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문제

정보를 좋아하는 고등학생 민솔이는 커플을 싫어한다. 그런데 요즘 주변에서 커플이 많이 출몰하는 것을 본 민솔이는 마음이 많이 심란하다. 민솔이는 이 문제를 해결하기 위해 정보를 매우 잘하는 '갓' 승원이를 찾아갔다.

승원이는 잠시 생각해 본 후, 학교의 모든 사람에 대해 그 사람이 좋아하는 사람의 수와 그 사람을 좋아하는 사람의 수의 차가 1 이하가 된다면 모든 커플을 깨트릴 수 있다는 것을 알아내었다. 다시 말해, 각 사람을 그래프의 노드로 보고, 'A가 B를 좋아한다'라는 것을 A에서 B를 가리키는 방향성 간선(즉, A -> B)으로 생각했을 때, 각 노드에 대해 |(그 노드로 들어오는 간선의 수) - (그 노드에서 나가는 간선의 수)|가 1 이하가 되면 된다는 것이다.

승원이는 '갓'이기 때문에, 학교 내에서 서로 알고 있는 학생의 쌍의 정보에 대해 모두 알고 있다. 그리고 승원이는 임의의 서로 아는 두 학생 A, B에 대해, A가 B를 좋아하거나, B가 A를 좋아하게 만들 수 있다. 즉, 어떤 무방향성 그래프가 주어지면, 승원이는 어떤 (s, e)를 잇는 간선에 대해 s -> e 또는 e -> s의 방향성 간선을 만들 수 있다는 것이다.

민솔이가 위의 조건을 만족하는 간선 방향 조합을 어떻게 생성하면 되는지 물어보려는 순간, 승원이는 "난 Persistent Segment Tree를 짜러 가야 해서... 그럼 이만!" 이라는 이상한 말과 함께 학생들 간의 관계 정보만을 남기고 떠나가버렸다.

어찌할 지 몰라 잉잉 울고 있는 민솔이를 도와 커플을 깨트릴 수 있는 간선 방향 조합을 찾아 승원이에게 알려주자!

입력

첫째 줄에는 공백으로 구분된 정수 N과 M이 주어진다(1 ≤ N ≤ 1000, 1 ≤ M ≤ 100000). N은 학생의 수, M은 두 학생이 서로 아는 관계의 수를 나타낸다.

다음 M개의 줄에는 각 줄별로 공백으로 구분된 정수 A, B가 주어진다(1 ≤ A, B ≤ N). 이는 A번 학생과 B번 학생이 서로 알고 있음을 나타낸다. (A, B)의 쌍은 중복해서 들어오지 않는다.

출력

만약 문제의 조건을 만족하도록 각 간선의 방향을 설정하는 것이 가능하다면 첫 번째 줄에 "Yes"를 출력하고, (따옴표 제외) 이후의 M개 줄에 각각 정수 A, B를 출력한다. 이는 A가 B를 좋아한다(즉, A -> B로 방향을 설정했다)라는 의미이다. 조건을 만족하도록 간선의 방향을 설정하는 방법이 여러 가지라면 그 중 아무 방법이나 출력하면 된다.

만약 문제의 조건을 만족하도록 간선의 방향을 설정하는 것이 불가능하면 첫 번째 줄에 "No"를 출력한다. (따옴표 제외)

예제 입력 1

5 7
1 2
1 3
4 1
1 5
3 2
4 5
3 5

예제 출력 1

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

힌트

예제에서는 5명의 학생과 7개의 서로 아는 관계가 있다. 예제 출력과 같이 간선 방향을 설정하고 나면, 1, 2, 4번 학생은 자신이 좋아하는 학생 수와 자신을 좋아하는 학생 수가 같으며, 3번 학생은 자신이 좋아하는 학생 수가 자신을 좋아하는 학생 수보다 1 많으며, 5번 학생은 자신을 좋아하는 학생 수가 자신이 좋아하는 학생 수보다 1 많게 되어 문제의 조건을 만족한다.

