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문제

지금은 화학 시간이다. 이번 시간에는 지능이 있는 박테리아를 연구하는 실험을 하고 있다. 상근이는 지루한 실험 대신 독특한 자신만의 실험을 하기로 했다.

먼저, 실험판을 N행 M열로 나눈다. 제일 윗 행은 1번, 마지막 행은 N번이고, 가장 왼쪽 열은 1번, 오른쪽은 M번 행이다. 그 다음 박테리아를 K마리 준비한다.

각 박테리아는 상근이가 지정한 칸에서 모험을 시작하게 되며, 위, 아래, 오른쪽 왼쪽 중 한 방향을 바라보고 있다. 각 박테리아는 일초동안 아래와 같은 일을 수행한다.

  1. 박테리아가 현재 있는 칸에 써있는 숫자 X를 읽는다. 이 숫자는 박테리아마다 다르며, 지능이 있는 박테리아이기 때문에 자신에게 해당하는 숫자를 읽을 수 있다.
  2. 시계방향으로 X번 90도 회전을 한다.
  3. 만약 바라보고 있는 방향에 있는 칸이 실험판의 경계를 넘어간다면, 180도 회전을 한다.
  4. 바라보고 있는 칸으로 한 칸 움직인다.

상근이는 한 칸에 덫을 설치해 놓았다. 모든 박테리아가 덫이 있는 칸으로 동시에 이동하면, 즉시 덫에 걸려 죽게 된다.

모든 박테리아가 죽는데 몇 초가 걸리는지 구하는 프로그램을 작성하시오.

입력

첫째 줄에 N, M, K가 주어진다. (3 ≤ N, M ≤ 50, 1 ≤ K ≤ 5)

다음 줄에는 덫이 설치된 곳의 행 X와 열 Y가 주어진다.

나머지 줄은 박테리아에 대한 설명이며, 1번 박테리아부터 K번까지 순서대로 주어진다.

첫 줄에는 박테리아의 시작 위치 Xi Yi와 바라보고 있는 방향 Ci가 주어진다. (Ci = U(위), R(오른쪽), D(아래), L(왼쪽))

그 다음 줄에는 N × M 크기의 행렬이 주어진다. 행렬을 구성하는 원소는 0과 9를 포함하는 사이의 숫자이며, 박테리아 i아 (x,y)를 방문했을 때 해당하는 X이다.

출력

첫째 줄에 모든 박테리아가 죽는데 걸리는 시간을 출력한다. (단위: 초) 만약, 박테리아가 모두 죽지 않는다면, -1을 출력한다.

