시간 제한메모리 제한제출정답맞힌 사람정답 비율
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문제

서강대학교의 축제 기간에 상근이는 매년 AS관 복도에 화려한 장식을 꾸민다. 장식은 전구 N개로 이루어져 있고, 전구는 왼쪽에서 오른쪽으로 일렬로 배열되어 있다. 각 전구는 불이 켜있을 수 있고, 꺼져있을 수도 있다.

상근이는 이 전구를 조작하기 위해서, 집에서 전구를 조작하는 기계를 가지고 왔다. 이 기계는 어떤 구간의 전구를 지정하면, 불이 켜있는 전구의 불을 끄고, 꺼져있는 전구의 불을 켜는 기능이 있다. 하지만, 이 기계는 상당히 오래된 기계로, 한 번 사용하면 다음 해까지 더 이상 사용할 수 없다.

서강대학교 학생들은 불이 켜있는 전구와 꺼져있는 전구가 번갈아가면서 나타나는 패턴을 좋아한다. 이러한 패턴을 교대 패턴이라고 한다. 따라서, 상근이는 이 기계를 1번만 사용해서 가장 긴 교대 패턴을 만들기로 했다.

예를 들어, 전구가 아래와 같이 배열되어 있다고 하자. (○는 불이 들어와 있는 전구, ●는 꺼져있는 전구)

○ ○ ● ● ○ ● ○ ○ ○ ●

4번째부터 7번째까지 4개 전구에 기계를 사용하면 아래와 같이 된다.

○ ○ ● ○ ● ○ ● ○ ○ ●

위의 경우에는 2번째부터 8번째까지 전구가 길이가 7인 교대 패턴을 이룬다.

또, 8번째 전구에만 기계를 조작하면 아래와 같이 된다.

○ ○ ● ● ○ ● ○ ● ○ ●

이렇게 되면, 4번째부터 10번째까지 전구가 길이가 7인 교대 패턴을 만든다.

즉, 기계를 최대 한 번만 사용해서 길이가 8 이상인 교대 패턴을 만들 수 없다.

전구의 정보가 주어졌을 때, 기계를 최대 한 번 사용해서 얻을 수 있는 가장 긴 교대 패턴의 길이를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 전구의 개수 N이 주어진다. (2 ≤ N ≤ 100,000)

두 번째 줄에는 전구의 상태가 왼쪽 전구부터 순서대로 주어진다. 전구의 상태는 1 또는 0이며, 1은 불이 켜져있는 상태, 0은 불이 꺼져있는 상태이다.

출력

첫째 줄에 상근이가 기계를 최대 한 번 사용해서 얻을 수 있는 가장 긴 교대 패턴의 길이를 출력한다.