[{"problem_id":"3204","problem_lang":"0","title":"\ucee4\ud50c \uae68\uae30","description":"<p>\uc815\ubcf4\ub97c \uc88b\uc544\ud558\ub294 \uace0\ub4f1\ud559\uc0dd \ubbfc\uc194\uc774\ub294 \ucee4\ud50c\uc744 \uc2eb\uc5b4\ud55c\ub2e4. \uadf8\ub7f0\ub370 \uc694\uc998 \uc8fc\ubcc0\uc5d0\uc11c \ucee4\ud50c\uc774 \ub9ce\uc774 \ucd9c\ubab0\ud558\ub294 \uac83\uc744 \ubcf8 \ubbfc\uc194\uc774\ub294 \ub9c8\uc74c\uc774 \ub9ce\uc774 \uc2ec\ub780\ud558\ub2e4. \ubbfc\uc194\uc774\ub294 \uc774 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574 \uc815\ubcf4\ub97c \ub9e4\uc6b0 \uc798\ud558\ub294 &#39;\uac13&#39; \uc2b9\uc6d0\uc774\ub97c \ucc3e\uc544\uac14\ub2e4.<\/p>\r\n\r\n<p>\uc2b9\uc6d0\uc774\ub294 \uc7a0\uc2dc \uc0dd\uac01\ud574 \ubcf8 \ud6c4, \ud559\uad50\uc758 \ubaa8\ub4e0 \uc0ac\ub78c\uc5d0 \ub300\ud574 \uadf8 \uc0ac\ub78c\uc774 \uc88b\uc544\ud558\ub294 \uc0ac\ub78c\uc758 \uc218\uc640 \uadf8 \uc0ac\ub78c\uc744 \uc88b\uc544\ud558\ub294 \uc0ac\ub78c\uc758 \uc218\uc758 \ucc28\uac00 1 \uc774\ud558\uac00 \ub41c\ub2e4\uba74 \ubaa8\ub4e0 \ucee4\ud50c\uc744 \uae68\ud2b8\ub9b4 \uc218 \uc788\ub2e4\ub294 \uac83\uc744 \uc54c\uc544\ub0b4\uc5c8\ub2e4. \ub2e4\uc2dc \ub9d0\ud574, \uac01 \uc0ac\ub78c\uc744 \uadf8\ub798\ud504\uc758 \ub178\ub4dc\ub85c \ubcf4\uace0, &#39;A\uac00 B\ub97c \uc88b\uc544\ud55c\ub2e4&#39;\ub77c\ub294 \uac83\uc744 A\uc5d0\uc11c B\ub97c \uac00\ub9ac\ud0a4\ub294 \ubc29\ud5a5\uc131 \uac04\uc120(\uc989, A -&gt; B)\uc73c\ub85c \uc0dd\uac01\ud588\uc744 \ub54c, \uac01 \ub178\ub4dc\uc5d0 \ub300\ud574 <strong>|(\uadf8 \ub178\ub4dc\ub85c \ub4e4\uc5b4\uc624\ub294 \uac04\uc120\uc758 \uc218) - (\uadf8 \ub178\ub4dc\uc5d0\uc11c \ub098\uac00\ub294 \uac04\uc120\uc758 \uc218)|\uac00 1 \uc774\ud558<\/strong>\uac00 \ub418\uba74 \ub41c\ub2e4\ub294 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc2b9\uc6d0\uc774\ub294 &#39;\uac13&#39;\uc774\uae30 \ub54c\ubb38\uc5d0, \ud559\uad50 \ub0b4\uc5d0\uc11c \uc11c\ub85c \uc54c\uace0 \uc788\ub294 \ud559\uc0dd\uc758 \uc30d\uc758 \uc815\ubcf4\uc5d0 \ub300\ud574 \ubaa8\ub450 \uc54c\uace0 \uc788\ub2e4. \uadf8\ub9ac\uace0 \uc2b9\uc6d0\uc774\ub294 \uc784\uc758\uc758 \uc11c\ub85c \uc544\ub294 \ub450 \ud559\uc0dd A, B\uc5d0 \ub300\ud574, A\uac00 B\ub97c \uc88b\uc544\ud558\uac70\ub098, B\uac00 A\ub97c \uc88b\uc544\ud558\uac8c \ub9cc\ub4e4 \uc218 \uc788\ub2e4. \uc989, \uc5b4\ub5a4 \ubb34\ubc29\ud5a5\uc131 \uadf8\ub798\ud504\uac00 \uc8fc\uc5b4\uc9c0\uba74, \uc2b9\uc6d0\uc774\ub294 \uc5b4\ub5a4 (s, e)\ub97c \uc787\ub294 \uac04\uc120\uc5d0 \ub300\ud574 s -&gt; e \ub610\ub294 e -&gt; s\uc758 \ubc29\ud5a5\uc131 \uac04\uc120\uc744 \ub9cc\ub4e4 \uc218 \uc788\ub2e4\ub294 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\ubbfc\uc194\uc774\uac00 \uc704\uc758 \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 \uac04\uc120 \ubc29\ud5a5 \uc870\ud569\uc744 \uc5b4\ub5bb\uac8c \uc0dd\uc131\ud558\uba74 \ub418\ub294\uc9c0 \ubb3c\uc5b4\ubcf4\ub824\ub294 \uc21c\uac04, \uc2b9\uc6d0\uc774\ub294 &quot;\ub09c Persistent Segment Tree\ub97c \uc9dc\ub7ec \uac00\uc57c \ud574\uc11c... \uadf8\ub7fc \uc774\ub9cc!&quot; \uc774\ub77c\ub294 \uc774\uc0c1\ud55c \ub9d0\uacfc \ud568\uaed8 \ud559\uc0dd\ub4e4 \uac04\uc758 \uad00\uacc4 \uc815\ubcf4\ub9cc\uc744 \ub0a8\uae30\uace0 \ub5a0\ub098\uac00\ubc84\ub838\ub2e4.<\/p>\r\n\r\n<p>\uc5b4\ucc0c\ud560 \uc9c0 \ubab0\ub77c \uc789\uc789 \uc6b8\uace0 \uc788\ub294 \ubbfc\uc194\uc774\ub97c \ub3c4\uc640 \ucee4\ud50c\uc744 \uae68\ud2b8\ub9b4 \uc218 \uc788\ub294 \uac04\uc120 \ubc29\ud5a5 \uc870\ud569\uc744 \ucc3e\uc544 \uc2b9\uc6d0\uc774\uc5d0\uac8c \uc54c\ub824\uc8fc\uc790!