



def 	snake_case__       (					__lowercase       )		->		str:







      """simple docstring"""

      if isinstance(__snake_case							,     __snake_case       ):
            raise TypeError("'float' object cannot be interpreted as an integer"       )
      if isinstance(__snake_case							,     __snake_case       ):
            raise TypeError("'str' object cannot be interpreted as an integer"       )

      if num == 0:
            return "0b0"

      A__	:							Optional[int]						    = False

      if num < 0:
            A__	:							Optional[int]						    = True
            A__	:							List[str]						    = -num

      A__	:							list[int]						    = []
      while num > 0:
            binary.insert(0							,     num % 2       )
            num >>= 1

      if negative:
            return "-0b" + "".join(str(__snake_case       ) for e in binary       )

      return "0b" + "".join(str(__snake_case       ) for e in binary       )


if __name__ == "__main__":
  import doctest

  doctest.testmod()




def 	snake_case__       (					__lowercase       )		->		int:







						"""simple docstring"""

						if divisor % 5 == 0 or divisor % 2 == 0:
												return 0
						A__	:							Tuple						    = 1
						A__	:							Union[str, Any]						    = 1
						while repunit:
												A__	:							Union[str, Any]						    = (1_0 * repunit + 1) % divisor
												repunit_index += 1
						return repunit_index
def 	snake_case__       (					__lowercase = 1_0_0_0_0_0_0       )		->		int:







						"""simple docstring"""

						A__	:							Dict						    = limit - 1
						if divisor % 2 == 0:
												divisor += 1
						while least_divisible_repunit(__lowercase       ) <= limit:
												divisor += 2
						return divisor


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