예제 입력 1

10
1 1 0 0 1 0 1 1 1 0

예제 출력 1

7

예제 입력 2

10
1 0 0 0 0 1 0 1 0 1

예제 출력 2

8

예제 입력 3

5
1 1 0 1 1

예제 출력 3

5

예제 입력 4

3
0 1 0

예제 출력 4

3
[{"problem_id":"5527","problem_lang":"0","title":"\uc804\uad6c \uc7a5\uc2dd","description":"<p>\uc11c\uac15\ub300\ud559\uad50\uc758 \ucd95\uc81c \uae30\uac04\uc5d0 \uc0c1\uadfc\uc774\ub294 \ub9e4\ub144 AS\uad00 \ubcf5\ub3c4\uc5d0 \ud654\ub824\ud55c \uc7a5\uc2dd\uc744 \uafb8\ubbfc\ub2e4. \uc7a5\uc2dd\uc740 \uc804\uad6c N\uac1c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, \uc804\uad6c\ub294 \uc67c\ucabd\uc5d0\uc11c \uc624\ub978\ucabd\uc73c\ub85c \uc77c\ub82c\ub85c \ubc30\uc5f4\ub418\uc5b4 \uc788\ub2e4. \uac01 \uc804\uad6c\ub294 \ubd88\uc774 \ucf1c\uc788\uc744 \uc218 \uc788\uace0, \uaebc\uc838\uc788\uc744 \uc218\ub3c4 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\ub294 \uc774 \uc804\uad6c\ub97c \uc870\uc791\ud558\uae30 \uc704\ud574\uc11c, \uc9d1\uc5d0\uc11c \uc804\uad6c\ub97c \uc870\uc791\ud558\ub294 \uae30\uacc4\ub97c \uac00\uc9c0\uace0 \uc654\ub2e4. \uc774 \uae30\uacc4\ub294 \uc5b4\ub5a4 \uad6c\uac04\uc758 \uc804\uad6c\ub97c \uc9c0\uc815\ud558\uba74, \ubd88\uc774 \ucf1c\uc788\ub294 \uc804\uad6c\uc758 \ubd88\uc744 \ub044\uace0, \uaebc\uc838\uc788\ub294 \uc804\uad6c\uc758 \ubd88\uc744 \ucf1c\ub294 \uae30\ub2a5\uc774 \uc788\ub2e4. \ud558\uc9c0\ub9cc, \uc774 \uae30\uacc4\ub294 \uc0c1\ub2f9\ud788 \uc624\ub798\ub41c \uae30\uacc4\ub85c, \ud55c \ubc88 \uc0ac\uc6a9\ud558\uba74 \ub2e4\uc74c \ud574\uae4c\uc9c0 \ub354 \uc774\uc0c1 \uc0ac\uc6a9\ud560 \uc218 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\uc11c\uac15\ub300\ud559\uad50 \ud559\uc0dd\ub4e4\uc740 \ubd88\uc774 \ucf1c\uc788\ub294 \uc804\uad6c\uc640 \uaebc\uc838\uc788\ub294 \uc804\uad6c\uac00 \ubc88\uac08\uc544\uac00\uba74\uc11c \ub098\ud0c0\ub098\ub294 \ud328\ud134\uc744 \uc88b\uc544\ud55c\ub2e4. \uc774\ub7ec\ud55c \ud328\ud134\uc744 \uad50\ub300 \ud328\ud134\uc774\ub77c\uace0 \ud55c\ub2e4. \ub530\ub77c\uc11c, \uc0c1\uadfc\uc774\ub294 \uc774 \uae30\uacc4\ub97c 1\ubc88\ub9cc \uc0ac\uc6a9\ud574\uc11c \uac00\uc7a5 \uae34 \uad50\ub300 \ud328\ud134\uc744 \ub9cc\ub4e4\uae30\ub85c \ud588\ub2e4.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, \uc804\uad6c\uac00 \uc544\ub798\uc640 \uac19\uc774 \ubc30\uc5f4\ub418\uc5b4 \uc788\ub2e4\uace0 \ud558\uc790. (\u25cb\ub294 \ubd88\uc774 \ub4e4\uc5b4\uc640 \uc788\ub294 \uc804\uad6c, \u25cf\ub294 \uaebc\uc838\uc788\ub294 \uc804\uad6c)<\/p>\r\n\r\n<p>\u25cb \u25cb \u25cf \u25cf \u25cb \u25cf \u25cb \u25cb \u25cb \u25cf<\/p>\r\n\r\n<p>4\ubc88\uc9f8\ubd80\ud130 7\ubc88\uc9f8\uae4c\uc9c0 4\uac1c \uc804\uad6c\uc5d0 \uae30\uacc4\ub97c \uc0ac\uc6a9\ud558\uba74 \uc544\ub798\uc640 \uac19\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\u25cb \u25cb \u25cf \u25cb \u25cf \u25cb \u25cf \u25cb \u25cb \u25cf<\/p>\r\n\r\n<p>\uc704\uc758 \uacbd\uc6b0\uc5d0\ub294 2\ubc88\uc9f8\ubd80\ud130 8\ubc88\uc9f8\uae4c\uc9c0 \uc804\uad6c\uac00 \uae38\uc774\uac00 7\uc778 \uad50\ub300 \ud328\ud134\uc744 \uc774\ub8ec\ub2e4.