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문제

농장에 있는 젖소들이 건강하지 못하다고 생각한 농부 존은 젖소들을 위한 마라톤 대회를 열었고, 농부 존의 총애를 받는 젖소 박승원 역시 이 대회에 참가할 예정이다.

마라톤 코스는 N (3 <= N <= 100000) 개의 체크포인트로 구성되어 있으며, 1번 체크포인트에서 시작해서 모든 체크 포인트를 순서대로 방문한 후 N번 체크포인트에서 끝나야지 마라톤이 끝난다. 게으른 젖소 박승원은 막상 대회에 참가하려 하니 귀찮아져서 중간에 있는 체크포인트 한개를 몰래 건너뛰려 한다. 단, 1번 체크포인트와 N번 체크포인트를 건너뛰면 너무 눈치가 보이니 두 체크포인트는 건너뛰지 않을 생각이다.

젖소 박승원이 체크포인트 한개를 건너뛰면서 달릴 수 있다면, 과연 승원이가 달려야 하는 최소 거리는 얼마일까?

참고로, 젖소 마라톤 대회는 서울시내 한복판에서 진행될 예정이기 때문에 거리는 택시 거리(Manhattan Distance)로 계산하려고 한다. 즉, (x1,y1)과 (x2,y2) 점 간의 거리는 |x1-x2| + |y1-y2| 로 표시할 수 있다. (|x|는 절댓값 기호다.)

입력

첫 번째 줄에 체크포인트의 수 N이 주어진다.

이후 N개의 줄에 정수가 두개씩 주어진다. i번째 줄의 첫 번째 정수는 체크포인트 i의 x 좌표, 두 번째 정수는 y 좌표이다.

체크 포인트의 좌표는 겹칠 수도 있다 - 젖소 박승원은 체크포인트를 건너뛸 때 그 번호의 체크포인트만 건너뛰며, 그 점에 있는 모든 체크포인트를 건너뛰지 않는다.

출력

젖소 박승원이 체크포인트 1개를 건너뛰고 달릴 수 있는 최소 거리를 출력하라.

예제 입력 1

4
0 0
8 3
11 -1
10 0

예제 출력 1

14

힌트

젖소 박승원은 2번째 혹은 3번째 체크포인트를 건너뛸 수 있는데, 여기서 두 번째 체크포인트를 건너뛸 경우 경로는 (0,0) -> (11,-1) -> (10,0) 이 되며 거리는 14이다. 박승원은 이것보다 더 짧게 달릴 수 없다.

