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문제

KSA 아침 점호는 급식실에서 출석 체크 형식으로 진행된다. KSA에는 총 $N \cdot M$명의 학생이 있고, 각 학생에게는 $1$번부터 $N \cdot M$번까지의 번호가 부여되어 있다. 출석부에는 $N$행 $M$열로 학생들의 번호가 적혀 있고, 각 학생은 자신의 번호를 찾아서 그 위에 동그라미를 그리면 아침 점호에 참여한 것으로 간주된다. $i$행 $j$열에는 $i+N(j-1)$가 적혀 있으며, 각 번호에는 동그라미를 한 번만 그릴 수 있다.

하지만 아침 점호에 참여하기 게으른 일부 학생들이 친구에게 점호를 대신 맡기기 시작했다. 점호를 대신 맡은 학생은 사감 선생님께서 지켜보고 계시지 않는 틈을 타서 재빠르게 자신과 점호를 맡긴 학생, 총 두 명의 번호 위에 동그라미를 그린다. 단, 사감 선생님께 걸리지 않기 위해 번호의 차가 $1$이면서 출석부 칸의 한 변이 인접한 학생에게만 점호를 대신 맡길 수 있다.

현재까지 학생들의 점호 참여 상황이 주어질 때, 모든 학생의 점호 참여를 완료하기 위해 필요한 추가 인원의 최솟값과 그 방법을 구해보자.

입력

첫 번째 줄에 두 개의 정수 $N$, $M$이 공백으로 구분되어 주어진다.

다음 $N$개의 줄 중 $i$번째 줄에 문자열 $S_i$가 주어진다. $S_i$는 OX로 구성된 길이 $M$의 문자열이고, $j$번째 문자가 O이면 $i+N(j-1)$번 학생이 점호를 이미 완료한 상태고, X이면 $i+N(j-1)$번 학생이 점호를 아직 완료하지 않은 상태라는 뜻이다.

출력

첫 번째 줄에 모든 학생의 점호 참여가 완료되기 위해 급식실에 와야 하는 학생 수의 최솟값 $k$를 출력한다.

다음 $k$개의 줄에 걸쳐 각 줄에 다음을 출력한다. 만약 자신의 점호만 완료하는 학생이라면 $1$과 그 학생의 번호를 공백으로 구분하여 출력하고, 만약 점호를 대신 맡은 친구라면 $2$와 두 학생의 번호를 공백으로 구분하여 출력한다.

이때 학생의 번호를 출력하는 순서와 $k$개의 줄의 순서는 중요하지 않다. 정답이 여러 개 존재한다면 그중 아무거나 출력해도 상관없다.

