





"""simple docstring"""






from math import ceil, sqrt

def       __A (     a_  :int = 1_00_00_00)						->						int:
    __a	:  Union[str, Any]         =					0

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






"""simple docstring"""






def       __A (     a_  :int = 1_00_00_00)						->						int:
				__a	:  Tuple         =					[i - 1 for i in range(limit + 1)]

				for i in range(2				,    limit + 1):
								if phi[i] == i - 1:
												for j in range(2 * i				,    limit + 1				,    a_):
																phi[j] -= phi[j] // i

				return sum(phi[2 : limit + 1])


if __name__ == "__main__":
		print(solution())