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문제

N-Queen 문제를 풀어본 일이 있을 것이다. 격자판에 N개의 Queen을 배치하되, 각 Queen이 서로를 공격할 수 없게 배치하려면 N은 최대 얼마까지 가능한지를 알아내는 문제이다.

이번에는 Rook을 가지고 같은 문제를 풀어 보자. Rook은 격자판의 같은 열, 혹은 같은 행에 다른 말이 있을 경우, 그 말을 공격할 수 있는 말이다.

다만, 이 경우에 문제가 그 가치를 확보하기 위해서는, 격자판을 약간 변형해야 한다. 격자판에 벽과 구덩이를 도입하자.

벽을 사이에 두고 있는 두 Rook은, 서로 볼 수 없으므로, 서로 공격할 수가 없다. 물론 벽이 놓여 있는 격자에는 Rook을 놓을 수 없다.

반면, 구덩이를 사이에 두고 있는 두 Rook은 서로 공격을 시도한다. (아마 공격 도중에 구덩이에 빠지겠지만.) 따라서 두 Rook이 구덩이를 사이에 두고 마주보도록 배치해서는 안 된다. 또, 구덩이를 파 놓은 격자에도 Rook을 놓을 수 없다.

격자판의 모양이 주어졌을 때, Rook을 가장 많이 배치하기 위한 방법을 알아내는 프로그램을 작성하시오.

입력

첫째 줄에 격자의 크기를 나타내는 두 자연수 M, N이 주어진다. 격자가 M행 N열로 이루어져 있다는 의미이다. (1<=M, N<=100) 둘째 줄부터는 격자의 모양을 나타내는 정보가 한 줄에 한 행씩 주어진다. 0은 빈 격자, 1은 구덩이가 파인 격자, 2는 벽이 놓인 격자를 의미한다.

출력

첫째 줄에, 배치할 수 있는 Rook의 최대 개수를 출력한다.

예제 입력 1

3 4
2 0 0 0
2 2 2 1
0 1 0 2

예제 출력 1

2

힌트

1행 2열과 3행 3열에 하나씩, 총 두 개의 Rook을 배치할 수 있다.