<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0\ub294 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub41c \uc815\uc218 N\uacfc M\uc774 \uc8fc\uc5b4\uc9c4\ub2e4(1 &le; N &le; 1000, 1 &le; M &le; 100000). N\uc740 \ud559\uc0dd\uc758 \uc218, M\uc740 \ub450 \ud559\uc0dd\uc774 \uc11c\ub85c \uc544\ub294 \uad00\uacc4\uc758 \uc218\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c M\uac1c\uc758 \uc904\uc5d0\ub294 \uac01 \uc904\ubcc4\ub85c \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub41c \uc815\uc218 A, B\uac00 \uc8fc\uc5b4\uc9c4\ub2e4(1 &le; A, B &le; N). \uc774\ub294 A\ubc88 \ud559\uc0dd\uacfc B\ubc88 \ud559\uc0dd\uc774 \uc11c\ub85c \uc54c\uace0 \uc788\uc74c\uc744 \ub098\ud0c0\ub0b8\ub2e4. (A, B)\uc758 \uc30d\uc740 \uc911\ubcf5\ud574\uc11c \ub4e4\uc5b4\uc624\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","output":"<p>\ub9cc\uc57d \ubb38\uc81c\uc758 \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub3c4\ub85d \uac01 \uac04\uc120\uc758 \ubc29\ud5a5\uc744 \uc124\uc815\ud558\ub294 \uac83\uc774 \uac00\ub2a5\ud558\ub2e4\uba74 \uccab \ubc88\uc9f8 \uc904\uc5d0 &quot;Yes&quot;\ub97c \ucd9c\ub825\ud558\uace0, (\ub530\uc634\ud45c \uc81c\uc678) \uc774\ud6c4\uc758 M\uac1c \uc904\uc5d0 \uac01\uac01 \uc815\uc218 A, B\ub97c \ucd9c\ub825\ud55c\ub2e4. \uc774\ub294 A\uac00 B\ub97c \uc88b\uc544\ud55c\ub2e4(\uc989, A -&gt; B\ub85c \ubc29\ud5a5\uc744 \uc124\uc815\ud588\ub2e4)\ub77c\ub294 \uc758\ubbf8\uc774\ub2e4. \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub3c4\ub85d \uac04\uc120\uc758 \ubc29\ud5a5\uc744 \uc124\uc815\ud558\ub294 \ubc29\ubc95\uc774 \uc5ec\ub7ec \uac00\uc9c0\ub77c\uba74 \uadf8 \uc911 \uc544\ubb34 \ubc29\ubc95\uc774\ub098 \ucd9c\ub825\ud558\uba74 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc57d \ubb38\uc81c\uc758 \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub3c4\ub85d \uac04\uc120\uc758 \ubc29\ud5a5\uc744 \uc124\uc815\ud558\ub294 \uac83\uc774 \ubd88\uac00\ub2a5\ud558\uba74 \uccab \ubc88\uc9f8 \uc904\uc5d0 &quot;No&quot;\ub97c \ucd9c\ub825\ud55c\ub2e4. (\ub530\uc634\ud45c \uc81c\uc678)<\/p>\r\n","hint":"<p>\uc608\uc81c\uc5d0\uc11c\ub294 5\uba85\uc758 \ud559\uc0dd\uacfc 7\uac1c\uc758 \uc11c\ub85c \uc544\ub294 \uad00\uacc4\uac00 \uc788\ub2e4. \uc608\uc81c \ucd9c\ub825\uacfc \uac19\uc774 \uac04\uc120 \ubc29\ud5a5\uc744 \uc124\uc815\ud558\uace0 \ub098\uba74, 1, 2, 4\ubc88 \ud559\uc0dd\uc740 \uc790\uc2e0\uc774 \uc88b\uc544\ud558\ub294 \ud559\uc0dd \uc218\uc640 \uc790\uc2e0\uc744 \uc88b\uc544\ud558\ub294 \ud559\uc0dd \uc218\uac00 \uac19\uc73c\uba70, 3\ubc88 \ud559\uc0dd\uc740 \uc790\uc2e0\uc774 \uc88b\uc544\ud558\ub294 \ud559\uc0dd \uc218\uac00 \uc790\uc2e0\uc744 \uc88b\uc544\ud558\ub294 \ud559\uc0dd \uc218\ubcf4\ub2e4 1 \ub9ce\uc73c\uba70, 5\ubc88 \ud559\uc0dd\uc740 \uc790\uc2e0\uc744 \uc88b\uc544\ud558\ub294 \ud559\uc0dd \uc218\uac00 \uc790\uc2e0\uc774 \uc88b\uc544\ud558\ub294 \ud559\uc0dd \uc218\ubcf4\ub2e4 1 \ub9ce\uac8c \ub418\uc5b4 \ubb38\uc81c\uc758 \uc870\uac74\uc744 \ub9cc\uc871\ud55c\ub2e4.<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3204","problem_lang":"1","title":"Like","description":"<p>Have you noticed, that if we remove the letter &lsquo;k&rsquo; from the word &ldquo;like&rdquo; and make all cyclic rotations, one of them will be &ldquo;eli&rdquo;? This could become a great task, however in this one you will deal neither with words, nor with cyclic rotations.