





def     lowerCamelCase__			(__lowerCamelCase = 1000	):
     _SCREAMING_SNAKE_CASE       :	Union[str, Any]						    =							-1
     _SCREAMING_SNAKE_CASE       :	Dict						    =							0
     for a in range(1,       n // 3	):
          # Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
          _SCREAMING_SNAKE_CASE       :	Dict						    =							(n * n - 2 * a * n) // (2 * n - 2 * a)
          _SCREAMING_SNAKE_CASE       :	Union[str, Any]						    =							n - a - b
          if c * c == (a * a + b * b):
               _SCREAMING_SNAKE_CASE       :	int						    =							a * b * c
               if candidate >= product:
                    _SCREAMING_SNAKE_CASE       :	List[str]						    =							candidate
     return product


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






from PIL import Image






def     lowerCamelCase__			(__lowerCamelCase	):
     _SCREAMING_SNAKE_CASE    ,			_SCREAMING_SNAKE_CASE       :	List[str]						    =							image.size
     _SCREAMING_SNAKE_CASE       :	Tuple						    =							0
     _SCREAMING_SNAKE_CASE       :	Dict						    =							image.load()
     for i in range(__lowerCamelCase	):
          for j in range(__lowerCamelCase	):
               _SCREAMING_SNAKE_CASE       :	List[Any]						    =							pixels[j, i]
               mean += pixel
     mean //= width * height

     for j in range(__lowerCamelCase	):
          for i in range(__lowerCamelCase	):
               _SCREAMING_SNAKE_CASE       :	int						    =							255 if pixels[i, j] > mean else 0
     return image


if __name__ == "__main__":
       UpperCamelCase__      =mean_threshold(Image.open('path_to_image').convert('L'))
       image.save('output_image_path')