시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 55 6 6 31.579%

문제

상근이는 지금 사악한 토끼들에게 위협받고 있다. 다행히도 상근이는 젊은 시절 편의점 아르바이트로 어마어마한 돈을 모은 덕분에 집에 초고성능 감시카메라를 설치할 수가 있다. 이 카메라는 매우 섬세하게 영상을 분석하여 몇 개의 점과 선으로 이루어진 영상을 전송해 준다. 하지만, 이 점과 선들로는 지금 집에 토끼가 들어왔는지 안전한지의 여부를 명확히 구분할 수가 없기 때문에 상근이는 마음 놓고 잠을 잘 수가 없다.

상근이는 두 가지 사실을 알고 있다. 모든 토끼는 네 개의 발을 갖고 있으며, 그 네 개의 발을 잇는 몸통으로 이루어져 있다는 것이다.

이제 상근이를 위해 감시 카메라가 포착한 영상에 토끼가 있을 가능성이 있는지를 판정하는 프로그램을 작성해주도록 하자.

입력

입력은 여러 테스트 케이스로 이루어져 있다.

테스트 케이스의 첫 줄에는 두 정수 n과 m이 공백으로 구분되어 주어진다. (0 ≤ n ≤ 10 000, 0 ≤ m ≤ 20 000)

n은 영상에 등장한 점의 갯수이며, m은 선의 갯수이다.

다음 m줄엔 두 정수 x와 y가 주어진다. (1 ≤ x, y ≤ n)

이는 x번째 점과 y번째 점을 직접 잇는 선분이 존재한다는 의미이다.

모든 테스트 케이스에 대해 어떤 두 점도 두 개 이상의 선분으로 연결되어 있지 않으며, 어떤 점도 자기 자신과 연결되어 있지 않다.

출력

각각의 입력에 대해, 만일 토끼가 존재할 가능성이 있다면 "YES" 를, 토끼가 없다면 "NO" 를 출력하면 된다. 만일 영상이 연결되어 있는 상태를 유지하며 몇 개의 점과 선을 제거하고 정확히 4개의 발을 가진 몸통을 만들 수 있다면, 토끼는 존재할 수 있다.

영상이 연결되어 있다는 것은 모든 두 점이 하나 혹은 그 이상의 선을 통해 연결되어 있다는 것을 의미하며, 발이라는 것은 정확히 하나의 다른 점과만 연결되며 단 하나의 선분으로 직접 연결되어 있는 한 점을 의미한다.

