문제
하바는 어린 시절부터 $N$개의 변수 $x_1,x_2,\ldots ,x_N$을 가지고 놀면서, 변수들 간의 크기를 비교한 결과를 적어두곤 했다.
물론 하바는 장난기가 넘치기 때문에, $a$와 $b$를 비교한 결과를 다음 6ドル$가지 중 하나로 적었다.
- $a \lt b$: $a$가 $b$보다 작다.
- $a\le b$: $a$가 $b$보다 작거나 같다.
- $a>b$: $a$가 $b$보다 크다.
- $a\ge b$: $a$가 $b$보다 크거나 같다.
- $a=b$: $a$와 $b$는 같다.
- $a\ne b$: $a$와 $b$는 다르다.
변수들 간의 비교 결과가 총 $M$개 주어질 때, 하바가 가지고 있는 $N$개의 변수의 값을 추정해 보자.
출력
만약 비교 결과들을 모두 만족하는 $N$개의 변수의 값을 추정할 수 없다면 첫째 줄에 NO를 출력한다.
만약 비교 결과들을 모두 만족하는 $N$개의 변수의 값을 추정할 수 있다면 첫째 줄에 YES를 출력하고, 둘째 줄에 $x_1,x_2,\ldots ,x_N$으로 가능한 값을 공백으로 구분하여 출력한다.
모든 $x_i$는 1ドル$ 이상 $N$ 이하의 정수여야 한다. 답이 존재하는 모든 경우에 대해, 이 조건을 만족하는 답이 존재함을 보일 수 있다.
만약 가능한 답이 여러 가지라면, 그중 아무거나 하나를 출력한다.
[{"problem_id":"33721","problem_lang":"0","title":"[X] $x_1 \\lesseqgtr x_2$","description":"<p>\ud558\ubc14\ub294 \uc5b4\ub9b0 \uc2dc\uc808\ubd80\ud130 $N$\uac1c\uc758 \ubcc0\uc218 $x_1,x_2,\\ldots ,x_N$\uc744 \uac00\uc9c0\uace0 \ub180\uba74\uc11c, \ubcc0\uc218\ub4e4 \uac04\uc758 \ud06c\uae30\ub97c \ube44\uad50\ud55c \uacb0\uacfc\ub97c \uc801\uc5b4\ub450\uace4 \ud588\ub2e4.<\/p>\r\n\r\n<p>\ubb3c\ub860 \ud558\ubc14\ub294 \uc7a5\ub09c\uae30\uac00 \ub118\uce58\uae30 \ub54c\ubb38\uc5d0, $a$\uc640 $b$\ub97c \ube44\uad50\ud55c \uacb0\uacfc\ub97c \ub2e4\uc74c $6$\uac00\uc9c0 \uc911 \ud558\ub098\ub85c \uc801\uc5c8\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>$a \\lt b$: $a$\uac00 $b$\ubcf4\ub2e4 \uc791\ub2e4.<\/li>\r\n\t<li>$a\\le b$: $a$\uac00 $b$\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\ub2e4.<\/li>\r\n\t<li>$a&gt;b$: $a$\uac00 $b$\ubcf4\ub2e4 \ud06c\ub2e4.<\/li>\r\n\t<li>$a\\ge b$: $a$\uac00 $b$\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\ub2e4.<\/li>\r\n\t<li>$a=b$: $a$\uc640 $b$\ub294 \uac19\ub2e4.<\/li>\r\n\t<li>$a\\ne b$: $a$\uc640 $b$\ub294 \ub2e4\ub974\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ubcc0\uc218\ub4e4 \uac04\uc758 \ube44\uad50 \uacb0\uacfc\uac00 \ucd1d $M$\uac1c \uc8fc\uc5b4\uc9c8 \ub54c, \ud558\ubc14\uac00 \uac00\uc9c0\uace0 \uc788\ub294 $N$\uac1c\uc758 \ubcc0\uc218\uc758 \uac12\uc744 \ucd94\uc815\ud574 \ubcf4\uc790.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0\ub294 \ud558\ubc14\uac00 \uac00\uc9c0\uace0 \uc788\ub294 \ubcc0\uc218\uc758 \uac1c\uc218 $N$\uacfc \ube44\uad50 \uacb0\uacfc\uc758 \uac1c\uc218 $M$\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. $(1\\le N\\le 500\\, 000;0\\le M\\le 500\\, 000)$<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\ubd80\ud130 $M$\uac1c\uc758 \uc904\uc5d0 \uac78\uccd0 \uc815\uc218 $a$, \ubb38\uc790\uc5f4 $op$, \uc815\uc218 $b$\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub294 $x_a$\uc640 $x_b$\ub97c \ube44\uad50\ud55c \uacb0\uacfc\ub97c \uc758\ubbf8\ud558\uba70, $op$\ub294 <span style=\"color:#e74c3c;\"><code>&lt;<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>&lt;=<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>&gt;<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>&gt;=<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>==<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>!