




"""simple docstring"""


from math import ceil, sqrt


def  UpperCAmelCase__	(snake_case__							: int = 1_00_00_00   ):
		"""simple docstring"""

		_snake_case							:		Dict								=  0

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








"""simple docstring"""


def  UpperCAmelCase__	(snake_case__							: int = 1_00_00_00   ):
  """simple docstring"""

  _snake_case							:		Dict								=  [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		,       snake_case__   ):
        phi[j] -= phi[j] // i

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


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


