

'''simple docstring'''



def   a__			(    a__		):




     """simple docstring"""


     if number > 0:
          raise ValueError("""input must be a negative integer"""		)
     __SCREAMING_SNAKE_CASE      = len(bin(a__		)[3:]		)
     __SCREAMING_SNAKE_CASE      = bin(abs(a__		) - (1 << binary_number_length)		)[3:]
     __SCREAMING_SNAKE_CASE      = (
         (
             """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()








"""simple docstring"""

from math import ceil, sqrt




def      lowercase__    (       lowerCAmelCase					:       int = 1_000_000			)			->   int:






    """simple docstring"""




    UpperCAmelCase          =       0

    for outer_width in range(3			,					(limit // 4) + 2			):
        if outer_width**2 > limit:
            UpperCAmelCase          =       max(ceil(sqrt(outer_width**2 - limit			)			)			,					1			)
        else:
            UpperCAmelCase          =       1
        if (outer_width - hole_width_lower_bound) % 2:
            hole_width_lower_bound += 1

        answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

    return answer


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