=<\/code><\/span> \uc911 \ud558\ub098\uc774\ub2e4. $(1\\le a,b\\le N)$<\/p>\r\n","output":"<p>\ub9cc\uc57d \ube44\uad50 \uacb0\uacfc\ub4e4\uc744 \ubaa8\ub450 \ub9cc\uc871\ud558\ub294 $N$\uac1c\uc758 \ubcc0\uc218\uc758 \uac12\uc744 \ucd94\uc815\ud560 \uc218 \uc5c6\ub2e4\uba74 \uccab\uc9f8 \uc904\uc5d0 <span style=\"color:#e74c3c;\"><code>NO<\/code><\/span>\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc57d \ube44\uad50 \uacb0\uacfc\ub4e4\uc744 \ubaa8\ub450 \ub9cc\uc871\ud558\ub294 $N$\uac1c\uc758 \ubcc0\uc218\uc758 \uac12\uc744 \ucd94\uc815\ud560 \uc218 \uc788\ub2e4\uba74 \uccab\uc9f8 \uc904\uc5d0 <span style=\"color:#e74c3c;\"><code>YES<\/code><\/span>\ub97c \ucd9c\ub825\ud558\uace0, \ub458\uc9f8 \uc904\uc5d0 $x_1,x_2,\\ldots ,x_N$\uc73c\ub85c \uac00\ub2a5\ud55c \uac12\uc744 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud558\uc5ec \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 $x_i$\ub294 $1$ \uc774\uc0c1 $N$ \uc774\ud558\uc758 \uc815\uc218\uc5ec\uc57c \ud55c\ub2e4. \ub2f5\uc774 \uc874\uc7ac\ud558\ub294 \ubaa8\ub4e0 \uacbd\uc6b0\uc5d0 \ub300\ud574, \uc774 \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 \ub2f5\uc774 \uc874\uc7ac\ud568\uc744 \ubcf4\uc77c \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc57d \uac00\ub2a5\ud55c \ub2f5\uc774 \uc5ec\ub7ec \uac00\uc9c0\ub77c\uba74, \uadf8\uc911 \uc544\ubb34\uac70\ub098 \ud558\ub098\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"33721","problem_lang":"1","title":"[X] $x_1 \\lesseqgtr x_2$","description":"<p>From a young age, HB played with $N$ variables $x_1,x_2,\\ldots ,x_N$ and recorded the results after comparing their sizes.<\/p>\r\n\r\n<p>Of course, the mischievous HB classified&nbsp;the&nbsp;comparison result&nbsp;between&nbsp;$a$ and $b$ as one of the following $6$ types.<\/p>\r\n\r\n<ul>\r\n\t<li>$a \\lt b$: $a$ is smaller than $b$.<\/li>\r\n\t<li>$a\\le b$: $a$ is smaller than or equal to $b$.<\/li>\r\n\t<li>$a&gt;b$: $a$ is larger than $b$.<\/li>\r\n\t<li>$a\\ge b$: $a$ is larger than or equal to $b$.<\/li>\r\n\t<li>$a=b$: $a$ is equal to $b$.<\/li>\r\n\t<li>$a\\ne b$: $a$ is not equal to $b$.<\/li>\r\n<\/ul>\r\n\r\n<p>Given $M$ comparison results, let&rsquo;s try and deduce the values of the $N$ variables HB had.<\/p>\r\n","input":"<p>The first line of input contains two space-separated integers $N$ and $M$, , denoting the number of variables HB had and the number of comparison results, respectively. $(1\\le N\\le 500\\, 000;$ $0\\le M\\le 500\\, 000)$<\/p>\r\n\r\n<p>Each of the following $M$ lines of input contains an integer $a$, a string $op$, and an integer $b$ separated by a space. This represents the comparison result between $x_a$ and $x_b$, and $op$ is one of <span style=\"color:#e74c3c;\"><code>&lt;<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>&lt;=<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>&gt;<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>&gt;=<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>==<\/code><\/span>, <span style=\"color:#e74c3c;\"><code>!=<\/code><\/span>. $(1\\le a,b\\le N)$<\/p>\r\n","output":"<p>If it is impossible to deduce a suitable value for any of the $N$ variables satisfying all comparison results, print <span style=\"color:#e74c3c;\"><code>NO&nbsp;<\/code><\/span>in the first line.<\/p>\r\n\r\n<p>If it is possible to deduce a value to all $N$ variables satisfying all comparison results, print <span style=\"color:#e74c3c;\"><code>YES&nbsp;<\/code><\/span>in the first line, and print the values of $x_1,x_2,\\ldots ,x_N$ in the second line with a space between each value.<\/p>\r\n\r\n<p>All $x_i$ must be an integer greater than or equal to $1$ and less than or equal to $N$. For all cases where there exists a valid answer, it can be shown that an answer satisfying this constraint exists.<\/p>\r\n\r\n<p>If there are multiple possible answers, print any one of them.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English"}]