

def     UpperCAmelCase_       (						_A				,		_A    ):





					'''simple docstring'''




					if a < 0 or b < 0:
										raise ValueError('''the value of both inputs must be positive'''    )

					SCREAMING_SNAKE_CASE__   =   str(bin(_A    )    )[2:]  # remove the leading "0b"
					SCREAMING_SNAKE_CASE__   =   str(bin(_A    )    )[2:]  # remove the leading "0b"

					SCREAMING_SNAKE_CASE__   =   max(len(_A    )				,		len(_A    )    )

					return "0b" + "".join(
					    str(int(char_a == '''1''' and char_b == '''1'''    )    )
					    for char_a, char_b in zip(a_binary.zfill(_A    )				,		b_binary.zfill(_A    )    )    )


if __name__ == "__main__":
							import doctest

							doctest.testmod()





def     UpperCAmelCase_       (						_A    ):





     '''simple docstring'''




     if not isinstance(_A				,		_A    ):
          raise ValueError('''multiplicative_persistence() only accepts integral values'''    )
     if num < 0:
          raise ValueError('''multiplicative_persistence() does not accept negative values'''    )

     SCREAMING_SNAKE_CASE__   =   0
     SCREAMING_SNAKE_CASE__   =   str(_A    )

     while len(_A    ) != 1:
          SCREAMING_SNAKE_CASE__   =   [int(_A    ) for i in num_string]

          SCREAMING_SNAKE_CASE__   =   1
          for i in range(0				,		len(_A    )    ):
               total *= numbers[i]

          SCREAMING_SNAKE_CASE__   =   str(_A    )

          steps += 1
     return steps
def     UpperCAmelCase_       (						_A    ):





     '''simple docstring'''




     if not isinstance(_A				,		_A    ):
          raise ValueError('''additive_persistence() only accepts integral values'''    )
     if num < 0:
          raise ValueError('''additive_persistence() does not accept negative values'''    )

     SCREAMING_SNAKE_CASE__   =   0
     SCREAMING_SNAKE_CASE__   =   str(_A    )

     while len(_A    ) != 1:
          SCREAMING_SNAKE_CASE__   =   [int(_A    ) for i in num_string]

          SCREAMING_SNAKE_CASE__   =   0
          for i in range(0				,		len(_A    )    ):
               total += numbers[i]

          SCREAMING_SNAKE_CASE__   =   str(_A    )

          steps += 1
     return steps


if __name__ == "__main__":
       import doctest

       doctest.testmod()


