시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
5 초 512 MB 140 40 31 40.260%

문제

일호는 매년 열리는 국제 체스대회의 심사 위원이다. 

국제 체스대회의 경기는 오로지 심판인 일호만 관전하며 일호가 경기 결과를 체스협회 회장인 진서에게  통보하면 진서가 결과들을 종합하여 순위를 발표하게 된다.

이러한 룰 때문에 일호가 경기 결과를 진서에게 실수로 잘못 통보한다면 아무도 경기 결과가 바뀐지 알 수 없다.

체스 경기는 우연이 아닌 기술의 게임이기 때문에 A플레이어의 기술 수준이 B플레이어의 기술 수준보다 더 높으면 A플레이어는 B플레이어를 항상 이길것이다. 이 때 두플레이어의 기술 수준이 같다면 경기를 비길 수도 있다.

우리는 일호가 경기 과정을 진서에게 전달 하는 과정에서 실수가 발생했을 수도 있으므로 선수들의 경기 결과가 일관성이 있는지 확인을 해야한다.

예를 들어 0 > 1 , 1 = 2 , 0 = 2 의 결과가 나왔다면 0번 선수의 기술 수준은 1번 선수의 기술 수준보다 높을 것이다. 

하지만 1번 선수의 기술 수준과 2번 선수의 기술 수준이 같고, 0번 선수의 기술 수준과 2번 선수의 기술 수준이 같다면 0번선수의 기술 수준과 1번 선수의 기술 수준이 같다는 결론을 도출할 수 있으므로, 0번 선수와 1번 선수의 기술 점수에 대한 모순이 생기게 되므로 일호가 진서에게 경기 결과를 잘못 전달한 것이다.

우리는 일관성을 판단하여 경기 결과가 잘 전달 됐는지 확인하는 프로그램을 만들면 된다.

입력

첫째 줄에 플레이어 수 N(2  ≤ N  ≤ 50 000) 와   경기 결과의 수 M(1  ≤ M  ≤ 250 000) 이 주어진다.

이어서 M개의 줄에 경기 결과 K S L이 주어진다.

K와 L은 경기를 치룬 선수이고 S는 '=' 혹은'>'혹은'<' 로 표현된다.

K > L 이면 해당 경기에서 K가 L을 이긴것이다.  

두 플레이어 간에는 최대 하나의 경기만 있으며, 각 플레이어는 적어도 하나의 경기에 참여한다. 

출력

주어진 경기 결과들이 일관성이 있다면 "consistent"를 출력하고 아니라면 "inconsistent"를 출력한다.

