





from math import ceil, sqrt




def _a (  SCREAMING_SNAKE_CASE__      :  int = 1_00_00_00       )	->    int:

							'''simple docstring'''






							SCREAMING_SNAKE_CASE__       :      List[str]     =						0

							for outer_width in range(3			,				(limit // 4) + 2       ):
														if outer_width**2 > limit:
																					SCREAMING_SNAKE_CASE__       :      List[Any]     =						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() = }")













def _a (  SCREAMING_SNAKE_CASE__      :  int       )	->    str:

							'''simple docstring'''






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

							if num == 0:
														return "0b0"

							SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						False

							if num < 0:
														SCREAMING_SNAKE_CASE__       :      Any     =						True
														SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						-num

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

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

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


if __name__ == "__main__":
		import doctest

		doctest.testmod()






