시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

상근이는 매우 큰 저택에 갇혔다. 이 저택은 정사각형 모양의 방이 격자 모양으로 배치되어 있고, N행 M열 형태이다. 왼쪽으로부터 x(1 ≤ x ≤ M)번째, 아래쪽으로부터 y(1 ≤ y ≤ N)번째 방을 (x,y)라고 한다.

모든 인접한 방의 사이에는 문이 있다. 문은 열려있을 수도 있고, 닫혀있을 수도 있다. 다른 방으로 이동하는데 걸리는 시간(문을 통과하는데 걸리는 시간)은 1분이다. 상근이는 항상 열려있는 문으로만 이동할 수 있고, 개폐 상태를 바꿀 수는 없다.

어떤 방의 중앙에는 스위치가 있다. 이 스위치를 1분동안 누르고 있으면, 집에 있는 모든 문의 개폐 상태가 바뀌게 된다. 즉, 열려있던 문은 닫히게 되고, 닫혀있던 문은 열리게 된다.

저택의 크기와 스위치가 있는 방의 정보가 주어진다. 상근이는 지금 (1,1)방의 중앙에 있고, (M,N)방의 중앙으로 이동하려고 한다. 이때, 이동할 수 있는 가장 빠른 시간을 구하는 프로그램을 작성하시오. 

가장 처음에 위아래로 인접한 방의 문만 열려있고, 나머지 문은 모두 닫혀있다.

입력

첫째 줄에 집의 크기 M, N과 스위치가 있는 방의 수 K가 주어진다. 둘째 줄부터 K개 줄에는 스위치가 있는 방의 위치 (xi, yi)가 주어진다. (2 ≤ M,N ≤ 100,000, 1 ≤ K ≤ 200,000)

출력

첫째 줄에 가장 빠른 시간을 출력한다. 만약, (M,N)에 도착할 수 없는 경우에는 -1을 출력한다.

예제 입력 1

3 2 1
1 2

예제 출력 1

4

(1,1)번에서 (3,2)으로 4분만에 이동할 수 있다.

  1. (1,2)로 이동
  2. (1,2)에 있는 스위치를 누른다.
  3. (2,2)로 이동
  4. (3,2)로 이동

집의 모습은 아래 그림에 나타나 있다. ×는 상근이의 위치, ○는 스위치이다. 

