
def        __UpperCamelCase					(    lowerCAmelCase__							:    int  ,       lowerCAmelCase__							:    int  ):
 if a < 0 or b < 0:
  raise ValueError('''the value of both inputs must be positive'''  )
 __a			:  Union[str, Any]		    =  str(bin(lowerCAmelCase__  )  )[2:]  # remove the leading "0b"
 __a			:  Dict		    =  str(bin(lowerCAmelCase__  )  )[2:]
 __a			:  List[str]		    =  max(len(lowerCAmelCase__  )  ,       len(lowerCAmelCase__  )  )
 return "0b" + "".join(
     str(int('''1''' in (char_a, char_b)  )  )
     for char_a, char_b in zip(a_binary.zfill(lowerCAmelCase__  )  ,       b_binary.zfill(lowerCAmelCase__  )  )  )


if __name__ == "__main__":
      import doctest

      doctest.testmod()


def        __UpperCamelCase					(    lowerCAmelCase__							:    int = 1_0_0_0  ):
 __a			:  int		    =  -1
 __a			:  Any		    =  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
  __a			:  List[Any]		    =  (n * n - 2 * a * n) // (2 * n - 2 * a)
  __a			:  Union[str, Any]		    =  n - a - b
  if c * c == (a * a + b * b):
   __a			:  Union[str, Any]		    =  a * b * c
   if candidate >= product:
    __a			:  List[Any]		    =  candidate
 return product


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