예제 입력 1

3 4 2
2 2
3 4 R
2327
6009
2112
3 2 R
1310
2101
1301

예제 출력 1

8

힌트

[{"problem_id":"5627","problem_lang":"0","title":"\ubc15\ud14c\ub9ac\uc544","description":"<p>\uc9c0\uae08\uc740 \ud654\ud559 \uc2dc\uac04\uc774\ub2e4. \uc774\ubc88 \uc2dc\uac04\uc5d0\ub294 \uc9c0\ub2a5\uc774 \uc788\ub294 \ubc15\ud14c\ub9ac\uc544\ub97c \uc5f0\uad6c\ud558\ub294 \uc2e4\ud5d8\uc744 \ud558\uace0 \uc788\ub2e4. \uc0c1\uadfc\uc774\ub294 \uc9c0\ub8e8\ud55c \uc2e4\ud5d8 \ub300\uc2e0 \ub3c5\ud2b9\ud55c \uc790\uc2e0\ub9cc\uc758 \uc2e4\ud5d8\uc744 \ud558\uae30\ub85c \ud588\ub2e4.<\/p>\r\n\r\n<p>\uba3c\uc800, \uc2e4\ud5d8\ud310\uc744 N\ud589 M\uc5f4\ub85c \ub098\ub208\ub2e4. \uc81c\uc77c \uc717 \ud589\uc740 1\ubc88, \ub9c8\uc9c0\ub9c9 \ud589\uc740 N\ubc88\uc774\uace0, \uac00\uc7a5 \uc67c\ucabd \uc5f4\uc740 1\ubc88, \uc624\ub978\ucabd\uc740 M\ubc88 \ud589\uc774\ub2e4. \uadf8 \ub2e4\uc74c \ubc15\ud14c\ub9ac\uc544\ub97c K\ub9c8\ub9ac \uc900\ube44\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ubc15\ud14c\ub9ac\uc544\ub294 \uc0c1\uadfc\uc774\uac00 \uc9c0\uc815\ud55c \uce78\uc5d0\uc11c \ubaa8\ud5d8\uc744 \uc2dc\uc791\ud558\uac8c \ub418\uba70, \uc704, \uc544\ub798, \uc624\ub978\ucabd \uc67c\ucabd \uc911 \ud55c \ubc29\ud5a5\uc744 \ubc14\ub77c\ubcf4\uace0 \uc788\ub2e4. \uac01 \ubc15\ud14c\ub9ac\uc544\ub294 \uc77c\ucd08\ub3d9\uc548 \uc544\ub798\uc640 \uac19\uc740 \uc77c\uc744 \uc218\ud589\ud55c\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>\ubc15\ud14c\ub9ac\uc544\uac00 \ud604\uc7ac \uc788\ub294 \uce78\uc5d0 \uc368\uc788\ub294 \uc22b\uc790 X\ub97c \uc77d\ub294\ub2e4. \uc774 \uc22b\uc790\ub294 \ubc15\ud14c\ub9ac\uc544\ub9c8\ub2e4 \ub2e4\ub974\uba70, \uc9c0\ub2a5\uc774 \uc788\ub294 \ubc15\ud14c\ub9ac\uc544\uc774\uae30 \ub54c\ubb38\uc5d0 \uc790\uc2e0\uc5d0\uac8c \ud574\ub2f9\ud558\ub294 \uc22b\uc790\ub97c \uc77d\uc744 \uc218 \uc788\ub2e4.<\/li>\r\n\t<li>\uc2dc\uacc4\ubc29\ud5a5\uc73c\ub85c X\ubc88 90\ub3c4 \ud68c\uc804\uc744 \ud55c\ub2e4.<\/li>\r\n\t<li>\ub9cc\uc57d \ubc14\ub77c\ubcf4\uace0 \uc788\ub294 \ubc29\ud5a5\uc5d0 \uc788\ub294 \uce78\uc774 \uc2e4\ud5d8\ud310\uc758 \uacbd\uacc4\ub97c \ub118\uc5b4\uac04\ub2e4\uba74, 180\ub3c4 \ud68c\uc804\uc744 \ud55c\ub2e4.<\/li>\r\n\t<li>\ubc14\ub77c\ubcf4\uace0 \uc788\ub294 \uce78\uc73c\ub85c \ud55c \uce78 \uc6c0\uc9c1\uc778\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uc0c1\uadfc\uc774\ub294 \ud55c \uce78\uc5d0 \ub36b\uc744 \uc124\uce58\ud574 \ub193\uc558\ub2e4. \ubaa8\ub4e0 \ubc15\ud14c\ub9ac\uc544\uac00 \ub36b\uc774 \uc788\ub294 \uce78\uc73c\ub85c \ub3d9\uc2dc\uc5d0 \uc774\ub3d9\ud558\uba74, \uc989\uc2dc \ub36b\uc5d0 \uac78\ub824 \uc8fd\uac8c \ub41c\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \ubc15\ud14c\ub9ac\uc544\uac00 \uc8fd\ub294\ub370 \uba87 \ucd08\uac00 \uac78\ub9ac\ub294\uc9c0 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 N, M, K\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (3 &le; N, M &le; 50, 1 &le; K &le; 5)<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc904\uc5d0\ub294 \ub36b\uc774 \uc124\uce58\ub41c \uacf3\uc758 \ud589 X\uc640 \uc5f4 Y\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub098\uba38\uc9c0 \uc904\uc740 \ubc15\ud14c\ub9ac\uc544\uc5d0 \ub300\ud55c \uc124\uba85\uc774\uba70, 1\ubc88 \ubc15\ud14c\ub9ac\uc544\ubd80\ud130 K\ubc88\uae4c\uc9c0 