<\/p>\r\n\r\n<p>\ub610, 8\ubc88\uc9f8 \uc804\uad6c\uc5d0\ub9cc \uae30\uacc4\ub97c \uc870\uc791\ud558\uba74 \uc544\ub798\uc640 \uac19\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\u25cb \u25cb \u25cf \u25cf \u25cb \u25cf \u25cb \u25cf \u25cb \u25cf<\/p>\r\n\r\n<p>\uc774\ub807\uac8c \ub418\uba74, 4\ubc88\uc9f8\ubd80\ud130 10\ubc88\uc9f8\uae4c\uc9c0 \uc804\uad6c\uac00 \uae38\uc774\uac00 7\uc778 \uad50\ub300 \ud328\ud134\uc744 \ub9cc\ub4e0\ub2e4.<\/p>\r\n\r\n<p>\uc989, \uae30\uacc4\ub97c \ucd5c\ub300 \ud55c \ubc88\ub9cc \uc0ac\uc6a9\ud574\uc11c \uae38\uc774\uac00 8 \uc774\uc0c1\uc778 \uad50\ub300 \ud328\ud134\uc744 \ub9cc\ub4e4 \uc218 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\uc804\uad6c\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uae30\uacc4\ub97c \ucd5c\ub300 \ud55c \ubc88 \uc0ac\uc6a9\ud574\uc11c \uc5bb\uc744 \uc218 \uc788\ub294 \uac00\uc7a5 \uae34 \uad50\ub300 \ud328\ud134\uc758 \uae38\uc774\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc804\uad6c\uc758 \uac1c\uc218 N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (2 &le; N &le; 100,000)<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0\ub294 \uc804\uad6c\uc758 \uc0c1\ud0dc\uac00 \uc67c\ucabd \uc804\uad6c\ubd80\ud130 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \uc804\uad6c\uc758 \uc0c1\ud0dc\ub294 1 \ub610\ub294 0\uc774\uba70, 1\uc740 \ubd88\uc774 \ucf1c\uc838\uc788\ub294 \uc0c1\ud0dc, 0\uc740 \ubd88\uc774 \uaebc\uc838\uc788\ub294 \uc0c1\ud0dc\uc774\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc0c1\uadfc\uc774\uac00 \uae30\uacc4\ub97c \ucd5c\ub300 \ud55c \ubc88 \uc0ac\uc6a9\ud574\uc11c \uc5bb\uc744 \uc218 \uc788\ub294 \uac00\uc7a5 \uae34 \uad50\ub300 \ud328\ud134\uc758 \uae38\uc774\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"5527","problem_lang":"2","title":"\u96fb\u98fe (Illumination)","description":"<p>JOI \u9ad8\u6821\u306e\u6587\u5316\u796d\u3067\u306f\u6bce\u5e74\u5eca\u4e0b\u306b\u96fb\u98fe\u304c\u98fe\u3089\u308c\u308b\uff0e\u96fb\u98fe\u306f N \u500b\u306e\u96fb\u7403\u3067\u69cb\u6210\u3055\u308c\u3066\u304a\u308a\uff0c\u96fb\u7403\u306f\u5eca\u4e0b\u306e\u897f\u5074\u304b\u3089\u6771\u5074\u306b\u4e00\u5217\u306b\u4e26\u3093\u3067\u3044\u308b\uff0e\u5404\u96fb\u7403\u306f\u660e\u304b\u308a\u304c\u3064\u3044\u3066\u3044\u308b\u304b\uff0c\u3064\u3044\u3066\u3044\u306a\u3044\u304b\u306e\u3044\u305a\u308c\u304b\u306e\u72b6\u614b\u3067\u3042\u308b\uff0e<\/p>\r\n\r\n<p>JOI \u9ad8\u6821\u306e\u5009\u5eab\u306b\u306f\u96fb\u7403\u3092\u64cd\u4f5c\u3059\u308b\u6a5f\u68b0\u304c\u7720\u3063\u3066\u3044\u308b\uff0e\u3053\u306e\u6a5f\u68b0\u306f\u96fb\u98fe\u5185\u3067\u9023\u7d9a\u3057\u305f\u96fb\u7403\u3092\u6307\u5b9a\u3059\u308b\u3068\uff0c\u6307\u5b9a\u3055\u308c\u305f\u96fb\u7403\u306e\u3046\u3061\uff0c\u660e\u304b\u308a\u304c\u3064\u3044\u3066\u3044\u308b\u96fb\u7403\u5168\u3066\u3092\u660e\u304b\u308a\u304c\u3064\u3044\u3066\u3044\u306a\u3044\u72b6\u614b\u306b\u3057\uff0c\u660e\u304b\u308a\u304c\u3064\u3044\u3066\u3044\u306a\u3044\u96fb\u7403\u5168\u3066\u3092\u660e\u304b\u308a\u304c\u3064\u3044\u3066\u3044\u308b\u72b6\u614b\u306b\u3059\u308b\uff0e\u305f\u3060\u3057\uff0c\u6a5f\u68b0\u306f\u8001\u673d\u5316\u306e\u305f\u3081\uff0c1 \u56de\u3057\u304b\u4f7f\u7528\u3067\u304d\u306a\u3044\uff0e<\/p>\r\n\r\n<p>JOI 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\u25cf<\/p>\r\n\r\n<p>\u3068\u306a\u3063\u3066\u3044\u305f\u3068\u3059\u308b\uff08\u25cb\u306f\u660e\u304b\u308a\u304c\u3064\u3044\u3066\u3044\u308b\u96fb\u7403\u3092\uff0c\u25cf\u306f\u660e\u304b\u308a\u304c\u3064\u3044\u3066\u3044\u306a\u3044\u96fb\u7403\u3092\u8868\u3059\uff09\uff0e\u3053\u306e\u3068\u304d\uff0c4 \u756a\u76ee\u304b\u3089 7 \u756a\u76ee\u307e\u3067\u306e 4 \u500b\u306e\u96fb\u7403\u306b\u5bfe\u3057\u3066\u6a5f\u68b0\u3092\u64cd\u4f5c\u3059\u308b\u3068\uff0c<\/p>\r\n\r\n<p>\u25cb \u25cb \u25cf <u>\u25cb \u25cf \u25cb \u25cf<\/u> \u25cb \u25cb \u25cf<\/p>\r\n\r\n<p>\u3068\u306a\u308a\uff0c2 \u756a\u76ee\u304b\u3089 8 \u756a\u76ee\u307e\u3067\u306e\u96fb\u7403\u304c\u9577\u3055 7 \u306e\u4ea4\u4e92\u5217\u3092\u306a\u3059\uff0e<\/p>\r\n\r\n<p>\u25cb <u>\u25cb \u25cf \u25cb \u25cf \u25cb \u25cf \u25cb<\/u> \u25cb \u25cf<\/p>\r\n\r\n<p>\u307e\u305f\uff0c8 \u756a\u76ee\u306e\u96fb\u7403\u306e\u307f\u306b\u5bfe\u3057\u3066\u6a5f\u68b0\u3092\u64cd\u4f5c\u3059\u308b\u3068\uff0c<\/p>\r\n\r\n<p>\u25cb \u25cb \u25cf \u25cf \u25cb \u25cf \u25cb <u>\u25cf<\/u> \u25cb \u25cf<\/p>\r\n\r\n<p>\u3068\u306a\u308a\uff0c4 \u756a\u76ee\u304b\u3089 10 \u756a\u76ee\u307e\u3067\u306e\u96fb\u7403\u304c\u9577\u3055 7 \u306e\u4ea4\u4e92\u5217\u3092\u306a\u3059\uff0e<\/p>\r\n\r\n<p>\u25cb \u25cb \u25cf <u>\u25cf \u25cb \u25cf \u25cb \u25cf \u25cb \u25cf<\/u><\/p>\r\n\r\n<p>\u6a5f\u68b0\u3092\u6700\u5927 1 \u56de\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\uff0c\u9577\u3055\u304c 8 \u4ee5\u4e0a\u306e\u4ea4\u4e92\u5217\u3092\u4f5c\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\uff0e<\/p>\r\n\r\n<p>\u96fb\u98fe\u306e\u60c5\u5831\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\uff0c\u6a5f\u68b0\u3092\u6700\u5927 1 \u56de\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u5f97\u3089\u308c\u308b\u96fb\u7403\u306e\u914d\u5217\u306b\u542b\u307e\u308c\u308b\u4ea4\u4e92\u5217\u306e\u9577\u3055\u3068\u3057\u3066\u8003\u3048\u3089\u308c\u308b\u3082\u306e\u306e\u6700\u5927\u5024\u3092\u6c42\u3081\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f5c\u6210\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\u6574\u6570 N \u304c\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e<\/li>\r\n\t<li>2 \u884c\u76ee\u306b\u306f N \u500b\u306e 0 \u307e\u305f\u306f 1 \u304c\u7a7a\u767d\u3092\u533a\u5207\u308a\u3068\u3057\u3066\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e\u5404\u6574\u6570\u306f\u6a5f\u68b0\u3092\u64cd\u4f5c\u3059\u308b\u524d\u306b\u304a\u3051\u308b\u96fb\u7403\u306e\u60c5\u5831\u3092\u8868\u3057\u3066\u3044\u308b\uff0e\u5de6\u304b\u3089 i ( 1 &le; i &le; N ) \u756a\u76ee\u306e\u6574\u6570\u306f\u897f\u5074\u304b\u3089 i \u756a\u76ee\u306e\u96fb\u7403\u306e\u60c5\u5831\u3092\u8868\u3057\u3066\u304a\u308a\uff0c\u6574\u6570\u304c 1 \u306a\u3089\u3070\u96fb\u7403\u306e\u660e\u304b\u308a\u304c\u3064\u3044\u3066\u3044\u3066\uff0c0 \u306a\u3089\u3070\u660e\u304b\u308a\u304c\u3064\u3044\u3066\u3044\u306a\u3044\u3053\u3068\u3092\u8868\u3059\uff0e<\/li>\r\n<\/ul>\r\n\r\n<p>2 &le; N &le; 100 000 \u96fb\u98fe\u3092\u69cb\u6210\u3059\u308b\u96fb\u7403\u306e\u500b\u6570<\/p>\r\n","output":"<p>\u6a19\u6e96\u51fa\u529b\u306b\uff0c\u4f5c\u6210\u53ef\u80fd\u306a\u96fb\u7403\u306e\u5217\u306b\u542b\u307e\u308c\u308b\u4ea4\u4e92\u5217\u306e\u9577\u3055\u306e\u6700\u5927\u5024\u3092\u8868\u3059\u6574\u6570\u3092 1 \u884c\u3067\u51fa\u529b\u305b\u3088.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Japanese","sample_explain_1":"<p>\u3053\u308c\u306f\u554f\u984c\u6587\u4e2d\u3067\u8aac\u660e\u3055\u308c\u305f\u4f8b\u3067\u3042\u308b\uff0e<\/p>\r\n","sample_explain_2":"<p>\u897f\u5074\u304b\u3089 4 \u756a\u76ee\u306e\u96fb\u7403\u306e\u307f\u3092\u64cd\u4f5c\u3059\u308b\u3068\uff0c\u6700\u5927\u5024 8 \u3092\u6e80\u305f\u3059\u4ea4\u4e92\u5217\u304c\u5f97\u3089\u308c\u308b\uff0e<\/p>\r\n","sample_explain_3":"<p>\u897f\u5074\u304b\u3089\u6570\u3048\u3066 2 \u756a\u76ee\u304b\u3089 4 \u756a\u76ee\u307e\u3067\u306e\u96fb\u7403\u3092\u64cd\u4f5c\u3059\u308b\u3068\uff0c\u5168\u3066\u306e\u96fb\u7403\u304b\u3089\u306a\u308b\u4ea4\u4e92\u5217\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067 \u304d\u308b\uff0e<\/p>\r\n","sample_explain_4":"<p>\u6a5f\u68b0\u3092\u4f7f\u7528\u3057\u306a\u304f\u3066\u3082\u826f\u3044\u5834\u5408\u304c\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u305b\u3088\uff0e<\/p>\r\n"}]

출처

Olympiad > Japanese Olympiad in Informatics > JOI 2012/2013 1번