시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 1024 MB36619516155.326%

문제

윤이는 엄청난 것을 훔쳐 갔다!

UDP 마을의 경찰인 달구와 포닉스는 윤이를 잡기 위해 출동했다. UDP 마을은 $N$개의 정점을 가진 트리 구조로 되어 있다. 트리는 $N$개의 정점과 $N-1$개의 간선으로 이루어진 연결 그래프이다. 트리에서 이웃한 정점이 하나밖에 없는 정점을 리프 노드라고 부른다.

트리의 각 정점에는 $1$번부터 $N$번까지 번호가 붙어 있다. 윤이는 정점 $a$에서 출발하고, 달구와 포닉스는 각각 정점 $b$, $c$에서 출발한다. 주어지는 세 정점은 서로 다르다. 윤이, 달구, 포닉스는 다음과 같이 번갈아 이동하며 추격전을 벌인다. 이동 도중 한 정점 위에 둘 이상이 존재해도 된다.

  • 먼저 윤이가 간선을 따라 이웃한 정점으로 이동한다.
  • 그다음 달구와 포닉스가 각각 간선을 따라 이웃한 정점으로 이동한다.

윤이는 경찰과 동일한 정점에 위치하는 즉시 경찰에게 잡힌다. 반면, 윤이가 경찰에게 잡히지 않고 리프 노드에 도달하면 즉시 이웃한 마을로 탈출할 수 있다. 윤이가 리프 노드에서 출발하는 경우도 마찬가지다.

윤이, 달구, 포닉스가 최선의 전략으로 추격전을 벌일 때, 윤이는 무사히 탈출할 수 있을까?

입력

첫 번째 줄에 UDP 마을의 정점 개수 $N$이 주어진다. ($3\le N\le 200\ 000$)

다음 $N-1$개의 줄에 트리의 간선 정보를 나타내는 정수 $u$, $v$가 주어진다. 정점 $u$와 $v$ 사이에 간선이 존재함을 나타낸다. ($1\le u,v\le N$)

그다음 줄에 윤이, 달구, 포닉스의 위치를 나타내는 정수 $a$, $b$, $c$가 주어진다. ($1\le a,b,c\le N$; $a$, $b$, $c$는 서로 다르다.)

출력

윤이가 탈출할 수 있으면 YES, 그렇지 않으면 NO를 출력한다.