[{"problem_id":"1760","problem_lang":"0","title":"N-Rook","description":"<p>N-Queen \ubb38\uc81c\ub97c \ud480\uc5b4\ubcf8 \uc77c\uc774 \uc788\uc744 \uac83\uc774\ub2e4. \uaca9\uc790\ud310\uc5d0 N\uac1c\uc758 Queen\uc744 \ubc30\uce58\ud558\ub418, \uac01 Queen\uc774 \uc11c\ub85c\ub97c \uacf5\uaca9\ud560 \uc218 \uc5c6\uac8c \ubc30\uce58\ud558\ub824\uba74 N\uc740 \ucd5c\ub300 \uc5bc\ub9c8\uae4c\uc9c0 \uac00\ub2a5\ud55c\uc9c0\ub97c \uc54c\uc544\ub0b4\ub294 \ubb38\uc81c\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc774\ubc88\uc5d0\ub294 Rook\uc744 \uac00\uc9c0\uace0 \uac19\uc740 \ubb38\uc81c\ub97c \ud480\uc5b4 \ubcf4\uc790. Rook\uc740 \uaca9\uc790\ud310\uc758 \uac19\uc740 \uc5f4, \ud639\uc740 \uac19\uc740 \ud589\uc5d0 \ub2e4\ub978 \ub9d0\uc774 \uc788\uc744 \uacbd\uc6b0, \uadf8 \ub9d0\uc744 \uacf5\uaca9\ud560 \uc218 \uc788\ub294 \ub9d0\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\ub9cc, \uc774 \uacbd\uc6b0\uc5d0 \ubb38\uc81c\uac00 \uadf8 \uac00\uce58\ub97c \ud655\ubcf4\ud558\uae30 \uc704\ud574\uc11c\ub294, \uaca9\uc790\ud310\uc744 \uc57d\uac04 \ubcc0\ud615\ud574\uc57c \ud55c\ub2e4. \uaca9\uc790\ud310\uc5d0&nbsp;\ubcbd\uacfc \uad6c\ub369\uc774\ub97c \ub3c4\uc785\ud558\uc790.<\/p>\r\n\r\n<p>\ubcbd\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc788\ub294 \ub450 Rook\uc740, \uc11c\ub85c \ubcfc \uc218 \uc5c6\uc73c\ubbc0\ub85c, \uc11c\ub85c \uacf5\uaca9\ud560 \uc218\uac00 \uc5c6\ub2e4. \ubb3c\ub860 \ubcbd\uc774 \ub193\uc5ec \uc788\ub294 \uaca9\uc790\uc5d0\ub294 Rook\uc744 \ub193\uc744 \uc218 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\ubc18\uba74, \uad6c\ub369\uc774\ub97c \uc0ac\uc774\uc5d0 \ub450\uace0 \uc788\ub294 \ub450 Rook\uc740 \uc11c\ub85c \uacf5\uaca9\uc744 \uc2dc\ub3c4\ud55c\ub2e4. (\uc544\ub9c8 \uacf5\uaca9 \ub3c4\uc911\uc5d0 \uad6c\ub369\uc774\uc5d0 \ube60\uc9c0\uaca0\uc9c0\ub9cc.) \ub530\ub77c\uc11c \ub450 Rook\uc774 \uad6c\ub369\uc774\ub97c \uc0ac\uc774\uc5d0 \ub450\uace0 \ub9c8\uc8fc\ubcf4\ub3c4\ub85d \ubc30\uce58\ud574\uc11c\ub294 \uc548 \ub41c\ub2e4. \ub610, \uad6c\ub369\uc774\ub97c \ud30c \ub193\uc740 \uaca9\uc790\uc5d0\ub3c4 Rook\uc744 \ub193\uc744 \uc218 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\uaca9\uc790\ud310\uc758 \ubaa8\uc591\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, Rook\uc744 \uac00\uc7a5 \ub9ce\uc774 \ubc30\uce58\ud558\uae30 \uc704\ud55c \ubc29\ubc95\uc744 \uc54c\uc544\ub0b4\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uaca9\uc790\uc758 \ud06c\uae30\ub97c \ub098\ud0c0\ub0b4\ub294 \ub450 \uc790\uc5f0\uc218 M, N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uaca9\uc790\uac00 M\ud589 N\uc5f4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4\ub294 \uc758\ubbf8\uc774\ub2e4. (1&lt;=M, N&lt;=100) \ub458\uc9f8 \uc904\ubd80\ud130\ub294 \uaca9\uc790\uc758 \ubaa8\uc591\uc744 \ub098\ud0c0\ub0b4\ub294 \uc815\ubcf4\uac00 \ud55c \uc904\uc5d0 \ud55c \ud589\uc529 \uc8fc\uc5b4\uc9c4\ub2e4. 0\uc740 \ube48 \uaca9\uc790, 1\uc740 \uad6c\ub369\uc774\uac00 \ud30c\uc778 \uaca9\uc790, 2\ub294 \ubcbd\uc774 \ub193\uc778 \uaca9\uc790\ub97c \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0, \ubc30\uce58\ud560 \uc218 \uc788\ub294 Rook\uc758 \ucd5c\ub300 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>1\ud589 2\uc5f4\uacfc 3\ud589 3\uc5f4\uc5d0 \ud558\ub098\uc529, \ucd1d \ub450 \uac1c\uc758 Rook\uc744 \ubc30\uce58\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"1760","problem_lang":"1","title":"Royal guards","description":"<p>Once upon a time, there was a kingdom. It had everything a kingdom needs, namely a king and his castle. The ground-plan of the castle was a rectangle that was divided into M&times;N unit squares. Some of the squares are walls, some of them are free. We will call each of the free squares a room. The king of our kingdom was extremely paranoid, so one day he decided to make hidden pits (with alligators at the bottom) in some of the rooms.<\/p>\r\n\r\n<p>But this was still not enough. One week later, he decided to place as many guards as possible inside his castle. However, this won&#39;t be so simple. The guards are trained so that immediately after they see someone, they shoot at him. And so the king has to place the guards carefully, because if two guards would see each other, they would shoot at themselves! Also evidently the king can&#39;t place a guard into a room with a pit.<\/p>\r\n\r\n<p>Two guards in a room see each other, so each room may contain at most one guard. Two guards in different rooms see each other if and only if the squares corresponding to their rooms are in the same row or in the same column of the plan of the castle and there is no wall between them. (The guard can see only in four directions, much like a rook in chess.)<\/p>\r\n\r\n<p>Your task is to find out, how many guards can the king place inside his castle (according to the rules above) and to find one possible assignment of that many guards into the rooms.<\/p>\r\n","input":"<p>The first line of the input file contains two numbers M, N, 1&lt;=M,N&lt;=200 - the dimensions of the ground-plan of the castle. The i-th of the following M lines contains N numbers a<sub>i,1<\/sub>, ..., a<sub>i,N<\/sub>, separated by single spaces, where:<\/p>\r\n\r\n<ul>\r\n\t<li>a<sub>i,j<\/sub>=0 means that the square is free (a room without a pit)<\/li>\r\n\t<li>a<sub>i,j<\/sub>=1 means that the square contains a pit<\/li>\r\n\t<li>a<sub>i,j<\/sub>=2 means that the square is a wall<\/li>\r\n<\/ul>\r\n\r\n<p>Note that the first coordinate of a square is the row and the second one is the column.<\/p>\r\n","output":"<p>The first line of the output file should contain the maximum number K of guards the king may place inside his castle. The following K lines should contain one possible assignment of K guards into the free rooms of the castle so that no two guards would see each other.<\/p>\r\n\r\n<p>More precisely, the i-th of these lines should contain two integers r<sub>i<\/sub>, c<sub>i<\/sub> separated by a single space - the coordinates of the room where i-th guard will be placed (r<sub>i<\/sub> is the row and c<sub>i<\/sub> is the column).<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/upload\/images\/2002-22-1.gif\" style=\"height:87px; width:285px\" \/><\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]