


def 	_UpperCamelCase					(    lowerCAmelCase_ = 1_0_0_0 )    ->Any:
   UpperCAmelCase      					=  -1
   UpperCAmelCase      					=  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
      UpperCAmelCase      					=  (n * n - 2 * a * n) // (2 * n - 2 * a)
      UpperCAmelCase      					=  n - a - b
      if c * c == (a * a + b * b):
         UpperCAmelCase      					=  a * b * c
         if candidate >= product:
            UpperCAmelCase      					=  candidate
   return product


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











from __future__ import annotations





def    __lowerCAmelCase   (    __snake_case							):
     __lowerCAmelCase             =       len(__snake_case							)
     # We need to create solution object to save path.
     __lowerCAmelCase             =       [[0 for _ in range(__snake_case							)] for _ in range(__snake_case							)]
     __lowerCAmelCase             =       run_maze(__snake_case       ,			0       ,			0       ,			__snake_case							)
     if solved:
          print("\n".join(str(__snake_case							) for row in solutions							)							)
     else:
          print("No solution exists!"							)
     return solved





def    __lowerCAmelCase   (    __snake_case       ,			__snake_case       ,			__snake_case       ,			__snake_case							):
     __lowerCAmelCase             =       len(__snake_case							)
     # Final check point.
     if i == j == (size - 1):
          __lowerCAmelCase             =       1
          return True

     __lowerCAmelCase             =       (not i < 0) and (not j < 0)  # Check lower bounds
     __lowerCAmelCase             =       (i < size) and (j < size)  # Check upper bounds

     if lower_flag and upper_flag:
          # check for already visited and block points.
          __lowerCAmelCase             =       (not solutions[i][j]) and (not maze[i][j])
          if block_flag:
               # check visited
               __lowerCAmelCase             =       1

               # check for directions
               if (
                   run_maze(__snake_case       ,			i + 1       ,			__snake_case       ,			__snake_case							)
                   or run_maze(__snake_case       ,			__snake_case       ,			j + 1       ,			__snake_case							)
                   or run_maze(__snake_case       ,			i - 1       ,			__snake_case       ,			__snake_case							)
                   or run_maze(__snake_case       ,			__snake_case       ,			j - 1       ,			__snake_case							)
               ):
                    return True

               __lowerCAmelCase             =       0
               return False
     return False


if __name__ == "__main__":
 import doctest

 doctest.testmod()






