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문제

상근이는 재환이와 함께 제주도에 여행을 가기로 했다.

제주시는 남북방향 도로 W개와 동서방향 도로 H개로 이루어져 있으며, 바둑판 모양을 이루고 있다.

남북방향 도로는 서쪽에서부터 차례대로 1, 2, ..., W가 매겨져 있고, 동서방향 도로는 남쪽에서부터 차례대로 1, 2, ..., H가 매겨져 있다. i번째 남북 도로와 j번째 동서 도로로 이루어진 교차로를 (i, j)로 나타낸다.

제주시에는 북동방향 도로도 존재한다. 가장 북쪽의 도로와 동쪽 도로에 있는 교차로를 제외한 모든 교차로에는 북동방향 도로가 존재한다. 즉, 교차로 (i,j)에서 (i-1,j-1)이나 (i+1,j+1)이 존재하는 경우에는 그 교차로로 한 번에 이동할 수 있다.

재환이는 자신이 방문하고 싶은 관광지 N개를 미리 정해왔다. i번째로 방문할 관광지는 (Xi, Yi)에 있다. 상근이는 여행에 걸리는 시간을 최소로 하기 위해서 통과해야 하는 길의 개수를 적게 하려고 한다. 관광지를 재환이가 정한 순서대로 방문하면서 지나야 하는 길의 최소 개수를 구하는 프로그램을 작성하시오.

여행은 (X1, Y1)에서 시작한다. 또한, 여행 도중에 도시 밖으로는 이동할 수 없다. 상근이와 재환이는 같은 길을 두 번 이상 통과할 수 있으며, 한 도로를 여러 번 방문하는 경우에는 방문하는 만큼 중복해서 계산한다.

입력

첫째 줄에 W, H, N이 주어진다. (2 ≤ W, H ≤ 10000, 1 ≤ N ≤ 1000)

둘째 줄부터 N개 줄에는 관광지의 위치 Xi, Yi가 주어진다.

출력

관광지를 재환이가 정한 순서대로 방문하면서 통과하는 길의 최소 개수를 출력한다. 

예제 입력 1

4 3 3
1 1
3 3
4 1

예제 출력 1

5

힌트

(1,1), (2,2), (3,3), (3,2), (4,2), (4,1) 순서로 방문하면 된다.