<\/p>\r\n\r\n<p>Elly is facing a big problem. Recently she was accused (not without a reason) that all boys in her class like her (while not paying any attention to the other girls), and she, on the other hand, is not paying any attention to the boys. This accusation was made mostly because some of her schoolmates were jealous that she is much more liked than she likes the others. Elly, on the other hand, is against relationships &ndash; that is also the reason why she ignores the boys in her class. Something more &ndash; she would be happy if there are as few as possible couples around her.<\/p>\r\n\r\n<p>In order to avoid future conflicts, she decided to make sure that for every person in the school the following holds: the number of people he likes differs from the number of people that like him by no more than 1. Put in a more human language, if we imagine that each person is a node in a graph and the fact that A likes B as directed edge from A to B in the graph, then she wants the number of incoming edges to differ from the number of outgoing edges by no more than 1.<\/p>\r\n\r\n<p>She has decided to use her charm and diplomacy (also known as deceit and manipulation) in order to achieve this. Elleonora knows all pairs of people in the school that know each-other (which we can assume is an undirected edge in the graph). She can make any pair of acquaintances change their relationship, so that one of them starts liking the other or viceversa, but not both at the same time (don&rsquo;t forget that she is against having couples in the school). She wants to execute her evil plan by &ldquo;directing&rdquo; all edges in the graph &ndash; i.e. each acquaintanceship to become a one-way crush.<\/p>\r\n\r\n<p>You decide to check if she can do that &ndash; and if she can to show one of the possible directions of the edges.&nbsp;<\/p>\r\n","input":"<p>On the first line of the standard input will be given two space separated integers N and M &ndash; the number of people in the school and the number of acquaintances, respectively. On each of the following M lines will be given a pair of space separated numbers P<sub>1<\/sub> and P<sub>2<\/sub>, where 1 &le; P<sub>1<\/sub>, P<sub>2<\/sub> &le; N, meaning that the students P<sub>1<\/sub> and P<sub>2<\/sub> know each-other. Each acquaintance will be given exactly once in the input. All numbers in the input will be positive integers. (1 &le; N &le; 1000, 1 &le; M &le; 100000)<\/p>\r\n","output":"<p>On the first line of the standard output print &ldquo;Yes&rdquo; if such direction of the edges is possible, or &ldquo;No&rdquo; otherwise (quotes for clarity only). If the answer is &ldquo;Yes&rdquo; on each of the next M lines print a pair of space separated integers P<sub>1<\/sub> P<sub>2<\/sub>, meaning that P<sub>1<\/sub> likes P<sub>2<\/sub>.<\/p>\r\n\r\n<p>If there exist more than one such way to direct the edges, print any of them.&nbsp;<\/p>\r\n","hint":"<p>There are 5 students and 7 acquaintances between them. After directing the edges in the graph, each student is liked by and likes equal amount of people, except 5, who is liked by one more person, and 3, who likes one more person.&nbsp;<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Olympiad > International Tournament in Informatics > Shumen 2010 A1번

  • 문제를 번역한 사람: kdh9949