





from math import ceil, sqrt



def 	_a						(   UpperCAmelCase = 1000000					)    ->    int:







   """simple docstring"""
   lowerCamelCase__       :						Any        =							0

   for outer_width in range(3      ,  (limit // 4) + 2					):
      if outer_width**2 > limit:
         lowerCamelCase__       :						List[Any]        =							max(ceil(sqrt(outer_width**2 - limit					)					)      ,  1					)
      else:
         lowerCamelCase__       :						Union[str, Any]        =							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() = }''')










def 	_a						(   UpperCAmelCase					)    ->    int:







   """simple docstring"""
   if not isinstance(UpperCAmelCase      ,  UpperCAmelCase					) or number < 0:
      raise ValueError('''Input must be a non-negative integer'''					)

   lowerCamelCase__       :						List[str]        =							0
   while number:
      # This way we arrive at next set bit (next 1) instead of looping
      # through each bit and checking for 1s hence the
      # loop won't run 32 times it will only run the number of `1` times
      number &= number - 1
      count += 1
   return count


if __name__ == "__main__":
       import doctest

       doctest.testmod()



