

def 		_lowercase			(					lowercase__						):
						if not isinstance(_lowerCAmelCase       ,     _lowerCAmelCase						):
												raise ValueError('''double_factorial() only accepts integral values'''						)
						if n < 0:
												raise ValueError('''double_factorial() not defined for negative values'''						)
						return 1 if n <= 1 else n * double_factorial(n - 2						)


if __name__ == "__main__":
	import doctest

	doctest.testmod()





def 		_lowercase			(					lowercase__       ,     lowercase__						):
      if len(str(lowercase__						)						) == 1 or len(str(lowercase__						)						) == 1:
            return a * b

      __lowerCAmelCase :						Any = max(len(str(lowercase__						)						)       ,     len(str(lowercase__						)						)						)
      __lowerCAmelCase :						Optional[int] = ma // 2

      __lowerCAmelCase,							__lowerCAmelCase :						Tuple = divmod(lowercase__       ,     1_0**ma						)
      __lowerCAmelCase,							__lowerCAmelCase :						Any = divmod(lowercase__       ,     1_0**ma						)

      __lowerCAmelCase :						str = karatsuba(lowercase__       ,     lowercase__						)
      __lowerCAmelCase :						Optional[int] = karatsuba((aa + aa)       ,     (ba + ba)						)
      __lowerCAmelCase :						List[Any] = karatsuba(lowercase__       ,     lowercase__						)

      return (z * 1_0 ** (2 * ma)) + ((y - z - x) * 1_0 ** (ma)) + (x)







def 		_lowercase			(					):
      print(karatsuba(1_5_4_6_3       ,     2_3_4_8_9						)						)


if __name__ == "__main__":
 main()