제한

  • $1 \le N, M \le 100$
  • 적어도 하나의 $S_i$는 X를 포함

서브태스크

번호배점제한
120

$M = 1$

280

추가 제약 조건 없음

예제 입력 1

3 2
XO
XX
XO

예제 출력 1

3
1 3
2 1 2
1 5

예제 입력 2

5 1
O
X
X
X
O

예제 출력 2

2
1 2
2 4 3

예제 입력 3

1 4
XXXX

예제 출력 3

2
2 2 1
2 3 4
[{"problem_id":"35296","problem_lang":"0","title":"\uc544\uce68 \uc810\ud638","description":"<p>KSA \uc544\uce68 \uc810\ud638\ub294 \uae09\uc2dd\uc2e4\uc5d0\uc11c \ucd9c\uc11d \uccb4\ud06c \ud615\uc2dd\uc73c\ub85c \uc9c4\ud589\ub41c\ub2e4. KSA\uc5d0\ub294 \ucd1d $N \\cdot M$\uba85\uc758 \ud559\uc0dd\uc774 \uc788\uace0, \uac01 \ud559\uc0dd\uc5d0\uac8c\ub294 $1$\ubc88\ubd80\ud130 $N \\cdot M$\ubc88\uae4c\uc9c0\uc758 \ubc88\ud638\uac00 \ubd80\uc5ec\ub418\uc5b4 \uc788\ub2e4. \ucd9c\uc11d\ubd80\uc5d0\ub294 $N$\ud589 $M$\uc5f4\ub85c \ud559\uc0dd\ub4e4\uc758 \ubc88\ud638\uac00 \uc801\ud600 \uc788\uace0, \uac01 \ud559\uc0dd\uc740 \uc790\uc2e0\uc758 \ubc88\ud638\ub97c \ucc3e\uc544\uc11c \uadf8 \uc704\uc5d0 \ub3d9\uadf8\ub77c\ubbf8\ub97c \uadf8\ub9ac\uba74 \uc544\uce68 \uc810\ud638\uc5d0 \ucc38\uc5ec\ud55c \uac83\uc73c\ub85c \uac04\uc8fc\ub41c\ub2e4. $i$\ud589 $j$\uc5f4\uc5d0\ub294 $i+N(j-1)$\uac00 \uc801\ud600 \uc788\uc73c\uba70, \uac01 \ubc88\ud638\uc5d0\ub294 \ub3d9\uadf8\ub77c\ubbf8\ub97c \ud55c \ubc88\ub9cc \uadf8\ub9b4 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/9abaa53f-d65c-458a-a2d9-95fde9a624db\/-\/preview\/\" style=\"width: 300px; max-width:100%\" \/><\/p>\r\n\r\n<p>\ud558\uc9c0\ub9cc \uc544\uce68 \uc810\ud638\uc5d0 \ucc38\uc5ec\ud558\uae30 \uac8c\uc73c\ub978 \uc77c\ubd80 \ud559\uc0dd\ub4e4\uc774 \uce5c\uad6c\uc5d0\uac8c \uc810\ud638\ub97c \ub300\uc2e0 \ub9e1\uae30\uae30 \uc2dc\uc791\ud588\ub2e4. \uc810\ud638\ub97c \ub300\uc2e0 \ub9e1\uc740 \ud559\uc0dd\uc740 \uc0ac\uac10 \uc120\uc0dd\ub2d8\uaed8\uc11c \uc9c0\ucf1c\ubcf4\uace0 \uacc4\uc2dc\uc9c0 \uc54a\ub294 \ud2c8\uc744 \ud0c0\uc11c \uc7ac\ube60\ub974\uac8c \uc790\uc2e0\uacfc \uc810\ud638\ub97c \ub9e1\uae34 \ud559\uc0dd, \ucd1d \ub450 \uba85\uc758 \ubc88\ud638 \uc704\uc5d0 \ub3d9\uadf8\ub77c\ubbf8\ub97c \uadf8\ub9b0\ub2e4. \ub2e8, \uc0ac\uac10 \uc120\uc0dd\ub2d8\uaed8 \uac78\ub9ac\uc9c0 \uc54a\uae30 \uc704\ud574 \ubc88\ud638\uc758 \ucc28\uac00 $1$\uc774\uba74\uc11c \ucd9c\uc11d\ubd80 \uce78\uc758 \ud55c \ubcc0\uc774 \uc778\uc811\ud55c \ud559\uc0dd\uc5d0\uac8c\ub9cc \uc810\ud638\ub97c \ub300\uc2e0 \ub9e1\uae38 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ud604\uc7ac\uae4c\uc9c0 \ud559\uc0dd\ub4e4\uc758 \uc810\ud638 \ucc38\uc5ec \uc0c1\ud669\uc774 \uc8fc\uc5b4\uc9c8 \ub54c, \ubaa8\ub4e0 \ud559\uc0dd\uc758 \uc810\ud638 \ucc38\uc5ec\ub97c \uc644\ub8cc\ud558\uae30 \uc704\ud574 \ud544\uc694\ud55c \ucd94\uac00 \uc778\uc6d0\uc758 \ucd5c\uc19f\uac12\uacfc \uadf8 \ubc29\ubc95\uc744 \uad6c\ud574\ubcf4\uc790.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \ub450 \uac1c\uc758 \uc815\uc218 $N$, $M$\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c $N$\uac1c\uc758 \uc904 \uc911 $i$\ubc88\uc9f8 \uc904\uc5d0 \ubb38\uc790\uc5f4 $S_i$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. $S_i$\ub294 <span style=\"color:#e74c3c;\"><code>O<\/code><\/span>\uc640 <span style=\"color:#e74c3c;\"><code>X<\/code><\/span>\ub85c \uad6c\uc131\ub41c \uae38\uc774 $M$\uc758 \ubb38\uc790\uc5f4\uc774\uace0, $j$\ubc88\uc9f8 \ubb38\uc790\uac00 <span style=\"color:#e74c3c;\"><code>O<\/code><\/span>\uc774\uba74 $i+N(j-1)$\ubc88 \ud559\uc0dd\uc774 \uc810\ud638\ub97c \uc774\ubbf8 \uc644\ub8cc\ud55c \uc0c1\ud0dc\uace0, <span style=\"color:#e74c3c;\"><code>X<\/code><\/span>\uc774\uba74 $i+N(j-1)$\ubc88 \ud559\uc0dd\uc774 \uc810\ud638\ub97c \uc544\uc9c1 \uc644\ub8cc\ud558\uc9c0 \uc54a\uc740 \uc0c1\ud0dc\ub77c\ub294 \ub73b\uc774\ub2e4.