[{"problem_id":"10655","problem_lang":"0","title":"\ub9c8\ub77c\ud1a4 1","description":"<p>\ub18d\uc7a5\uc5d0 \uc788\ub294 \uc816\uc18c\ub4e4\uc774 \uac74\uac15\ud558\uc9c0 \ubabb\ud558\ub2e4\uace0 \uc0dd\uac01\ud55c \ub18d\ubd80 \uc874\uc740 \uc816\uc18c\ub4e4\uc744 \uc704\ud55c \ub9c8\ub77c\ud1a4 \ub300\ud68c\ub97c \uc5f4\uc5c8\uace0, \ub18d\ubd80 \uc874\uc758 \ucd1d\uc560\ub97c \ubc1b\ub294 \uc816\uc18c \ubc15\uc2b9\uc6d0 \uc5ed\uc2dc \uc774 \ub300\ud68c\uc5d0 \ucc38\uac00\ud560 \uc608\uc815\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub9c8\ub77c\ud1a4 \ucf54\uc2a4\ub294 N (3 &lt;= N &lt;= 100000) \uac1c\uc758 \uccb4\ud06c\ud3ec\uc778\ud2b8\ub85c \uad6c\uc131\ub418\uc5b4 \uc788\uc73c\uba70, 1\ubc88 \uccb4\ud06c\ud3ec\uc778\ud2b8\uc5d0\uc11c \uc2dc\uc791\ud574\uc11c \ubaa8\ub4e0 \uccb4\ud06c \ud3ec\uc778\ud2b8\ub97c \uc21c\uc11c\ub300\ub85c \ubc29\ubb38\ud55c \ud6c4 N\ubc88 \uccb4\ud06c\ud3ec\uc778\ud2b8\uc5d0\uc11c \ub05d\ub098\uc57c\uc9c0 \ub9c8\ub77c\ud1a4\uc774 \ub05d\ub09c\ub2e4. \uac8c\uc73c\ub978 \uc816\uc18c \ubc15\uc2b9\uc6d0\uc740 \ub9c9\uc0c1 \ub300\ud68c\uc5d0 \ucc38\uac00\ud558\ub824 \ud558\ub2c8 \uadc0\ucc2e\uc544\uc838\uc11c \uc911\uac04\uc5d0 \uc788\ub294 \uccb4\ud06c\ud3ec\uc778\ud2b8 \ud55c\uac1c\ub97c \ubab0\ub798 \uac74\ub108\ub6f0\ub824 \ud55c\ub2e4. \ub2e8, 1\ubc88 \uccb4\ud06c\ud3ec\uc778\ud2b8\uc640 N\ubc88 \uccb4\ud06c\ud3ec\uc778\ud2b8\ub97c \uac74\ub108\ub6f0\uba74 \ub108\ubb34 \ub208\uce58\uac00 \ubcf4\uc774\ub2c8 \ub450 \uccb4\ud06c\ud3ec\uc778\ud2b8\ub294 \uac74\ub108\ub6f0\uc9c0 \uc54a\uc744 \uc0dd\uac01\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc816\uc18c \ubc15\uc2b9\uc6d0\uc774 \uccb4\ud06c\ud3ec\uc778\ud2b8 \ud55c\uac1c\ub97c \uac74\ub108\ub6f0\uba74\uc11c \ub2ec\ub9b4 \uc218 \uc788\ub2e4\uba74, \uacfc\uc5f0 \uc2b9\uc6d0\uc774\uac00 \ub2ec\ub824\uc57c \ud558\ub294 \ucd5c\uc18c \uac70\ub9ac\ub294 \uc5bc\ub9c8\uc77c\uae4c?<\/p>\r\n\r\n<p>\ucc38\uace0\ub85c, \uc816\uc18c \ub9c8\ub77c\ud1a4 \ub300\ud68c\ub294 \uc11c\uc6b8\uc2dc\ub0b4 \ud55c\ubcf5\ud310\uc5d0\uc11c \uc9c4\ud589\ub420 \uc608\uc815\uc774\uae30 \ub54c\ubb38\uc5d0 \uac70\ub9ac\ub294 \ud0dd\uc2dc \uac70\ub9ac(Manhattan Distance)\ub85c \uacc4\uc0b0\ud558\ub824\uace0 \ud55c\ub2e4. \uc989, (x1,y1)\uacfc (x2,y2) \uc810 \uac04\uc758 \uac70\ub9ac\ub294 |x1-x2| + |y1-y2| \ub85c \ud45c\uc2dc\ud560 \uc218 \uc788\ub2e4. (|x|\ub294 \uc808\ub313\uac12 \uae30\ud638\ub2e4.)<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \uccb4\ud06c\ud3ec\uc778\ud2b8\uc758 \uc218 N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uc774\ud6c4 N\uac1c\uc758 \uc904\uc5d0 \uc815\uc218\uac00 \ub450\uac1c\uc529 \uc8fc\uc5b4\uc9c4\ub2e4. i\ubc88\uc9f8 \uc904\uc758 \uccab \ubc88\uc9f8 \uc815\uc218\ub294 \uccb4\ud06c\ud3ec\uc778\ud2b8 i\uc758 x \uc88c\ud45c, \ub450 \ubc88\uc9f8 \uc815\uc218\ub294 y \uc88c\ud45c\uc774\ub2e4.<\/p>\r\n\r\n<p>\uccb4\ud06c \ud3ec\uc778\ud2b8\uc758 \uc88c\ud45c\ub294 \uacb9\uce60 \uc218\ub3c4 \uc788\ub2e4 - \uc816\uc18c \ubc15\uc2b9\uc6d0\uc740 \uccb4\ud06c\ud3ec\uc778\ud2b8\ub97c \uac74\ub108\ub6f8 \ub54c \uadf8 \ubc88\ud638\uc758 \uccb4\ud06c\ud3ec\uc778\ud2b8\ub9cc \uac74\ub108\ub6f0\uba70, \uadf8 \uc810\uc5d0 \uc788\ub294 \ubaa8\ub4e0 \uccb4\ud06c\ud3ec\uc778\ud2b8\ub97c \uac74\ub108\ub6f0\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n","output":"<p>\uc816\uc18c \ubc15\uc2b9\uc6d0\uc774 \uccb4\ud06c\ud3ec\uc778\ud2b8 1\uac1c\ub97c \uac74\ub108\ub6f0\uace0 \ub2ec\ub9b4 \uc218 \uc788\ub294 \ucd5c\uc18c \uac70\ub9ac\ub97c \ucd9c\ub825\ud558\ub77c.