예제 입력 1

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

예제 출력 1

YES

예제 입력 2

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

예제 출력 2

NO
[{"problem_id":"27924","problem_lang":"0","title":"\uc724\uc774\ub294 \uc5c4\uccad\ub09c \uac83\uc744 \ud6d4\uccd0\uac14\uc2b5\ub2c8\ub2e4","description":"<p>\uc724\uc774\ub294 \uc5c4\uccad\ub09c \uac83\uc744 \ud6d4\uccd0 \uac14\ub2e4!<\/p>\r\n\r\n<p>UDP \ub9c8\uc744\uc758 \uacbd\ucc30\uc778 \ub2ec\uad6c\uc640 \ud3ec\ub2c9\uc2a4\ub294 \uc724\uc774\ub97c \uc7a1\uae30 \uc704\ud574 \ucd9c\ub3d9\ud588\ub2e4. UDP \ub9c8\uc744\uc740 $N$\uac1c\uc758 \uc815\uc810\uc744 \uac00\uc9c4 \ud2b8\ub9ac \uad6c\uc870\ub85c \ub418\uc5b4 \uc788\ub2e4. \ud2b8\ub9ac\ub294 $N$\uac1c\uc758 \uc815\uc810\uacfc $N-1$\uac1c\uc758 \uac04\uc120\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc5f0\uacb0 \uadf8\ub798\ud504\uc774\ub2e4. \ud2b8\ub9ac\uc5d0\uc11c \uc774\uc6c3\ud55c \uc815\uc810\uc774 \ud558\ub098\ubc16\uc5d0 \uc5c6\ub294 \uc815\uc810\uc744 \ub9ac\ud504 \ub178\ub4dc\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\r\n\r\n<p>\ud2b8\ub9ac\uc758 \uac01 \uc815\uc810\uc5d0\ub294 $1$\ubc88\ubd80\ud130 $N$\ubc88\uae4c\uc9c0 \ubc88\ud638\uac00 \ubd99\uc5b4 \uc788\ub2e4. \uc724\uc774\ub294 \uc815\uc810 $a$\uc5d0\uc11c \ucd9c\ubc1c\ud558\uace0, \ub2ec\uad6c\uc640 \ud3ec\ub2c9\uc2a4\ub294 \uac01\uac01 \uc815\uc810 $b$, $c$\uc5d0\uc11c \ucd9c\ubc1c\ud55c\ub2e4. \uc8fc\uc5b4\uc9c0\ub294 \uc138 \uc815\uc810\uc740 \uc11c\ub85c \ub2e4\ub974\ub2e4. \uc724\uc774, \ub2ec\uad6c, \ud3ec\ub2c9\uc2a4\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \ubc88\uac08\uc544 \uc774\ub3d9\ud558\uba70 \ucd94\uaca9\uc804\uc744 \ubc8c\uc778\ub2e4. \uc774\ub3d9 \ub3c4\uc911 \ud55c \uc815\uc810 \uc704\uc5d0 \ub458 \uc774\uc0c1\uc774 \uc874\uc7ac\ud574\ub3c4 \ub41c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uba3c\uc800 \uc724\uc774\uac00 \uac04\uc120\uc744 \ub530\ub77c \uc774\uc6c3\ud55c \uc815\uc810\uc73c\ub85c \uc774\ub3d9\ud55c\ub2e4.<\/li>\r\n\t<li>\uadf8\ub2e4\uc74c \ub2ec\uad6c\uc640 \ud3ec\ub2c9\uc2a4\uac00 \uac01\uac01 \uac04\uc120\uc744 \ub530\ub77c \uc774\uc6c3\ud55c \uc815\uc810\uc73c\ub85c \uc774\ub3d9\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc724\uc774\ub294 \uacbd\ucc30\uacfc \ub3d9\uc77c\ud55c \uc815\uc810\uc5d0 \uc704\uce58\ud558\ub294 \uc989\uc2dc \uacbd\ucc30\uc5d0\uac8c \uc7a1\ud78c\ub2e4. \ubc18\uba74, \uc724\uc774\uac00 \uacbd\ucc30\uc5d0\uac8c \uc7a1\ud788\uc9c0 \uc54a\uace0 \ub9ac\ud504 \ub178\ub4dc\uc5d0 \ub3c4\ub2ec\ud558\uba74 \uc989\uc2dc \uc774\uc6c3\ud55c \ub9c8\uc744\ub85c \ud0c8\ucd9c\ud560 \uc218 \uc788\ub2e4. \uc724\uc774\uac00 \ub9ac\ud504 \ub178\ub4dc\uc5d0\uc11c \ucd9c\ubc1c\ud558\ub294 \uacbd\uc6b0\ub3c4 \ub9c8\ucc2c\uac00\uc9c0\ub2e4.<\/p>\r\n\r\n<p>\uc724\uc774, \ub2ec\uad6c, \ud3ec\ub2c9\uc2a4\uac00 \ucd5c\uc120\uc758 \uc804\ub7b5\uc73c\ub85c \ucd94\uaca9\uc804\uc744 \ubc8c\uc77c \ub54c, \uc724\uc774\ub294 \ubb34\uc0ac\ud788 \ud0c8\ucd9c\ud560 \uc218 \uc788\uc744\uae4c?