예제 입력 1

3 3
0 > 1
1 = 2
0 = 2

예제 출력 1

inconsistent

예제 입력 2

5 5
0 = 1
1 = 2
3 = 4
0 > 3
1 > 4

예제 출력 2

consistent

예제 입력 3

6 5
0 > 1
1 > 2
3 = 4
4 = 5
5 > 3

예제 출력 3

inconsistent

힌트

[{"problem_id":"13344","problem_lang":"0","title":"\uad6d\uc81c \uccb4\uc2a4\ub300\ud68c","description":"<p>\uc77c\ud638\ub294 \ub9e4\ub144 \uc5f4\ub9ac\ub294 \uad6d\uc81c \uccb4\uc2a4\ub300\ud68c\uc758 \uc2ec\uc0ac \uc704\uc6d0\uc774\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\uad6d\uc81c \uccb4\uc2a4\ub300\ud68c\uc758 \uacbd\uae30\ub294 \uc624\ub85c\uc9c0 \uc2ec\ud310\uc778 \uc77c\ud638\ub9cc \uad00\uc804\ud558\uba70 \uc77c\ud638\uac00 \uacbd\uae30 \uacb0\uacfc\ub97c \uccb4\uc2a4\ud611\ud68c \ud68c\uc7a5\uc778 \uc9c4\uc11c\uc5d0\uac8c &nbsp;\ud1b5\ubcf4\ud558\uba74 \uc9c4\uc11c\uac00 \uacb0\uacfc\ub4e4\uc744 \uc885\ud569\ud558\uc5ec \uc21c\uc704\ub97c \ubc1c\ud45c\ud558\uac8c \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc774\ub7ec\ud55c \ub8f0 \ub54c\ubb38\uc5d0 \uc77c\ud638\uac00 \uacbd\uae30 \uacb0\uacfc\ub97c \uc9c4\uc11c\uc5d0\uac8c \uc2e4\uc218\ub85c \uc798\ubabb \ud1b5\ubcf4\ud55c\ub2e4\uba74 \uc544\ubb34\ub3c4 \uacbd\uae30 \uacb0\uacfc\uac00 \ubc14\ub010\uc9c0 \uc54c \uc218 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\uccb4\uc2a4 \uacbd\uae30\ub294 \uc6b0\uc5f0\uc774 \uc544\ub2cc \uae30\uc220\uc758 \uac8c\uc784\uc774\uae30 \ub54c\ubb38\uc5d0 A\ud50c\ub808\uc774\uc5b4\uc758 \uae30\uc220 \uc218\uc900\uc774 B\ud50c\ub808\uc774\uc5b4\uc758 \uae30\uc220 \uc218\uc900\ubcf4\ub2e4 \ub354 \ub192\uc73c\uba74 A\ud50c\ub808\uc774\uc5b4\ub294 B\ud50c\ub808\uc774\uc5b4\ub97c \ud56d\uc0c1 \uc774\uae38\uac83\uc774\ub2e4. \uc774 \ub54c \ub450\ud50c\ub808\uc774\uc5b4\uc758 \uae30\uc220 \uc218\uc900\uc774 \uac19\ub2e4\uba74 \uacbd\uae30\ub97c \ube44\uae38 \uc218\ub3c4 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc6b0\ub9ac\ub294 \uc77c\ud638\uac00 \uacbd\uae30 \uacfc\uc815\uc744 \uc9c4\uc11c\uc5d0\uac8c \uc804\ub2ec \ud558\ub294 \uacfc\uc815\uc5d0\uc11c \uc2e4\uc218\uac00 \ubc1c\uc0dd\ud588\uc744 \uc218\ub3c4 \uc788\uc73c\ubbc0\ub85c \uc120\uc218\ub4e4\uc758 \uacbd\uae30 \uacb0\uacfc\uac00 \uc77c\uad00\uc131\uc774 \uc788\ub294\uc9c0 \ud655\uc778\uc744 \ud574\uc57c\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4 0 &gt; 1 , 1 = 2 , 0 = 2 \uc758 \uacb0\uacfc\uac00 \ub098\uc654\ub2e4\uba74 0\ubc88 \uc120\uc218\uc758 \uae30\uc220 \uc218\uc900\uc740 1\ubc88 \uc120\uc218\uc758 \uae30\uc220 \uc218\uc900\ubcf4\ub2e4 \ub192\uc744 \uac83\uc774\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\ud558\uc9c0\ub9cc 1\ubc88 \uc120\uc218\uc758 \uae30\uc220 \uc218\uc900\uacfc 2\ubc88 \uc120\uc218\uc758 \uae30\uc220 \uc218\uc900\uc774 \uac19\uace0, 0\ubc88 \uc120\uc218\uc758 \uae30\uc220 \uc218\uc900\uacfc 2\ubc88 \uc120\uc218\uc758 \uae30\uc220 \uc218\uc900\uc774 \uac19\ub2e4\uba74 0\ubc88\uc120\uc218\uc758 \uae30\uc220 \uc218\uc900\uacfc 1\ubc88 \uc120\uc218\uc758 \uae30\uc220 \uc218\uc900\uc774 \uac19\ub2e4\ub294 \uacb0\ub860\uc744 \ub3c4\ucd9c\ud560 \uc218 \uc788\uc73c\ubbc0\ub85c,&nbsp;<span style=\"font-family:Arial,&quot;Helvetica Neue&quot;,Helvetica,Tahoma,sans-serif\">0\ubc88 \uc120\uc218\uc640 1\ubc88 \uc120\uc218\uc758 \uae30\uc220 \uc810\uc218\uc5d0 \ub300\ud55c \ubaa8\uc21c\uc774 \uc0dd\uae30\uac8c \ub418\ubbc0\ub85c \uc77c\ud638\uac00 \uc9c4\uc11c\uc5d0\uac8c \uacbd\uae30 \uacb0\uacfc\ub97c \uc798\ubabb \uc804\ub2ec\ud55c \uac83\uc774\ub2e4.