예제 입력 1

2 1
1 2
5 4
1 2
1 3
1 4
1 5

예제 출력 1

NO
YES
[{"problem_id":"9275","problem_lang":"0","title":"\ud1a0\ub07c\uc640 \uc0c1\uadfc","description":"<p>\uc0c1\uadfc\uc774\ub294 \uc9c0\uae08 \uc0ac\uc545\ud55c \ud1a0\ub07c\ub4e4\uc5d0\uac8c \uc704\ud611\ubc1b\uace0 \uc788\ub2e4. \ub2e4\ud589\ud788\ub3c4 \uc0c1\uadfc\uc774\ub294 \uc80a\uc740 \uc2dc\uc808 \ud3b8\uc758\uc810 \uc544\ub974\ubc14\uc774\ud2b8\ub85c \uc5b4\ub9c8\uc5b4\ub9c8\ud55c \ub3c8\uc744 \ubaa8\uc740 \ub355\ubd84\uc5d0 \uc9d1\uc5d0 \ucd08\uace0\uc131\ub2a5&nbsp;\uac10\uc2dc\uce74\uba54\ub77c\ub97c \uc124\uce58\ud560 \uc218\uac00 \uc788\ub2e4. \uc774&nbsp;\uce74\uba54\ub77c\ub294 \ub9e4\uc6b0 \uc12c\uc138\ud558\uac8c \uc601\uc0c1\uc744 \ubd84\uc11d\ud558\uc5ec \uba87 \uac1c\uc758 \uc810\uacfc \uc120\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc601\uc0c1\uc744 \uc804\uc1a1\ud574 \uc900\ub2e4. \ud558\uc9c0\ub9cc, \uc774 \uc810\uacfc \uc120\ub4e4\ub85c\ub294 \uc9c0\uae08 \uc9d1\uc5d0&nbsp;\ud1a0\ub07c\uac00 \ub4e4\uc5b4\uc654\ub294\uc9c0 \uc548\uc804\ud55c\uc9c0\uc758 \uc5ec\ubd80\ub97c&nbsp;\uba85\ud655\ud788 \uad6c\ubd84\ud560 \uc218\uac00 \uc5c6\uae30&nbsp;\ub54c\ubb38\uc5d0 \uc0c1\uadfc\uc774\ub294 \ub9c8\uc74c \ub193\uace0 \uc7a0\uc744 \uc798 \uc218\uac00 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\ub294 \ub450 \uac00\uc9c0&nbsp;\uc0ac\uc2e4\uc744 \uc54c\uace0 \uc788\ub2e4. \ubaa8\ub4e0 \ud1a0\ub07c\ub294 \ub124 \uac1c\uc758 \ubc1c\uc744 \uac16\uace0 \uc788\uc73c\uba70, \uadf8 \ub124 \uac1c\uc758 \ubc1c\uc744 \uc787\ub294 \ubab8\ud1b5\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4\ub294 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc774\uc81c \uc0c1\uadfc\uc774\ub97c \uc704\ud574 \uac10\uc2dc \uce74\uba54\ub77c\uac00 \ud3ec\ucc29\ud55c \uc601\uc0c1\uc5d0 \ud1a0\ub07c\uac00 \uc788\uc744 \uac00\ub2a5\uc131\uc774 \uc788\ub294\uc9c0\ub97c \ud310\uc815\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud574\uc8fc\ub3c4\ub85d \ud558\uc790.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758&nbsp;\uccab \uc904\uc5d0\ub294 \ub450 \uc815\uc218 n\uacfc m\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. (0 &le; n &le; 10 000, 0 &le; m &le; 20 000)<\/p>\r\n\r\n<p>n\uc740 \uc601\uc0c1\uc5d0 \ub4f1\uc7a5\ud55c \uc810\uc758 \uac2f\uc218\uc774\uba70, m\uc740 \uc120\uc758 \uac2f\uc218\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c m\uc904\uc5d4 \ub450 \uc815\uc218 x\uc640 y\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;(1 &le; x, y &le; n)<\/p>\r\n\r\n<p>\uc774\ub294 x\ubc88\uc9f8 \uc810\uacfc y\ubc88\uc9f8 \uc810\uc744 \uc9c1\uc811&nbsp;\uc787\ub294 \uc120\ubd84\uc774 \uc874\uc7ac\ud55c\ub2e4\ub294 \uc758\ubbf8\uc774\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574&nbsp;\uc5b4\ub5a4 \ub450 \uc810\ub3c4 \ub450 \uac1c \uc774\uc0c1\uc758 \uc120\ubd84\uc73c\ub85c \uc5f0\uacb0\ub418\uc5b4 \uc788\uc9c0 \uc54a\uc73c\uba70, \uc5b4\ub5a4 \uc810\ub3c4 \uc790\uae30 \uc790\uc2e0\uacfc \uc5f0\uacb0\ub418\uc5b4 \uc788\uc9c0 \uc54a\ub2e4.<\/p>\r\n","output":"<p>\uac01\uac01\uc758 \uc785\ub825\uc5d0 \ub300\ud574, \ub9cc\uc77c \ud1a0\ub07c\uac00 \uc874\uc7ac\ud560 \uac00\ub2a5\uc131\uc774 \uc788\ub2e4\uba74 &quot;YES&quot; \ub97c, \ud1a0\ub07c\uac00 \uc5c6\ub2e4\uba74 &quot;NO&quot; \ub97c \ucd9c\ub825\ud558\uba74 \ub41c\ub2e4. \ub9cc\uc77c \uc601\uc0c1\uc774 \uc5f0\uacb0\ub418\uc5b4 \uc788\ub294 \uc0c1\ud0dc\ub97c \uc720\uc9c0\ud558\uba70&nbsp;\uba87 \uac1c\uc758 \uc810\uacfc \uc120\uc744 \uc81c\uac70\ud558\uace0 \uc815\ud655\ud788 4\uac1c\uc758 \ubc1c\uc744 \uac00\uc9c4 \ubab8\ud1b5\uc744 \ub9cc\ub4e4 \uc218 \uc788\ub2e4\uba74, \ud1a0\ub07c\ub294 \uc874\uc7ac\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc601\uc0c1\uc774 \uc5f0\uacb0\ub418\uc5b4 \uc788\ub2e4\ub294 \uac83\uc740 \ubaa8\ub4e0 \ub450 \uc810\uc774 \ud558\ub098 \ud639\uc740 \uadf8 \uc774\uc0c1\uc758 \uc120\uc744 \ud1b5\ud574 \uc5f0\uacb0\ub418\uc5b4 \uc788\ub2e4\ub294 \uac83\uc744 \uc758\ubbf8\ud558\uba70, \ubc1c\uc774\ub77c\ub294 \uac83\uc740&nbsp;\uc815\ud655\ud788 \ud558\ub098\uc758 \ub2e4\ub978 \uc810\uacfc\ub9cc \uc5f0\uacb0\ub418\uba70 \ub2e8 \ud558\ub098\uc758 \uc120\ubd84\uc73c\ub85c \uc9c1\uc811 \uc5f0\uacb0\ub418\uc5b4 \uc788\ub294 \ud55c \uc810\uc744 \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9275","problem_lang":"1","title":"Furry Nuisance","description":"<p>In order to protect himself from evil bunnies, Freddy decided to install an automatic system to detect them in pictures from surveillance cameras. Sophisticated software detects important points in the picture and lines between them. Unfortunately, the terrain in the pictures is quite varied and lot of the points and lines are actually not bunnies.<\/p>\r\n\r\n<p>You have made the following observation: Each bunny has four paws and a body joining them. Based on this observation, write a program to decide whether a given picture can possibly contain a bunny.<\/p>\r\n","input":"<p>The input contains several test cases. The \ufb01rst line of each test case contains two integers n and m (0 &le; n &le; 10 000, 0 &le; m &le; 20 000), giving the number of points and lines in the image, respectively. Each of the m following lines contains two distinct integers x and y (1 &le; x, y &le; n), indicating that the points x and y are directly joined by a line. You may assume that each pair of points is joined by at most one direct line and that no point is directly joined with itself.<\/p>\r\n","output":"<p>For each input instance, output &ldquo;YES&rdquo; if the picture can contain a bunny, and &ldquo;NO&rdquo; otherwise. The picture can contain a bunny if it is possible to remove some of the points and lines so that the resulting image is connected and has exactly 4 paws.<\/p>\r\n\r\n<p>The image is said to be connected if (and only if) each two points are joined with each other by one or more successive lines. A paw is a point which is directly joined with exactly one other point.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]