





      for a in range(3_00						):
            for b in range(a + 1		,					4_00						):
                  for c in range(b + 1		,					5_00						):
                        if (a + b + c) == 10_00 and (a**2) + (b**2) == (c**2):
                              return a * b * c

      return -1





def   lowerCAmelCase_ (				)->  Dict:






      '''simple docstring'''





      for a in range(3_00						):
            for b in range(4_00						):
                  UpperCAmelCase    : List[str]      =10_00 - a - b
                  if a < b < c and (a**2) + (b**2) == (c**2):
                        return a * b * c

      return -1





def   lowerCAmelCase_ (				)->  List[Any]:






      '''simple docstring'''





      import timeit

      print(
          timeit.timeit('''solution()'''		,					setup='''from __main__ import solution'''		,					number=10_00						)						)
      print(
          timeit.timeit(
              '''solution_fast()'''		,					setup='''from __main__ import solution_fast'''		,					number=10_00						)						)


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

import math





def   lowerCAmelCase_ (				__lowerCAmelCase						)->  list[int]:






      '''simple docstring'''





      if not isinstance(__lowerCAmelCase		,					__lowerCAmelCase						):
            UpperCAmelCase    : Union[str, Any]      =f'''Input value of [number={number}] must be an integer'''
            raise TypeError(__lowerCAmelCase						)
      if number < 1:
            UpperCAmelCase    : Dict      =f'''Input value of [number={number}] must be a positive integer'''
            raise ValueError(__lowerCAmelCase						)
      UpperCAmelCase    : Dict      =[number]
      while number != 1:
            if number % 2 == 0:
                  UpperCAmelCase    : Optional[Any]      =math.floor(math.sqrt(__lowerCAmelCase						)						)
            else:
                  UpperCAmelCase    : List[str]      =math.floor(
                      math.sqrt(__lowerCAmelCase						) * math.sqrt(__lowerCAmelCase						) * math.sqrt(__lowerCAmelCase						)						)
            sequence.append(__lowerCAmelCase						)
      return sequence


if __name__ == "__main__":
     import doctest

     doctest.testmod()