<\/span><\/p>\r\n\r\n<p>\uc6b0\ub9ac\ub294 \uc77c\uad00\uc131\uc744 \ud310\ub2e8\ud558\uc5ec \uacbd\uae30 \uacb0\uacfc\uac00 \uc798 \uc804\ub2ec \ub410\ub294\uc9c0 \ud655\uc778\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \ub9cc\ub4e4\uba74 \ub41c\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud50c\ub808\uc774\uc5b4 \uc218 N(2 &nbsp;&le; N &nbsp;&le; 50 000) \uc640 &nbsp; \uacbd\uae30 \uacb0\uacfc\uc758 \uc218 M(1 &nbsp;&le; M &nbsp;&le; 250 000) \uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uc774\uc5b4\uc11c M\uac1c\uc758 \uc904\uc5d0 \uacbd\uae30 \uacb0\uacfc K S L\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>K\uc640 L\uc740 \uacbd\uae30\ub97c \uce58\ub8ec \uc120\uc218\uc774\uace0 S\ub294 &#39;=&#39; \ud639\uc740&#39;&gt;&#39;\ud639\uc740&#39;&lt;&#39; \ub85c \ud45c\ud604\ub41c\ub2e4.<\/p>\r\n\r\n<p>K &gt; L \uc774\uba74 \ud574\ub2f9 \uacbd\uae30\uc5d0\uc11c K\uac00 L\uc744 \uc774\uae34\uac83\uc774\ub2e4. &nbsp;<\/p>\r\n\r\n<p>\ub450 \ud50c\ub808\uc774\uc5b4 \uac04\uc5d0\ub294 \ucd5c\ub300 \ud558\ub098\uc758 \uacbd\uae30\ub9cc \uc788\uc73c\uba70, \uac01 \ud50c\ub808\uc774\uc5b4\ub294 \uc801\uc5b4\ub3c4 \ud558\ub098\uc758 \uacbd\uae30\uc5d0 \ucc38\uc5ec\ud55c\ub2e4.&nbsp;<\/p>\r\n","output":"<p>\uc8fc\uc5b4\uc9c4 \uacbd\uae30 \uacb0\uacfc\ub4e4\uc774 \uc77c\uad00\uc131\uc774 \uc788\ub2e4\uba74 &quot;consistent&quot;\ub97c \ucd9c\ub825\ud558\uace0 \uc544\ub2c8\ub77c\uba74 &quot;inconsistent&quot;\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"13344","problem_lang":"1","title":"Chess Tournament","description":"<p>Your friend is an organizer of the International Chess Playing Championship. He is worried&nbsp;that some of the contestants may be cheating, and he has asked you to help out. The chess&nbsp;players are allowed to report matches to the jury themselves, and this is not checked with the&nbsp;reported opponent. So, it is possible for competitors to make up matches and falsely report&nbsp;themselves as the winners.<\/p>\r\n\r\n<p>Since chess is a game of skill, and not of chance, a player will always beat their opponent if&nbsp;their skill level is higher. A game will result in a draw if and only if the two players&rsquo; skills&nbsp;are exactly equal.<\/p>\r\n\r\n<p>However, the skill level of the players is not known. He has therefore asked you to write&nbsp;a program that, given a list of reported matches, determines whether this list is consistent&nbsp;or not. The list is inconsistent if we can determine that at least reported match is falsely&nbsp;reported, otherwise it is consistent.<\/p>\r\n","input":"<p>The first line contains two integers N (2 &le; N &le; 50 000) and M (1 &le; M &le; 250 000), to&nbsp;describe a championship with N players and M reported matches.<\/p>\r\n\r\n<p>The following M lines each consist of an integer K, a symbol which is either &lsquo;=&rsquo; or &lsquo;&gt;&rsquo;, and&nbsp;another integer L. The integers K and L each uniquely identify a player (0 &le; K, L &lt; N). If&nbsp;the symbol is &lsquo;=&rsquo;, then the game between K and L was a draw. If the symbol is &lsquo;&gt;&rsquo;, then K&nbsp;beat L in a match.<\/p>\r\n\r\n<p>You may assume that there is at most one reported match between any given pair of players.&nbsp;Also, each player takes part in at least one reported match.<\/p>\r\n","output":"<p>Output a single line containing a single word: &ldquo;consistent&rdquo; if the list of recorded matches&nbsp;is consistent, and &ldquo;inconsistent&rdquo; if it is not.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]