[{"problem_id":"10041","problem_lang":"0","title":"\uad00\uad11","description":"<p>\uc0c1\uadfc\uc774\ub294 \uc7ac\ud658\uc774\uc640 \ud568\uaed8 \uc81c\uc8fc\ub3c4\uc5d0 \uc5ec\ud589\uc744 \uac00\uae30\ub85c \ud588\ub2e4.<\/p>\r\n\r\n<p>\uc81c\uc8fc\uc2dc\ub294 \ub0a8\ubd81\ubc29\ud5a5 \ub3c4\ub85c W\uac1c\uc640 \ub3d9\uc11c\ubc29\ud5a5 \ub3c4\ub85c H\uac1c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uc73c\uba70, \ubc14\ub451\ud310 \ubaa8\uc591\uc744 \uc774\ub8e8\uace0 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ub0a8\ubd81\ubc29\ud5a5 \ub3c4\ub85c\ub294 \uc11c\ucabd\uc5d0\uc11c\ubd80\ud130 \ucc28\ub840\ub300\ub85c 1, 2, ..., W\uac00 \ub9e4\uaca8\uc838 \uc788\uace0, \ub3d9\uc11c\ubc29\ud5a5 \ub3c4\ub85c\ub294 \ub0a8\ucabd\uc5d0\uc11c\ubd80\ud130 \ucc28\ub840\ub300\ub85c 1, 2, ..., H\uac00 \ub9e4\uaca8\uc838 \uc788\ub2e4. i\ubc88\uc9f8 \ub0a8\ubd81 \ub3c4\ub85c\uc640 j\ubc88\uc9f8 \ub3d9\uc11c \ub3c4\ub85c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uad50\ucc28\ub85c\ub97c (i, j)\ub85c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p>\uc81c\uc8fc\uc2dc\uc5d0\ub294 \ubd81\ub3d9\ubc29\ud5a5 \ub3c4\ub85c\ub3c4 \uc874\uc7ac\ud55c\ub2e4. \uac00\uc7a5 \ubd81\ucabd\uc758 \ub3c4\ub85c\uc640 \ub3d9\ucabd \ub3c4\ub85c\uc5d0 \uc788\ub294 \uad50\ucc28\ub85c\ub97c \uc81c\uc678\ud55c \ubaa8\ub4e0 \uad50\ucc28\ub85c\uc5d0\ub294 \ubd81\ub3d9\ubc29\ud5a5 \ub3c4\ub85c\uac00 \uc874\uc7ac\ud55c\ub2e4. \uc989, \uad50\ucc28\ub85c (i,j)\uc5d0\uc11c (i-1,j-1)\uc774\ub098 (i+1,j+1)\uc774 \uc874\uc7ac\ud558\ub294 \uacbd\uc6b0\uc5d0\ub294 \uadf8 \uad50\ucc28\ub85c\ub85c \ud55c \ubc88\uc5d0 \uc774\ub3d9\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/2014-yo-t3-fig01-ko.png\" style=\"height:250px; width:320px\" \/><\/p>\r\n\r\n<p>\uc7ac\ud658\uc774\ub294 \uc790\uc2e0\uc774 \ubc29\ubb38\ud558\uace0 \uc2f6\uc740 \uad00\uad11\uc9c0 N\uac1c\ub97c \ubbf8\ub9ac \uc815\ud574\uc654\ub2e4. i\ubc88\uc9f8\ub85c \ubc29\ubb38\ud560 \uad00\uad11\uc9c0\ub294 (X<sub>i<\/sub>, Y<sub>i<\/sub>)\uc5d0 \uc788\ub2e4. \uc0c1\uadfc\uc774\ub294 \uc5ec\ud589\uc5d0 \uac78\ub9ac\ub294 \uc2dc\uac04\uc744 \ucd5c\uc18c\ub85c \ud558\uae30 \uc704\ud574\uc11c \ud1b5\uacfc\ud574\uc57c \ud558\ub294 \uae38\uc758 \uac1c\uc218\ub97c \uc801\uac8c \ud558\ub824\uace0 \ud55c\ub2e4. \uad00\uad11\uc9c0\ub97c \uc7ac\ud658\uc774\uac00 \uc815\ud55c \uc21c\uc11c\ub300\ub85c \ubc29\ubb38\ud558\uba74\uc11c \uc9c0\ub098\uc57c \ud558\ub294 \uae38\uc758 \ucd5c\uc18c \uac1c\uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n\r\n<p>\uc5ec\ud589\uc740 (X<sub>1<\/sub>, Y<sub>1<\/sub>)\uc5d0\uc11c \uc2dc\uc791\ud55c\ub2e4. \ub610\ud55c, \uc5ec\ud589 \ub3c4\uc911\uc5d0 \ub3c4\uc2dc \ubc16\uc73c\ub85c\ub294 \uc774\ub3d9\ud560 \uc218 \uc5c6\ub2e4. \uc0c1\uadfc\uc774\uc640 \uc7ac\ud658\uc774\ub294 \uac19\uc740 \uae38\uc744 \ub450 \ubc88 \uc774\uc0c1 \ud1b5\uacfc\ud560 \uc218 \uc788\uc73c\uba70, \ud55c \ub3c4\ub85c\ub97c \uc5ec\ub7ec \ubc88 \ubc29\ubb38\ud558\ub294 \uacbd\uc6b0\uc5d0\ub294 \ubc29\ubb38\ud558\ub294 \ub9cc\ud07c \uc911\ubcf5\ud574\uc11c \uacc4\uc0b0\ud55c\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 W, H, N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (2 &le; W, H &le; 10000, 1 &le; N &le; 1000)<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\ubd80\ud130 N\uac1c \uc904\uc5d0\ub294 \uad00\uad11\uc9c0\uc758 \uc704\uce58 X<sub>i<\/sub>, Y<sub>i<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uad00\uad11\uc9c0\ub97c \uc7ac\ud658\uc774\uac00 \uc815\ud55c \uc21c\uc11c\ub300\ub85c \ubc29\ubb38\ud558\uba74\uc11c \ud1b5\uacfc\ud558\ub294 \uae38\uc758 \ucd5c\uc18c \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.&nbsp;<\/p>\r\n","hint":"<p>(1,1), (2,2), (3,3), (3,2), (4,2), (4,1) \uc21c\uc11c\ub85c \ubc29\ubb38\ud558\uba74 \ub41c\ub2e4.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"10041","problem_lang":"2","title":"\u8d85\u90fd\u89b3\u5149 (Super Metropolis)","description":"<p>JOI \u541b\u306f\uff0cIOI \u56fd\u306b\u3042\u308b\u8d85\u90fd\u3068\u3044\u3046\u90fd\u5e02\u306e\u89b3\u5149\u30c4\u30a2\u30fc\u3092\u8a08\u753b\u3059\u308b\u3053\u3068\u306b\u306a\u3063\u305f\uff0e<\/p>\r\n\r\n<p>\u8d85\u90fd\u306f\uff0c\u5357\u5317\u65b9\u5411\u306b\u307e\u3063\u3059\u3050\u306b\u4f38\u3073\u308b W \u672c\u306e\u9053\u8def\u3068\uff0c\u6771\u897f\u65b9\u5411\u306b\u307e\u3063\u3059\u3050\u306b\u4f38\u3073\u308b H \u672c\u306e\u9053\u8def\u306b\u3088\u308a\uff0c\u7881\u76e4\u306e\u76ee\u306e\u5f62\u306b\u533a\u5206\u3051\u3055\u308c\u3066\u3044\u308b\uff0e<\/p>\r\n\r\n<p>\u5357\u5317\u65b9\u5411\u306e W \u672c\u306e\u9053\u8def\u306b\u306f\uff0c\u897f\u304b\u3089\u9806\u306b 1, 2, ... , W \u306e\u756a\u53f7\u304c\u4ed8\u3051\u3089\u308c\u3066\u3044\u308b\uff0e\u307e\u305f\uff0c\u6771\u897f\u65b9\u5411\u306e H \u672c\u306e\u9053\u8def\u306b\u306f\uff0c\u5357\u304b\u3089\u9806\u306b 1, 2, ... , H \u306e\u756a\u53f7\u304c\u4ed8\u3051\u3089\u308c\u3066\u3044\u308b\uff0e\u897f\u304b\u3089 i \u756a\u76ee\u306e\u5357\u5317\u65b9\u5411\u306e\u9053\u8def\u3068\uff0c\u5357\u304b\u3089 j \u756a\u76ee\u306e\u6771\u897f\u65b9\u5411\u306e\u9053\u8def\u3068\u306e\u4ea4\u5dee\u70b9\u3092 (i, j) \u3067\u8868\u3059\uff0e<\/p>\r\n\r\n<p>\u3055\u3089\u306b\uff0c\u4e0b\u56f3\u306e\u3088\u3046\u306b\uff0c\u5404\u4ea4\u5dee\u70b9\u304b\u3089\u306f\uff11\u3064\u5317\u6771\u306e\u4ea4\u5dee\u70b9\u3078\u306e\u9053\u304c\u3042\u308b\uff08\u6700\u3082\u5317\u306e\u9053\u8def\u4e0a\u306e\u4ea4\u5dee\u70b9\u3068\u6700\u3082\u6771\u306e\u9053\u8def\u4e0a\u306e\u4ea4\u5dee\u70b9\u3092\u9664\u304f\uff09\uff0e \u307e\u305f\uff0c\uff11\u3064\u5357\u897f\u306e\u4ea4\u5dee\u70b9\u3078\u306e\u9053\u3082\u3042\u308b\uff08\u6700\u3082\u5357\u306e\u9053\u8def\u4e0a\u306e\u4ea4\u5dee\u70b9\u3068\u6700\u3082\u897f\u306e\u9053\u8def\u4e0a\u306e\u4ea4\u5dee\u70b9\u3092\u9664\u304f\uff09\uff0e \u3059\u306a\u308f\u3061\uff0c\u4ea4\u5dee\u70b9 (i, j) \u304b\u3089\u306f\uff0c\u3082\u3057\u4ea4\u5dee\u70b9 (i - 1, j), (i + 1, j), (i, j - 1), (i, j + 1) \u304c\u3042\u308b\u3068\u304d\u306f\uff0c\u305d\u308c\u3089\u306e\u4ea4\u5dee\u70b9\u3078\uff11\u672c\u306e\u9053\u3092\u4f7f\u3063\u3066\u884c\u304f\u3053\u3068\u304c\u51fa\u6765\u308b\uff0e\u305d\u308c\u306b\u52a0\u3048\uff0c\u3082\u3057\u4ea4\u5dee\u70b9 (i - 1, j - 1), (i + 1, j + 1) \u304c\u3042\u308b\u3068\u304d\u306f\uff0c\u305d\u308c\u3089\u306e\u4ea4\u5dee\u70b9\u3078\u3082\uff11\u672c\u306e\u9053\u3092\u4f7f\u3063\u3066\u884c\u304f\u3053\u3068\u304c\u51fa\u6765\u308b\uff0e<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/2014-yo-t3-fig01.png\" style=\"height:250px; width:320px\" \/><\/p>\r\n\r\n<p>JOI \u541b\u306f\u30c4\u30a2\u30fc\u306e\u8a08\u753b\u3068\u3057\u3066\u65e2\u306b N \u500b\u306e\u89b3\u5149\u30b9\u30dd\u30c3\u30c8\u3092\u3069\u306e\u3088\u3046\u306a\u9806\u756a\u3067\u8a2a\u308c\u308b\u304b\u3092\u6c7a\u3081\u3066\u3044\u308b\uff0e i \u756a\u76ee (1 \u2266 i \u2266 N) \u306b\u8a2a\u308c\u308b\u89b3\u5149\u30b9\u30dd\u30c3\u30c8\u306f\u4ea4\u5dee\u70b9 (Xi, Yi) \u306b\u3042\u308b\uff0e JOI \u541b\u306f\uff0c\u30c4\u30a2\u30fc\u306b\u304b\u304b\u308b\u6642\u9593\u3092\u3067\u304d\u308b\u3060\u3051\u77ed\u304f\u3059\u308b\u305f\u3081\u306b\uff0c\u901a\u3089\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u9053\u306e\u672c\u6570\u3092\u5c11\u306a\u304f\u3057\u305f\u3044\uff0e \u89b3\u5149\u30b9\u30dd\u30c3\u30c8\u3092\u4e8b\u524d\u306b\u6c7a\u3081\u305f\u9806\u756a\u3067\u8a2a\u308c\u308b\u305f\u3081\u306b\u901a\u3089\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u9053\u306e\u672c\u6570\u306e\u5408\u8a08\u306e\u6700\u5c0f\u5024\u3092\u6c42\u3081\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f5c\u6210\u305b\u3088\uff0e<\/p>\r\n\r\n<p>\u305f\u3060\u3057\uff0c\u30c4\u30a2\u30fc\u306e\u958b\u59cb\u5730\u70b9\u306f\u4ea4\u5dee\u70b9 (X1, Y1) \u3067\u3042\u308b\uff0e\u307e\u305f\uff0c\u30c4\u30a2\u30fc\u306e\u9014\u4e2d\u3067\u8d85\u90fd\u306e\u5916\u3078\u79fb\u52d5\u3057\u3066\u306f\u306a\u3089\u306a\u3044\u3082\u306e\u3068\u3059\u308b\uff0e \u307e\u305f\uff0cJOI \u541b\u306f\uff0c\u89b3\u5149\u30b9\u30dd\u30c3\u30c8\u306e\u3042\u308b\u4ea4\u5dee\u70b9\u3092\uff0c\u89b3\u5149\u30b9\u30dd\u30c3\u30c8\u3092\u8a2a\u308c\u305a\u306b\u901a\u904e\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u308b\uff0e<\/p>\r\n\r\n<p><strong>\uff08\u4e88\u9078\u7af6\u6280\u5b9f\u65bd\u5f8c\u306b\u8ffd\u8a18\uff09<\/strong> \u300c\u9053\u306e\u672c\u6570\u306e\u5408\u8a08\u300d\u306b\u3064\u3044\u3066\u306e\u88dc\u8db3\uff0e\u30c4\u30a2\u30fc\u306e\u9014\u4e2d\u3067\u540c\u3058\u9053\u3092\uff12\u56de\u4ee5\u4e0a\u901a\u308b\u3053\u3068\u3082\u3067\u304d\u308b\uff0e\u305d\u306e\u5834\u5408\uff0c\u300c\u9053\u306e\u672c\u6570\u306e\u5408\u8a08\u300d\u3068\u3057\u3066\u306f\uff0c\u305d\u306e\u9053\u306b\u3064\u3044\u3066\u306f\u901a\u3063\u305f\u56de\u6570\u3060\u3051\u91cd\u8907\u3057\u3066\u6570\u3048\u308b\u3082\u306e\u3068\u3059\u308b\uff0e<\/p>\r\n","input":"<p>\u5165\u529b\u306f 1 + N \u884c\u304b\u3089\u306a\u308b\uff0e<\/p>\r\n\r\n<p>1 \u884c\u76ee\u306b\u306f\uff0c\u7a7a\u767d\u3092\u533a\u5207\u308a\u3068\u3057\u3066 3 \u3064\u306e\u6574\u6570 W, H, N (2 \u2266 W \u2266 10000, 2 \u2266 H \u2266 10000, 1 \u2266 N \u2266 1000) \u304c\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e<\/p>\r\n\r\n<p>\u7d9a\u304f N \u884c\u306e\u3046\u3061\u306e i \u884c\u76ee (1 \u2266 i \u2266 N) \u306b\u306f\uff0c2 \u3064\u306e\u6574\u6570 Xi, Yi (1 \u2266 Xi \u2266 W, 1 \u2266 Yi \u2266 H) \u304c\u7a7a\u767d\u3092\u533a\u5207\u308a\u3068\u3057\u3066\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e\u3053\u308c\u306f\uff0ci \u756a\u76ee\u306b\u8a2a\u308c\u308b\u89b3\u5149\u30b9\u30dd\u30c3\u30c8\u306e\u3042\u308b\u4ea4\u5dee\u70b9\u304c (Xi, Yi) \u3067\u3042\u308b\u3053\u3068\u3092\u8868\u3059\uff0e<\/p>\r\n","output":"<p>\u89b3\u5149\u30b9\u30dd\u30c3\u30c8\u3092\u9806\u756a\u306b\u8a2a\u308c\u308b\u305f\u3081\u306b\u901a\u308b\u9053\u306e\u672c\u6570\u306e\u5408\u8a08\u306e\u6700\u5c0f\u5024\u3092 1 \u884c\u3067\u51fa\u529b\u305b\u3088\uff0e<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"<p>\u5165\u51fa\u529b\u4f8b \u3067\u306f\uff0c\u4f8b\u3048\u3070 (1, 1), (2, 2), (3, 3), (3, 2), (4, 2), (4, 1) \u306e\u9806\u3067\u4ea4\u5dee\u70b9\u3092\u8a2a\u308c\u308c\u3070\u826f\u3044\uff0e<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"Japanese"}]

출처

Olympiad > Japanese Olympiad in Informatics > Japanese Olympiad in Informatics Qualification Round > JOI 2013/2014 예선 3번