

def 					__lowercase      (     _A			)     ->						str:
      if number > 0:
            raise ValueError("""input must be a negative integer"""			)
      SCREAMING_SNAKE_CASE :      Dict       =   len(bin(_A			)[3:]			)
      SCREAMING_SNAKE_CASE :      Tuple       =   bin(abs(_A			) - (1 << binary_number_length)			)[3:]
      SCREAMING_SNAKE_CASE :      Tuple       =   (
          (
              """1"""
              + """0""" * (binary_number_length - len(_A			))
              + twos_complement_number
          )
          if number < 0
          else """0"""
      )
      return "0b" + twos_complement_number


if __name__ == "__main__":
  import doctest

  doctest.testmod()







def 					__lowercase      (     _A			)     ->						list[int]:
      SCREAMING_SNAKE_CASE :      int       =   [0 for i in range(len(_A			)			)]

      # initialize interval's left pointer and right pointer
      SCREAMING_SNAKE_CASE     ,	SCREAMING_SNAKE_CASE :      Dict       =   0, 0

      for i in range(1						,    len(_A			)			):
            # case when current index is inside the interval
            if i <= right_pointer:
                  SCREAMING_SNAKE_CASE :      Any       =   min(right_pointer - i + 1						,    z_result[i - left_pointer]			)
                  SCREAMING_SNAKE_CASE :      Optional[Any]       =   min_edge

            while go_next(_A						,    _A						,    _A			):
                  z_result[i] += 1

            # if new index's result gives us more right interval,
            # we've to update left_pointer and right_pointer
            if i + z_result[i] - 1 > right_pointer:
                  SCREAMING_SNAKE_CASE     ,	SCREAMING_SNAKE_CASE :      List[Any]       =   i, i + z_result[i] - 1

      return z_result






def 					__lowercase      (     _A						,    _A						,    _A			)     ->						bool:
      return i + z_result[i] < len(_A			) and s[z_result[i]] == s[i + z_result[i]]






def 					__lowercase      (     _A						,    _A			)     ->						int:
      SCREAMING_SNAKE_CASE :      Any       =   0
      # concatenate 'pattern' and 'input_str' and call z_function
      # with concatenated string
      SCREAMING_SNAKE_CASE :      List[Any]       =   z_function(pattern + input_str			)

      for val in z_result:
            # if value is greater then length of the pattern string
            # that means this index is starting position of substring
            # which is equal to pattern string
            if val >= len(_A			):
                  answer += 1

      return answer


if __name__ == "__main__":
  import doctest

  doctest.testmod()




