시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
5 초 128 MB 49 10 8 24.242%

문제

용인 시는 버스 정류장이 N개 있는 버스 노선을 짜려고 한다. 각 버스 정류장은 거리의 모퉁이에 있다. 용인 시는 현대적으로 설계된 도시이기 때문에 지리 구조가 정사각형 격자 모양으로 짜여 있다. 우리는 이 버스 정류장들 가운데 두 곳을, 중심지로서 H1, H2라는 이름으로 선택하려고 한다. 중심지를 선택하고 나면, 두 중심지 사이에는 버스가 가는 길이 생기며, 중심지를 제외한 나머지 N-2개의 버스 정류장들은 H1 아니면 H2 중 한 곳(두 중심지 모두와 연결되는 것은 아님.)과 직통하게 될 것이다. 이렇게 버스 노선이 결정된다.

이 문제에서 임의의 두 지점 사이의 거리는, 두 곳을 수평 수직 방향으로만 통행하는 가장 가까운 거리이다. 다시 말해, 위치를 (x, y) 좌표로 표현했을 때, 두 지점 (x1, y1)과 (x2, y2)의 거리는 |x1-x2|+|y1-y2|로 정의된다는 뜻이다. 한편, 버스 정류장 A와 B가 같은 중심지 H1과 연결돼 있으면 두 정류장 사이의 거리는 A와 H1 사이의 거리와 H1과 B 사이의 거리의 합이 된다. 그리고 A와 B가 각각 다른 중심지인 H1, H2와 연결돼 있으면 두 정류장 사이의 거리는 A와 H1, H1과 H2, H2와 B 사이의 거리들의 합이 된다.

용인 시의 도시 계획부는, 모든 시민이 도시의 모든 구역에 최대한 빨리 도착할 수 있게 하길 원한다. 따라서 도시 계획자들은 버스 정거장들 중, 서로 가장 멀리 떨어져 있는 두 곳 사이의 거리를 최소화할 수 있게끔 중심지 두 곳을 고르려고 한다. 이 거리를 최소화하게 중심지를 고른 뒤, 서로 거리가 가장 먼 두 정류장 사이의 거리를 계산하는 프로그램을 작성하시오.

입력

첫째 줄에는 버스 정류장의 개수인 정수 N(2≤N≤500)이 있다. 그리고 다음 N 개의 줄에는 버스 정류장의 x, y좌표가 있다. (가로 먼저, 다음 세로) 각 좌표들은 5000과 같거나 작은 자연수이다. 정류장들은 모두 서로 다른 위치에 있으며, 겹치는 경우가 없다.

출력

거리가 가장 먼 두 정류장 사이의 거리의 최솟값을 나타내는 자연수 하나를 한 줄에다 출력한다.

예제 입력 1

6
1 7
16 6
12 4
4 4
1 1
11 1

예제 출력 1

20

힌트

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(\uac00\ub85c \uba3c\uc800, \ub2e4\uc74c \uc138\ub85c) \uac01 \uc88c\ud45c\ub4e4\uc740 5000\uacfc \uac19\uac70\ub098 \uc791\uc740 \uc790\uc5f0\uc218\uc774\ub2e4. \uc815\ub958\uc7a5\ub4e4\uc740 \ubaa8\ub450 \uc11c\ub85c \ub2e4\ub978 \uc704\uce58\uc5d0 \uc788\uc73c\uba70, \uacb9\uce58\ub294 \uacbd\uc6b0\uac00 \uc5c6\ub2e4.<\/p>\r\n","output":"<p>\uac70\ub9ac\uac00 \uac00\uc7a5 \uba3c \ub450 \uc815\ub958\uc7a5 \uc0ac\uc774\uc758 \uac70\ub9ac\uc758 \ucd5c\uc19f\uac12\uc744 \ub098\ud0c0\ub0b4\ub294 \uc790\uc5f0\uc218 \ud558\ub098\ub97c \ud55c \uc904\uc5d0\ub2e4 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/upload\/images\/terminal.png\" style=\"height:194px; width:286px\" \/><\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2209","problem_lang":"1","title":"Bus Terminals","description":"<p>Yong-In city plans to build a bus network with N bus stops. Each bus stop is at a street corner. Yong-In is a modern city, so its map is a grid of square blocks of equal size. Two of these bus stops are to be selected as hubs H1 and H2. The hubs will be connected to each other by a direct bus line and each of the remaining N &minus; 2 bus stops will be connected directly to either H1 or H2 &nbsp;(but not to both), but not to any other bus stop.<\/p>\r\n\r\n<p>The distance between any two bus stops is the length of the shortest possible route following the streets. That is, if a bus stop is represented as (x, y) with x-coordinate x and y-coordinate y, then the distance between two bus stops (x1, y1) and (x2, y2) is |x1-x2| + |y1-y2| . If bus stops A and B are connected to the same hub H1, then the length of the route from A to B is the sum of the distances from A to H1 and from H1 to B. If bus stops A and B are connected to different hubs, e.g., A to H1 and B to H2, then the length of the route from A to B is the sum of the distances from A to H1, from H1 to H2, and from H2 to B.<\/p>\r\n\r\n<p>The planning authority of Yong-In city would like to make sure that every citizen can reach every point within the city as quickly as possible. Therefore, city planners want to choose two bus stops to be hubs in such a way that in the resulting bus network the length of the longest route between any two bus stops is as short as possible.&nbsp;<\/p>\r\n\r\n<p>One choice P of two hubs and assignments of bus stops to those hubs is better than another choice Q if the length of the longest bus route is shorter in P than in Q. &nbsp;Your task is to write a program to compute the length of this longest route for the best choice P. &nbsp;<\/p>\r\n","input":"<p>Your program is to read from standard input. The first line contains one positive integer N, 2 &le; N &le; 500, the number of bus stops. Each of the remaining N lines contains the x-coordinate followed by the y-coordinate of a bus stop. The x- and y-coordinates are positive integers &le; 5000. &nbsp;No two bus stops are at the same location.<\/p>\r\n","output":"<p>Your program is to write to standard output. The output contains one line with a single positive integer, the minimum length of the longest bus route for the input.<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/upload\/images\/terminal.png\" style=\"height:194px; opacity:0.9; width:286px\" \/><\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]