<\/p>\r\n","hint":"<p>\r\n\t\uc816\uc18c \ubc15\uc2b9\uc6d0\uc740 2\ubc88\uc9f8 \ud639\uc740 3\ubc88\uc9f8 \uccb4\ud06c\ud3ec\uc778\ud2b8\ub97c \uac74\ub108\ub6f8 \uc218 \uc788\ub294\ub370, \uc5ec\uae30\uc11c \ub450 \ubc88\uc9f8 \uccb4\ud06c\ud3ec\uc778\ud2b8\ub97c \uac74\ub108\ub6f8 \uacbd\uc6b0 \uacbd\ub85c\ub294 (0,0) -&gt; (11,-1) -&gt; (10,0) \uc774 \ub418\uba70 \uac70\ub9ac\ub294 14\uc774\ub2e4. \ubc15\uc2b9\uc6d0\uc740 \uc774\uac83\ubcf4\ub2e4 \ub354 \uc9e7\uac8c \ub2ec\ub9b4 \uc218 \uc5c6\ub2e4.\r\n<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"10655","problem_lang":"1","title":"Marathon","description":"<p>Unhappy with the poor health of his cows, Farmer John enrolls them in an assortment of different physical fitness activities. &nbsp;His prize cow Bessie is enrolled in a running class, where she is eventually expected to run a marathon through the downtown area of the city near Farmer John&#39;s farm!<\/p>\r\n\r\n<p>The marathon course consists of N checkpoints (3 &lt;= N &lt;= 100,000) to be visited in sequence, where checkpoint 1 is the starting location and checkpoint N is the finish. &nbsp;Bessie is supposed to visit all of these checkpoints one by one, but being the lazy cow she is, she decides that she will skip up to one checkpoint in order to shorten her total journey. &nbsp;She cannot skip checkpoints 1 or N, however, since that would be too noticeable.<\/p>\r\n\r\n<p>Please help Bessie find the minimum distance that she has to run if she can skip up to one checkpoint. &nbsp;<\/p>\r\n\r\n<p>Note that since the course is set in a downtown area with a grid of streets, the distance between two checkpoints at locations (x1, y1) and (x2, y2) is given by |x1-x2| + |y1-y2|. &nbsp;This way of measuring distance -- by the difference in x plus the difference in y -- is sometimes known as &quot;Manhattan&quot; distance because it reflects the fact that in a downtown grid, you can travel parallel to the x or y axes, but you cannot travel along a direct line &quot;as the crow flies&quot;.<\/p>\r\n","input":"<p>The first line gives the value of N.<\/p>\r\n\r\n<p>The next N lines each contain two space-separated integers, x and y, representing a checkpoint (-1000 &lt;= x &lt;= 1000, -1000 &lt;= y &lt;= 1000). The checkpoints are given in the order that they must be visited. Note that the course might cross over itself several times, with several checkpoints occurring at the same physical location. &nbsp;When Bessie skips such a checkpoint, she only skips one instance of the checkpoint -- she does not skip every checkpoint occurring at the same location.<\/p>\r\n","output":"<p>Output the minimum distance that Bessie can run by skipping up to one checkpoint. &nbsp;Don&#39;t forget to end your output with a newline. &nbsp;In the sample case shown here, skipping the checkpoint at (8, 3) leads to the minimum total distance of 14.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]