





"""simple docstring"""
def 					__lowerCamelCase       (							a_					:		int							)      ->				list[int]:

      if num <= 0:
            raise ValueError('''Input must be a positive integer'''							)

      __SCREAMING_SNAKE_CASE       :Dict		    =  [True] * (num + 1)

      __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  2
      while p * p <= num:
            if primes[p]:
                  for i in range(p * p			,       num + 1			,       a_							):
                        __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  False
            p += 1

      return [prime for prime in range(2			,       num + 1							) if primes[prime]]


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  lowerCamelCase_       =		int(input("Enter a positive integer: ").strip())
  print(prime_sieve_eratosthenes(user_num))






"""simple docstring"""
def 					__lowerCamelCase       (							a_					:		Union[str, Any]			,       a_					:		Optional[Any]							)      ->				Union[str, Any]:
      return (pointa[0] - pointa[0]) ** 2 + (pointa[1] - pointa[1]) ** 2



def 					__lowerCamelCase       (							a_					:		Optional[int]			,       a_					:		Any=0							)      ->				Optional[Any]:
      return sorted(a_			,       key=lambda a_							: x[column]							)



def 					__lowerCamelCase       (							a_					:		Optional[Any]			,       a_					:		Optional[int]			,       a_					:		str=float('''inf'''							)							)      ->				str:

      for i in range(points_counts - 1							):
            for j in range(i + 1			,       a_							):
                  __SCREAMING_SNAKE_CASE       :Dict		    =  euclidean_distance_sqr(points[i]			,       points[j]							)
                  if current_dis < min_dis:
                        __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  current_dis
      return min_dis



def 					__lowerCamelCase       (							a_					:		List[Any]			,       a_					:		Any			,       a_					:		Optional[int]=float('''inf'''							)							)      ->				Optional[Any]:

      for i in range(min(6			,       points_counts - 1							)			,       a_							):
            for j in range(max(0			,       i - 6							)			,       a_							):
                  __SCREAMING_SNAKE_CASE       :Dict		    =  euclidean_distance_sqr(points[i]			,       points[j]							)
                  if current_dis < min_dis:
                        __SCREAMING_SNAKE_CASE       :int		    =  current_dis
      return min_dis



def 					__lowerCamelCase       (							a_					:		str			,       a_					:		List[Any]			,       a_					:		int							)      ->				Optional[int]:

      # base case
      if points_counts <= 3:
            return dis_between_closest_pair(a_			,       a_							)

      # recursion
      __SCREAMING_SNAKE_CASE       :int		    =  points_counts // 2
      __SCREAMING_SNAKE_CASE       :Dict		    =  closest_pair_of_points_sqr(
          a_			,       points_sorted_on_y[:mid]			,       a_							)
      __SCREAMING_SNAKE_CASE       :Any		    =  closest_pair_of_points_sqr(
          a_			,       points_sorted_on_y[mid:]			,       points_counts - mid							)
      __SCREAMING_SNAKE_CASE       :Union[str, Any]		    =  min(a_			,       a_							)
      __SCREAMING_SNAKE_CASE       :str		    =  []
      for point in points_sorted_on_x:
            if abs(point[0] - points_sorted_on_x[mid][0]							) < closest_pair_dis:
                  cross_strip.append(a_							)

      __SCREAMING_SNAKE_CASE       :Dict		    =  dis_between_closest_in_strip(
          a_			,       len(a_							)			,       a_							)
      return min(a_			,       a_							)



def 					__lowerCamelCase       (							a_					:		int			,       a_					:		Tuple							)      ->				List[Any]:
      __SCREAMING_SNAKE_CASE       :Union[str, Any]		    =  column_based_sort(a_			,       column=0							)
      __SCREAMING_SNAKE_CASE       :int		    =  column_based_sort(a_			,       column=1							)
      return (
          closest_pair_of_points_sqr(
              a_			,       a_			,       a_							)
      ) ** 0.5


if __name__ == "__main__":
  lowerCamelCase_       =		[(2, 3), (1_2, 3_0), (4_0, 5_0), (5, 1), (1_2, 1_0), (3, 4)]
  print("Distance:", closest_pair_of_points(points, len(points)))