<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 UDP \ub9c8\uc744\uc758 \uc815\uc810 \uac1c\uc218 $N$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. ($3\\le N\\le 200\\ 000$)<\/p>\r\n\r\n<p>\ub2e4\uc74c $N-1$\uac1c\uc758 \uc904\uc5d0 \ud2b8\ub9ac\uc758 \uac04\uc120 \uc815\ubcf4\ub97c \ub098\ud0c0\ub0b4\ub294 \uc815\uc218 $u$, $v$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc815\uc810 $u$\uc640 $v$ \uc0ac\uc774\uc5d0 \uac04\uc120\uc774 \uc874\uc7ac\ud568\uc744 \ub098\ud0c0\ub0b8\ub2e4. ($1\\le u,v\\le N$)<\/p>\r\n\r\n<p>\uadf8\ub2e4\uc74c \uc904\uc5d0 \uc724\uc774, \ub2ec\uad6c, \ud3ec\ub2c9\uc2a4\uc758 \uc704\uce58\ub97c \ub098\ud0c0\ub0b4\ub294 \uc815\uc218 $a$, $b$, $c$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. ($1\\le a,b,c\\le N$; $a$, $b$, $c$\ub294 \uc11c\ub85c \ub2e4\ub974\ub2e4.)<\/p>\r\n","output":"<p>\uc724\uc774\uac00 \ud0c8\ucd9c\ud560 \uc218 \uc788\uc73c\uba74 <span style=\"color:#e74c3c;\"><code>YES<\/code><\/span>, \uadf8\ub807\uc9c0 \uc54a\uc73c\uba74 <span style=\"color:#e74c3c;\"><code>NO<\/code><\/span>\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"27924","problem_lang":"1","title":"Yunee Stole the Precious Thing","description":"<p>Yunee stole the precious thing!<\/p>\r\n\r\n<p>Dalgoo and Ponix, police in UDP village,&nbsp;were dispatched to catch Yunee. UDP village has a tree structure consisting of $N$ vertices. A tree is a connected&nbsp;graph consisting of $N$ vertices and $N-1$ edges. A vertex with only one neighboring vertex in the tree is called a leaf node.&nbsp;<\/p>\r\n\r\n<p>Each vertex of the tree is numbered from $1$ to $N$. Yunee starts at&nbsp;vertex $a$, and Dalgoo&nbsp;and Ponix&nbsp;start at the vertices $b$ and $c$, respectively. The three vertices given are different from each other.&nbsp;Yunee, Dalgoo, and Ponix engage in a chase moving alternately as follows. During the chase, a vertex may contain two or more of them.<\/p>\r\n\r\n<ul>\r\n\t<li>First, Yunee&nbsp;moves along the edge to the adjacent vertex.<\/li>\r\n\t<li>Then,&nbsp;Dalgoo and Ponix move along the edge to the adjacent vertices, respectively.<\/li>\r\n<\/ul>\r\n\r\n<p>Yunee gets caught by the police as soon as&nbsp;Yunee is on&nbsp;the same vertex as any police. On the other hand, as soon as Yunee reaches a leaf node without getting caught by the police, Yunee&nbsp;can escape&nbsp;to a neighboring village. The same applies if Yunee starts at a leaf node.<\/p>\r\n\r\n<p>When Yunee, Daloo, and Ponix chase with their best strategies, will Yunee&nbsp;escape safely?<\/p>\r\n","input":"<p>The first line contains a single integer $N$ &mdash; the number of vertices in UDP village.&nbsp;($3\\le N\\le 200\\ 000$)<\/p>\r\n\r\n<p>The following $N-1$ line consists of two integers $u$, $v$ &mdash;&nbsp;denoting an edge connecting vertex $u$ and vertex $v$.&nbsp;It is guaranteed that the given edges form a tree. ($1\\le u,v\\le N$)<\/p>\r\n\r\n<p>The next line contains three integers $a$, $b$, $c$ &mdash;&nbsp;starting vertex of Yunee, Dalgoo, and Ponix. It is guaranteed these vertices are different from each other.&nbsp;($1\\le a,b,c\\le N$)<\/p>\r\n","output":"<p>In a single line, print <span style=\"color:#e74c3c;\"><code>YES<\/code><\/span> if Yunee can escape, and <span style=\"color:#e74c3c;\"><code>NO<\/code><\/span> otherwise.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English"}]