
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     str				)			->						bool:
       SCREAMING_SNAKE_CASE_							:				Optional[Any]		=0
       for ch in input_str:
              SCREAMING_SNAKE_CASE_							:				List[Any]		=ord(UpperCAmelCase_				)
              SCREAMING_SNAKE_CASE_							:				str		=pow(2			,							UpperCAmelCase_				)

              # If we already turned on bit for current character's unicode
              if bitmap >> ch_unicode & 1 == 1:
                     return False
              bitmap |= ch_bit_index_on
       return True


if __name__ == "__main__":
 import doctest

 doctest.testmod()


from math import ceil, sqrt
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     int = 1_0_0_0_0_0_0				)			->						int:
       SCREAMING_SNAKE_CASE_							:				List[Any]		=0

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