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문제

스마트폰을 새로 산 준규는 Flood-it이란 재밌는 게임을 내려 받았다. 

Flood-It은 상하좌우 4방향으로 인접한 N X N 행렬이 주어진다. 각 칸은 1~6의 6가지 색깔로 이루어져 있고 시작점은 제일 왼쪽 윗칸이다.

시작점부터 인접한 4방향 중 한칸의 색을 골라 기존 칸의 색을 바꾸고 최종적으로 모든 칸의 색이 같아지면 게임이 끝난다. 이때, 가장 적은 횟수로 모든 칸의 색을 같게 하는 것이 게임의 목적이다.

만약 다음과 같은 게임판이 주어졌을 때, 시작점에서 3을 선택하여 색을 바꾸면 다음과 같다.

이어서, 인접한 칸 중 가장 많은 빈도를 보이는 색은 4이므로 4를 선택하면 다음과 같이 게임판이 바뀐다.

이와 같이 진행하여 모든 칸의 색을 통일시키면 게임이 클리어된다.

이 때, 최소횟수로 색을 선택하여 게임을 클리어하는 경우를 출력한다.

입력

첫 줄은 테스트 케이스가 주어진다. 

각 테스트 케이스는 행,열을 나타내는 정수 N이 주어진다.(1 ≤ N ≤ 20)

다음 N줄에는 게임판에 들어갈 수가 입련된다. (1~6만 들어온다.)

출력

각 테스트 케이스는 2줄에 걸쳐 출력된다.

첫 줄은 게임을 클리어할 때까지 색을 선택한 횟수, 다음 줄의 i 번째 수는 게임판에서 i 색깔이 선택된 횟수를 출력한다.

예제 입력 1

4
6
123423
334521
433123
543621
324343
234156
5
12121
21212
12121
21212
12121
5
12345
12345
12345
12345
12345
5
11131
12211
31311
21111
11111