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uccab \uc904\uc5d0\ub294 \ubc15\ud14c\ub9ac\uc544\uc758 \uc2dc\uc791 \uc704\uce58 Xi Yi\uc640 \ubc14\ub77c\ubcf4\uace0 \uc788\ub294 \ubc29\ud5a5 Ci\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (Ci = U(\uc704), R(\uc624\ub978\ucabd), D(\uc544\ub798), L(\uc67c\ucabd))<\/p>\r\n\r\n<p>\uadf8 \ub2e4\uc74c \uc904\uc5d0\ub294 N &times; M \ud06c\uae30\uc758 \ud589\ub82c\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ud589\ub82c\uc744 \uad6c\uc131\ud558\ub294 \uc6d0\uc18c\ub294 0\uacfc 9\ub97c \ud3ec\ud568\ud558\ub294 \uc0ac\uc774\uc758 \uc22b\uc790\uc774\uba70, \ubc15\ud14c\ub9ac\uc544 i\uc544 (x,y)\ub97c \ubc29\ubb38\ud588\uc744 \ub54c \ud574\ub2f9\ud558\ub294 X\uc774\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \ubaa8\ub4e0 \ubc15\ud14c\ub9ac\uc544\uac00 \uc8fd\ub294\ub370 \uac78\ub9ac\ub294 \uc2dc\uac04\uc744 \ucd9c\ub825\ud55c\ub2e4. (\ub2e8\uc704: \ucd08) \ub9cc\uc57d, \ubc15\ud14c\ub9ac\uc544\uac00 \ubaa8\ub450 \uc8fd\uc9c0 \uc54a\ub294\ub2e4\uba74, -1\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"5627","problem_lang":"1","title":"BAKTERIJE","description":"<p>Luka is bored in chemistry class yet again. This time, he&#39;s playing with intelligent bacteria. He has arranged his K bacteria on a rectangular board divided in N rows, labelled with numbers from 1 to N starting from the top, and M columns, labelled with numbers from 1 to M starting from the left.<\/p>\r\n\r\n<p>Each bacterium begins its adventure in a certain cell, facing one of the four neighbouring cells, and carries out the following actions every second:<\/p>\r\n\r\n<ol>\r\n\t<li>Reads the number X dedicated to that bacterium in the current cell.<\/li>\r\n\t<li>Turns 90 degrees clockwise, X times.<\/li>\r\n\t<li>If it is facing a cell outside the board, it turns 180 degrees.<\/li>\r\n\t<li>Finally, it moves to the cell that it is facing.<\/li>\r\n<\/ol>\r\n\r\n<p>Luka has placed a trap in one cell. The trap will activate and kill the bacteria as soon as they all step on that cell in the same second.<\/p>\r\n\r\n<p>Since Luka only has two hours of chemistry class today, help him determine how long the game will last, in seconds.<\/p>\r\n","input":"<p>The first line of input contains the positive integers N (3 &le; N &le; 50), M (3 &le; M &le; 50), and K (1 &le; K &le; 5).<\/p>\r\n\r\n<p>The second line of input contains the positive integers X and Y, the row and column where Luka has placed the trap.<\/p>\r\n\r\n<p>The remainder of the input consists of bacteria descriptions, for each bacterium i from 1 to K:<\/p>\r\n\r\n<ul>\r\n\t<li>two positive integers X<sub>i<\/sub>, Y<sub>i<\/sub> &ndash; the row and column of the starting cell of bacterium i, and the character C<sub>i<\/sub> representing the starting direction that the bacterium is facing (U &ndash; up, R &ndash; right, D &ndash; down, L &ndash; left).<\/li>\r\n\t<li>&nbsp;N by M matrix of digits between 0 and 9, inclusive; the digit in row x and column y represents the number in cell (x, y) dedicated to bacterium i.<\/li>\r\n<\/ul>\r\n","output":"<p>The first and only line of output must contain the total duration of Luka&#39;s game, in seconds. If the game will never end, output -1.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]