




def      __lowerCAmelCase			(					UpperCamelCase = 1000      )     ->	int:
  lowerCAmelCase__				:  Optional[int]		       =     -1
  lowerCAmelCase__				:  List[str]		       =     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
    lowerCAmelCase__				:  Dict		       =     (n * n - 2 * a * n) // (2 * n - 2 * a)
    lowerCAmelCase__				:  Union[str, Any]		       =     n - a - b
    if c * c == (a * a + b * b):
      lowerCAmelCase__				:  List[str]		       =     a * b * c
      if candidate >= product:
        lowerCAmelCase__				:  str		       =     candidate
  return product


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







def      __lowerCAmelCase			(					UpperCamelCase      )     ->	bool:
  if not isinstance(UpperCamelCase	,      UpperCamelCase      ):
    raise ValueError('''Input series is not valid, valid series - [2, 4, 6]'''      )
  if len(UpperCamelCase      ) == 0:
    raise ValueError('''Input list must be a non empty list'''      )
  if len(UpperCamelCase      ) == 1:
    return True
  lowerCAmelCase__				:  Tuple		       =     series[1] - series[0]
  for index in range(len(UpperCamelCase      ) - 1      ):
    if series[index + 1] - series[index] != common_diff:
      return False
  return True



def      __lowerCAmelCase			(					UpperCamelCase      )     ->	float:
  if not isinstance(UpperCamelCase	,      UpperCamelCase      ):
    raise ValueError('''Input series is not valid, valid series - [2, 4, 6]'''      )
  if len(UpperCamelCase      ) == 0:
    raise ValueError('''Input list must be a non empty list'''      )
  lowerCAmelCase__				:  int		       =     0
  for val in series:
    answer += val
  return answer / len(UpperCamelCase      )


if __name__ == "__main__":
     import doctest

     doctest.testmod()