예제 출력 1

12
2 2 4 2 1 1
8
4 4 0 0 0 0
4
0 1 1 1 1 0
4
1 2 1 0 0 0
[{"problem_id":"9337","problem_lang":"0","title":"Flood-It","description":"<p>\uc2a4\ub9c8\ud2b8\ud3f0\uc744 \uc0c8\ub85c \uc0b0 \uc900\uaddc\ub294&nbsp;Flood-it\uc774\ub780&nbsp;\uc7ac\ubc0c\ub294 \uac8c\uc784\uc744 \ub0b4\ub824 \ubc1b\uc558\ub2e4.&nbsp;<\/p>\r\n\r\n<p>Flood-It\uc740 \uc0c1\ud558\uc88c\uc6b0 4\ubc29\ud5a5\uc73c\ub85c \uc778\uc811\ud55c N X N \ud589\ub82c\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \uce78\uc740 1~6\uc758 6\uac00\uc9c0 \uc0c9\uae54\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0 \uc2dc\uc791\uc810\uc740 \uc81c\uc77c \uc67c\ucabd&nbsp;\uc717\uce78\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc2dc\uc791\uc810\ubd80\ud130 \uc778\uc811\ud55c 4\ubc29\ud5a5 \uc911 \ud55c\uce78\uc758 \uc0c9\uc744 \uace8\ub77c \uae30\uc874 \uce78\uc758 \uc0c9\uc744 \ubc14\uafb8\uace0 \ucd5c\uc885\uc801\uc73c\ub85c \ubaa8\ub4e0 \uce78\uc758 \uc0c9\uc774 \uac19\uc544\uc9c0\uba74 \uac8c\uc784\uc774 \ub05d\ub09c\ub2e4. \uc774\ub54c, \uac00\uc7a5 \uc801\uc740 \ud69f\uc218\ub85c \ubaa8\ub4e0 \uce78\uc758 \uc0c9\uc744 \uac19\uac8c \ud558\ub294 \uac83\uc774 \uac8c\uc784\uc758 \ubaa9\uc801\uc774\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/upload\/images\/floodit1.png\" style=\"height:133px; width:164px\" \/><\/p>\r\n\r\n<p>\ub9cc\uc57d&nbsp;\ub2e4\uc74c\uacfc&nbsp;\uac19\uc740 \uac8c\uc784\ud310\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc2dc\uc791\uc810\uc5d0\uc11c 3\uc744 \uc120\ud0dd\ud558\uc5ec \uc0c9\uc744 \ubc14\uafb8\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/upload\/images\/floodit2.png\" style=\"height:131px; width:168px\" \/><\/p>\r\n\r\n<p>\uc774\uc5b4\uc11c, \uc778\uc811\ud55c \uce78 \uc911 \uac00\uc7a5 \ub9ce\uc740 \ube48\ub3c4\ub97c \ubcf4\uc774\ub294 \uc0c9\uc740 4\uc774\ubbc0\ub85c 4\ub97c \uc120\ud0dd\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\uc774 \uac8c\uc784\ud310\uc774 \ubc14\ub010\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/upload\/images\/floodit3.png\" style=\"height:133px; width:166px\" \/><\/p>\r\n\r\n<p>\uc774\uc640 \uac19\uc774 \uc9c4\ud589\ud558\uc5ec \ubaa8\ub4e0 \uce78\uc758 \uc0c9\uc744 \ud1b5\uc77c\uc2dc\ud0a4\uba74 \uac8c\uc784\uc774 \ud074\ub9ac\uc5b4\ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc774 \ub54c, \ucd5c\uc18c\ud69f\uc218\ub85c \uc0c9\uc744 \uc120\ud0dd\ud558\uc5ec \uac8c\uc784\uc744 \ud074\ub9ac\uc5b4\ud558\ub294 \uacbd\uc6b0\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","input":"<p>\uccab&nbsp;\uc904\uc740&nbsp;\ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ud589,\uc5f4\uc744 \ub098\ud0c0\ub0b4\ub294 \uc815\uc218 N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.(1&nbsp;&le; N&nbsp;&le; 20)<\/p>\r\n\r\n<p>\ub2e4\uc74c N\uc904\uc5d0\ub294 \uac8c\uc784\ud310\uc5d0 \ub4e4\uc5b4\uac08 \uc218\uac00 \uc785\ub828\ub41c\ub2e4. (1~6\ub9cc \ub4e4\uc5b4\uc628\ub2e4.)<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 2\uc904\uc5d0 \uac78\uccd0&nbsp;\ucd9c\ub825\ub41c\ub2e4.<\/p>\r\n\r\n<p>\uccab&nbsp;\uc904\uc740 \uac8c\uc784\uc744 \ud074\ub9ac\uc5b4\ud560 \ub54c\uae4c\uc9c0&nbsp;\uc0c9\uc744 \uc120\ud0dd\ud55c&nbsp;\ud69f\uc218,&nbsp;\ub2e4\uc74c \uc904\uc758 i \ubc88\uc9f8 \uc218\ub294 \uac8c\uc784\ud310\uc5d0\uc11c i \uc0c9\uae54\uc774&nbsp;\uc120\ud0dd\ub41c&nbsp;\ud69f\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9337","problem_lang":"1","title":"Flood-It","description":"<p>Flood-It is a popular one player game on many smart phones. The player is given an n &times; n board of tiles where each tile is given one of 6 colours (numbered 1&ndash;6). Each tile is connected to up to 4 adjacent tiles in the North, South, East, and West directions. A tile is connected to the origin (the tile in the upper left corner) if it has the same colour as the origin and there is a path to the origin consisting only of tiles of this colour.<\/p>\r\n\r\n<p>A player makes a move by choosing one of the 6 colours. After the choice is made, all tiles that are connected to the origin are changed to the chosen colour. The game proceeds until all tiles have the same colour. The goal of the game is to change all the tiles to the same colour, preferably with the fewest number of moves possible.<\/p>\r\n\r\n<p>It has been proven that \ufb01nding the optimal moves is a very hard problem. For this problem, you will simulate a very simple greedy strategy to see how well it works:<\/p>\r\n\r\n<p>for each move, choose the colour that will result in the largest number of tiles connected to the origin;<br \/>\r\nif there is a tie, break ties by choosing the lowest numbered colour.<\/p>\r\n\r\n<p>To illustrate this, we look at the \ufb01rst test case in the sample input, the original board is:<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/floodit1.png\" style=\"height:133px; width:164px\" \/><\/p>\r\n\r\n<p>If we choose colour 3 for the \ufb01rst move, the result will be:<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/floodit2.png\" style=\"height:131px; width:168px\" \/><\/p>\r\n\r\n<p>where the tiles connected to the origin are shaded. In the next move, we choose colour 4 because we can increase the number of tiles connected to the origin by 5 tiles:<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/floodit3.png\" style=\"height:133px; width:166px\" \/><\/p>\r\n","input":"<p>The input consists of multiple test cases. The \ufb01rst line of input is a single integer, not more than 20, indicating the number of test cases to follow. Each case starts with a line containing the integer n (1 &le; n &le; 20). The next n lines each contains n characters, giving the initial colours of the n &times; n board of tiles. Each colour is speci\ufb01ed by a digit from 1 to 6.<\/p>\r\n","output":"<p>For each case, display two lines of output. The \ufb01rst line speci\ufb01es the number of moves needed to change all the tiles to the same colour. The second line speci\ufb01es 6 integers separated by a single space. The ith integer gives the number of times colour i is chosen as a move in the game.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]