<\/p>\r\n","output":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \ubaa8\ub4e0 \ud559\uc0dd\uc758 \uc810\ud638 \ucc38\uc5ec\uac00 \uc644\ub8cc\ub418\uae30 \uc704\ud574 \uae09\uc2dd\uc2e4\uc5d0 \uc640\uc57c \ud558\ub294 \ud559\uc0dd \uc218\uc758 \ucd5c\uc19f\uac12 $k$\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c $k$\uac1c\uc758 \uc904\uc5d0 \uac78\uccd0 \uac01 \uc904\uc5d0 \ub2e4\uc74c\uc744 \ucd9c\ub825\ud55c\ub2e4. \ub9cc\uc57d \uc790\uc2e0\uc758 \uc810\ud638\ub9cc \uc644\ub8cc\ud558\ub294 \ud559\uc0dd\uc774\ub77c\uba74 $1$\uacfc \uadf8 \ud559\uc0dd\uc758 \ubc88\ud638\ub97c \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud558\uc5ec \ucd9c\ub825\ud558\uace0, \ub9cc\uc57d \uc810\ud638\ub97c \ub300\uc2e0 \ub9e1\uc740 \uce5c\uad6c\ub77c\uba74 $2$\uc640 \ub450 \ud559\uc0dd\uc758 \ubc88\ud638\ub97c \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud558\uc5ec \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc774\ub54c \ud559\uc0dd\uc758 \ubc88\ud638\ub97c \ucd9c\ub825\ud558\ub294 \uc21c\uc11c\uc640 $k$\uac1c\uc758 \uc904\uc758 \uc21c\uc11c\ub294 \uc911\uc694\ud558\uc9c0 \uc54a\ub2e4. \uc815\ub2f5\uc774 \uc5ec\ub7ec \uac1c \uc874\uc7ac\ud55c\ub2e4\uba74 \uadf8\uc911 \uc544\ubb34\uac70\ub098 \ucd9c\ub825\ud574\ub3c4 \uc0c1\uad00\uc5c6\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n<li>$1 \\le N, M \\le 100$<\/li>\r\n<li>\uc801\uc5b4\ub3c4 \ud558\ub098\uc758 $S_i$\ub294 <span style=\"color:#e74c3c;\"><code>X<\/code><\/span>\ub97c \ud3ec\ud568<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$M = 1$<\/p>\r\n","subtask2":"<p>\ucd94\uac00 \uc81c\uc57d \uc870\uac74 \uc5c6\uc74c<\/p>\r\n"},{"problem_id":"35296","problem_lang":"1","title":"Morning Roll Call","description":"<p>At KSA, the morning roll call is conducted in the cafeteria in the form of an attendance check. There are a total of $N \\cdot M$ students at KSA, and each student is assigned a distinct number from $1$ to $N \\cdot M$. The attendance sheet is arranged in $N$ rows and $M$ columns, with students&#39; numbers written in the cells. Each student finds their own number and draws a circle on it to indicate participation in the morning roll call. In the cell of the $i$-th row and $j$-th column, the number $i + N(j-1)$ is written. Each number can be circled at most once.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/d6bdc3d2-72fa-44cd-ad1b-6f3dd3d5ee96\/-\/preview\/\" style=\"width: 300px; max-width:100%\" \/><\/p>\r\n\r\n<p>However, some lazy students have started asking their friends to attend roll call for them. A student who attends roll call for someone else quickly draws two circles around their number and the other student&#39;s number while the dorm supervisor is not watching. To avoid being caught, a student can only attend for another student if their numbers differ by exactly $1$ and their cells on the attendance sheet share a side.<\/p>\r\n\r\n<p>Given the current attendance status of the students, determine the minimum number of additional students who must come so that attendance for all students can be completed.<\/p>\r\n","input":"<p>The first line contains two space-separated integers $N$ and $M$.<\/p>\r\n\r\n<p>The $i$-th line of the following $N$ lines contains a string $S_i$. Each $S_i$ is a string of length $M$ consisting only of characters <code><span style=\"color:#e74c3c;\">O<\/span><\/code> and <span style=\"color:#e74c3c;\"><code>X<\/code><\/span>.<\/p>\r\n\r\n<p>If the $j$-th character of $S_i$ is <span style=\"color:#e74c3c;\"><code>O<\/code><\/span>, then student number $i+N(j&minus;1)$ has already completed the morning roll call. If it is <code><span style=\"color:#e74c3c;\">X<\/span><\/code>, then student number $i+N(j&minus;1)$ has not yet completed the morning roll call.<\/p>\r\n","output":"<p>On the first line, print $k$, the minimum number of students who must come to the cafeteria so that every student&#39;s roll call can be completed.<\/p>\r\n\r\n<p>Print one of the following on each of the next $k$ lines. If the student only completes their own roll call, print $1$ and their number, separated by a space. If the student attends roll call for someone else, print $2$ and the two students&#39; numbers, separated by spaces.<\/p>\r\n\r\n<p>The order of the student numbers and the $k$ lines does not matter. If there are multiple solutions, print any of them.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$1 \\le N, M \\le 100$<\/li>\r\n\t<li>At least one of $S_i$ contains an&nbsp;<span style=\"color:#e74c3c;\"><code>X<\/code><\/span><\/li>\r\n<\/ul>\r\n","subtask1":"<p>$M = 1$<\/p>\r\n","subtask2":"<p>No additional constraints<\/p>\r\n"}]

채점 및 기타 정보

  • 예제는 채점하지 않는다.
  • 이 문제의 채점 우선 순위는 2이다.