예제 입력 2

3 2 1
2 1

예제 출력 2

-1

예제 입력 3

8 9 15
3 1
3 2
3 7
3 8
1 1
4 5
4 3
5 6
5 8
6 3
6 2
7 5
8 9
8 6
8 5

예제 출력 3

25

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M,N &le; 100,000, 1 &le; K &le; 200,000)<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uac00\uc7a5 \ube60\ub978 \uc2dc\uac04\uc744 \ucd9c\ub825\ud55c\ub2e4. \ub9cc\uc57d, (M,N)\uc5d0 \ub3c4\ucc29\ud560 \uc218 \uc5c6\ub294 \uacbd\uc6b0\uc5d0\ub294 -1\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean","sample_explain_1":"<p>(1,1)\ubc88\uc5d0\uc11c (3,2)\uc73c\ub85c 4\ubd84\ub9cc\uc5d0 \uc774\ub3d9\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>(1,2)\ub85c \uc774\ub3d9<\/li>\r\n\t<li>(1,2)\uc5d0 \uc788\ub294 \uc2a4\uc704\uce58\ub97c \ub204\ub978\ub2e4.<\/li>\r\n\t<li>(2,2)\ub85c \uc774\ub3d9<\/li>\r\n\t<li>(3,2)\ub85c \uc774\ub3d9<\/li>\r\n<\/ol>\r\n\r\n<p>\uc9d1\uc758 \ubaa8\uc2b5\uc740 \uc544\ub798 \uadf8\ub9bc\uc5d0 \ub098\ud0c0\ub098 \uc788\ub2e4. &times;\ub294 \uc0c1\uadfc\uc774\uc758 \uc704\uce58, \u25cb\ub294 \uc2a4\uc704\uce58\uc774\ub2e4.&nbsp;<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/804fa677-fe65-436f-b12d-ebce5414f015\/-\/preview\/\" style=\"width: 636px; height: 80px;\" \/><\/p>\r\n","sample_explain_3":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/e04a6316-c56b-463b-ae73-9253ddd212c8\/-\/preview\/\" style=\"width: 279px; height: 314px;\" \/><\/p>\r\n"},{"problem_id":"5529","problem_lang":"2","title":"\u73fe\u4ee3\u7684\u306a\u5c4b\u6577 (Modern Mansion)","description":"<p>\u3042\u306a\u305f\u306f\uff0c\u3042\u308b\u5927\u304d\u306a\u5c4b\u6577\u306b\u8ff7\u3044\u8fbc\u3093\u3067\u3057\u307e\u3063\u305f\uff0e\u3053\u306e\u5c4b\u6577\u306f\u6b63\u65b9\u5f62\u306e\u90e8\u5c4b\u304c\u6771\u897f\u5357\u5317\u306b\u683c\u5b50\u72b6\u306b\uff0c\u6771\u897f\u65b9\u5411\u306b M \u5217\uff0c\u5357\u5317\u65b9\u5411\u306b N \u884c\u306e\u5408\u8a08 M \u0002 N \u500b\u4e26\u3093\u3060\u69cb\u9020\u3092\u3057\u3066\u3044\u308b\uff0e\u897f\u304b\u3089 x \u5217\u76ee (1 &le; x &le; M)\uff0c\u5357\u304b\u3089 y \u884c\u76ee (1 &le; y &le; N) \u306b\u3042\u308b\u90e8\u5c4b\u3092 (x, y) \u3067\u8868\u3059\uff0e<\/p>\r\n\r\n<p>\u6771\u897f\u5357\u5317\u306b\u96a3\u308a\u5408\u3046 2 \u90e8\u5c4b\u306e\u9593\u306f\uff0c\u58c1\u306e\u4e2d\u592e\u306b\u3042\u308b\u6249\u306b\u3088\u308a\u7d50\u3070\u308c\u3066\u3044\u308b\uff0e\u305d\u308c\u305e\u308c\u306e\u6249\u306f\uff0c\u9589\u3058\u3066\u3044\u3066\u901a\u884c\u4e0d\u53ef\u80fd\u306a\u72b6\u614b\u304b\uff0c\u958b\u3044\u3066\u3044\u3066\u901a\u884c\u53ef\u80fd\u306a\u72b6\u614b\u306e\u3044\u305a\u308c\u304b\u306b\u3042\u308b\uff0e\u6249\u304c\u958b\u3044\u3066\u3044\u308b\u3068\u304d\uff0c\u305d\u308c\u3089\u306e\u90e8\u5c4b\u306e\u4e2d\u592e\u9593\u3092\u79fb\u52d5\u3059\u308b\u306e\u306b 1 \u5206\u9593\u304b\u304b\u308b\uff0e\u307e\u305f\uff0c\u3044\u304f\u3064\u304b\u306e\u90e8\u5c4b\u306e\u4e2d\u592e\u306b\u306f\u30b9\u30a4\u30c3\u30c1\u304c\u3042\u308a\uff0c\u30b9\u30a4\u30c3\u30c1\u30921 \u5206\u9593\u62bc\u3057\u7d9a\u3051\u308b\u3068\uff0c\u5c4b\u6577\u5185\u306e\u3059\u3079\u3066\u306e\u6249\u306e\u958b\u9589\u306e\u72b6\u614b\u304c\u5207\u308a\u66ff\u308f\u308b\uff0e<\/p>\r\n\r\n<p>\u4eca\uff0c\u6771\u897f\u306b\u96a3\u308a\u5408\u3046 2 \u90e8\u5c4b\u3092\u7d50\u3076\u3059\u3079\u3066\u306e\u6249\u306f\u9589\u3058\u3066\u3044\u3066\uff0c\u5357\u5317\u306b\u96a3\u308a\u5408\u3046 2 \u90e8\u5c4b\u3092\u7d50\u3076\u3059\u3079\u3066\u306e\u6249\u306f\u958b\u3044\u3066\u3044\u308b\uff0e\u3042\u306a\u305f\u306f\u4eca\u90e8\u5c4b (1, 1) \u306e\u4e2d\u592e\u306b\u3044\u3066\uff0c\u90e8\u5c4b (M, N) \u306e\u4e2d\u592e\u307e\u3067\u6700\u77ed\u6642\u9593\u3067\u79fb\u52d5\u3057\u305f\u3044\uff0e<\/p>\r\n\r\n<p>\u5c4b\u6577\u306e\u5927\u304d\u3055 M, N \u304a\u3088\u3073\uff0c\u30b9\u30a4\u30c3\u30c1\u306e\u3042\u308b K \u500b\u306e\u90e8\u5c4b\u306e\u4f4d\u7f6e (X<sub>1<\/sub>, Y<sub>1<\/sub>),(X<sub>2<\/sub>, Y<sub>2<\/sub>), ... , (X<sub>K<\/sub>, Y<sub>K<\/sub>) \u304c\u4e0e\u3048\u3089\u308c\u308b\uff0e\u6771\u897f\u306b\u96a3\u308a\u5408\u3046 2 \u90e8\u5c4b\u3092\u7d50\u3076\u3059\u3079\u3066\u306e\u6249\u306f\u9589\u3058\u3066\u3044\u3066\uff0c\u5357\u5317\u306b\u96a3\u308a\u5408\u3046 2 \u90e8\u5c4b\u3092\u7d50\u3076\u3059\u3079\u3066\u306e\u6249\u306f\u958b\u3044\u3066\u3044\u308b\u72b6\u614b\u304b\u3089\u59cb\u3081\u3066\uff0c\u90e8\u5c4b (1, 1) \u306e\u4e2d\u592e\u304b\u3089\u90e8\u5c4b (M, N) \u306e\u4e2d\u592e\u307e\u3067\u79fb\u52d5\u3059\u308b\u306e\u306b\u6700\u77ed\u3067\u4f55\u5206\u304b\u304b\u308b\u304b\u3092\u6c42\u3081\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f5c\u6210\u305b\u3088\uff0e\u305f\u3060\u3057\uff0c\u90e8\u5c4b (M, N) \u306b\u8fbf\u308a\u7740\u304f\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u3068\u304d\u306f\u305d\u308c\u3092\u6307\u6458\u305b\u3088\uff0e<\/p>\r\n","input":"<p>\u6a19\u6e96\u5165\u529b\u304b\u3089\u4ee5\u4e0b\u306e\u30c7\u30fc\u30bf\u3092\u8aad\u307f\u8fbc\u3081\uff0e<\/p>\r\n\r\n<ul>\r\n\t<li>1 \u884c\u76ee\u306b\u306f\uff0c\u6574\u6570 M, N, K \u304c\u7a7a\u767d\u3092\u533a\u5207\u308a\u3068\u3057\u3066\u66f8\u304b\u308c\u3066\u3044\u308b\uff0eM \u306f\u5c4b\u6577\u306e\u6771\u897f\u65b9\u5411\u306e\u90e8\u5c4b\u306e\u500b\u6570\uff0cN \u306f\u5c4b\u6577\u306e\u5357\u5317\u65b9\u5411\u306e\u90e8\u5c4b\u306e\u500b\u6570\uff0cK \u306f\u30b9\u30a4\u30c3\u30c1\u306e\u3042\u308b\u90e8\u5c4b\u306e\u500b\u6570\u3092\u8868\u3059\uff0e<\/li>\r\n\t<li>\u7d9a\u304f K \u884c\u306e\u3046\u3061\u306e i \u884c\u76ee (1 &le; i &le; K) \u306b\u306f\uff0c\u6574\u6570 X<sub>i<\/sub>, Y<sub>i<\/sub> \u304c\u7a7a\u767d\u3092\u533a\u5207\u308a\u3068\u3057\u3066\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e\u3053\u308c\u306f\uff0c\u90e8\u5c4b (X<sub>i<\/sub>, Y<sub>i<\/sub>) \u306e\u4e2d\u592e\u306b\u30b9\u30a4\u30c3\u30c1\u304c\u3042\u308b\u3053\u3068\u3092\u8868\u3059\uff0eK \u500b\u306e\u7d44 (X<sub>1<\/sub>, Y<sub>1<\/sub>), (X<sub>2<\/sub>, Y<sub>2<\/sub>), ... , (X<sub>K<\/sub>, Y<sub>K<\/sub>) \u306f\u4e92\u3044\u306b\u7570\u306a\u308b\uff0e<\/li>\r\n<\/ul>\r\n","output":"<p>\u6a19\u6e96\u51fa\u529b\u306b\uff0c\u79fb\u52d5\u306b\u6700\u77ed\u3067\u4f55\u5206\u304b\u304b\u308b\u304b\u3092\u8868\u3059\u6574\u6570\u3092 1 \u884c\u3067\u51fa\u529b\u305b\u3088\uff0e\u305f\u3060\u3057\uff0c\u90e8\u5c4b (M, N) \u306b\u8fbf\u308a\u7740\u304f\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u3068\u304d\u306f\u4ee3\u308f\u308a\u306b\u6574\u6570 1 \u3092\u51fa\u529b\u305b\u3088\uff0e<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Japanese","limit":"<ul>\r\n\t<li>2 &le; M &le; 100 000 \u5c4b\u6577\u306e\u6771\u897f\u65b9\u5411\u306e\u90e8\u5c4b\u306e\u500b\u6570<\/li>\r\n\t<li>2 &le; N &le; 100 000 \u5c4b\u6577\u306e\u5357\u5317\u65b9\u5411\u306e\u90e8\u5c4b\u306e\u500b\u6570<\/li>\r\n\t<li>1 &le; K &le; 200 000 \u30b9\u30a4\u30c3\u30c1\u306e\u3042\u308b\u90e8\u5c4b\u306e\u500b\u6570<\/li>\r\n\t<li>1 &le; X<sub>i<\/sub> &le; M \u30b9\u30a4\u30c3\u30c1\u306e\u3042\u308b\u90e8\u5c4b\u306e\u6771\u897f\u65b9\u5411\u306e\u4f4d\u7f6e<\/li>\r\n\t<li>1 &le; Y<sub>i<\/sub> &le; N \u30b9\u30a4\u30c3\u30c1\u306e\u3042\u308b\u90e8\u5c4b\u306e\u5357\u5317\u65b9\u5411\u306e\u4f4d\u7f6e<\/li>\r\n<\/ul>\r\n","sample_explain_1":"<p>\u3053\u306e\u4f8b\u3067\u306f\uff0c\u4ee5\u4e0b\u306e\u884c\u52d5\u306b\u3088\u3063\u3066 4 \u5206\u9593\u3067\u90e8\u5c4b (1, 1) \u306e\u4e2d\u592e\u304b\u3089\u90e8\u5c4b (3, 2) \u306e\u4e2d\u592e\u3078\u79fb\u52d5\u3059\u308b\u3053\u3068\u304c\u3067\u304d\uff0c \u3053\u308c\u304c\u6700\u77ed\u3067\u3042\u308b\uff0e<\/p>\r\n\r\n<ol>\r\n\t<li>\u90e8\u5c4b (1, 2) \u306e\u4e2d\u592e\u3078\u79fb\u52d5\u3059\u308b\uff0e<\/li>\r\n\t<li>\u90e8\u5c4b (1, 2) \u306e\u4e2d\u592e\u306e\u30b9\u30a4\u30c3\u30c1\u3092\u62bc\u3059\uff0e<\/li>\r\n\t<li>\u90e8\u5c4b (2, 2) \u306e\u4e2d\u592e\u3078\u79fb\u52d5\u3059\u308b\uff0e<\/li>\r\n\t<li>\u90e8\u5c4b (3, 2) \u306e\u4e2d\u592e\u3078\u79fb\u52d5\u3059\u308b\uff0e<\/li>\r\n<\/ol>\r\n\r\n<p>\u3053\u306e\u3068\u304d\u306e\u5c4b\u6577\u306e\u69d8\u5b50\u304c\u4ee5\u4e0b\u306e\u56f3\u306b\u8868\u3055\u308c\u3066\u3044\u308b\uff0e\u56f3\u3067\u306f\u53f3\u65b9\u5411\u304c\u6771\uff0c\u4e0a\u65b9\u5411\u304c\u5317\u3067\u3042\u308a\uff0c&times;\u5370\u306f\u3042\u306a \u305f\u306e\u4f4d\u7f6e\uff0c\u25cb\u5370\u306f\u30b9\u30a4\u30c3\u30c1\u3092\u8868\u3059\uff0e<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/804fa677-fe65-436f-b12d-ebce5414f015\/-\/preview\/\" style=\"width: 636px; height: 80px;\" \/><\/p>\r\n","sample_explain_2":"<p>\u3053\u306e\u4f8b\u3067\u306f\uff0c\u3042\u306a\u305f\u306f\u90e8\u5c4b (3, 2) \u306b\u8fbf\u308a\u7740\u304f\u3053\u3068\u304c\u3067\u304d\u306a\u3044\uff0e<\/p>\r\n","sample_explain_3":"<p>\u3053\u306e\u4f8b\u3067\u306f\uff0c\u6700\u521d\u306e\u5c4b\u6577\u306e\u69d8\u5b50\u306f\u4ee5\u4e0b\u306e\u56f3\u306e\u3088\u3046\u306b\u306a\u3063\u3066\u3044\u308b\uff0e\u90e8\u5c4b (1, 1) \u3084\u90e8\u5c4b (M, N) \u306e\u4e2d\u592e\u306b\u30b9\u30a4\u30c3 \u30c1\u304c\u3042\u308b\u53ef\u80fd\u6027\u3082\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u305b\u3088\uff0e<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/e04a6316-c56b-463b-ae73-9253ddd212c8\/-\/preview\/\" style=\"width: 279px; height: 314px;\" \/><\/p>\r\n"}]

출처

Olympiad > Japanese Olympiad in Informatics > JOI 2013 3번