시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 54 1 1 2.273%

문제

상근이는 실험용 쥐를 이용해서 실험을 하고 있다. 상근이는 쥐를 N×N개의 정사각형 칸으로 이루어진 우리에 가두었다. 각각의 칸은 빨간색이거나 흰색이다. 행은 위에서부터 1번부터 N번이며, 열은 왼쪽에서부터 1번이다.

쥐는 네 방향(왼쪽, 오른쪽, 위, 아래)으로 이동한다. 하지만, 빨간색을 무서워하기 때문에, 절대로 빨간 칸에는 들어가지 않는다.

이제 쥐를 크기가 K×K인 박스안에 가둔다. 박스의 변은 모두 우리의 변에 평행하다. 박스 안은 매우 어둡지만 쥐는 어디가 빨간색 칸인지 정확하게 알고 있기 때문에 빨간 칸에 들어가지 않는다.

상근이는 박스 안에 있는 쥐의 위치를 볼 수 없고, 박스의 움직임만 밖에서 볼 수 있다. 쥐가 박스의 가장자리를 미는 경우에 박스가 그 방향으로 움직이게 된다.

위의 그림은 예제를 나타낸 것이다. 검정 동그라미는 쥐, 회색 직사각형은 박스를 나타낸다.

박스의 처음 위치와 박스가 움직인 방향이 모두 주어졌을 때, 그러한 움직임을 만드려면 쥐가 최소 몇 번 이동해야 하는지 구하는 프로그램을 작성하시오.

입력

첫째 줄에 우리의 크기 N과 박스의 크기 K가 주어진다. (2 ≤ K ≤ 10, K < N ≤ 100)

다음 N개 줄에는 우리의 각 칸이 빨간 칸('r')인지 흰 칸('w')인지 주어진다.

다음 줄에는 박스의 처음 위치 R과 C가 주어지며, 이 좌표는 박스의 왼쪽 위 꼭짓점이다. (1 ≤ R, C ≤ N-K+1)

다음 줄에는 박스가 움직인 횟수 M (1 ≤ M ≤ 1,00,000)이 주어진다.

마지막 줄에는 박스가 움직인 방향이 순서대로 주어진다. (L, R, U, D)

출력

첫째 줄에 쥐가 최소 몇 번 움직이면 입력으로 주어진 방향대로 움직이는지 출력한다.

예제 입력 1

5 3
wwwww
wrwrw
wwwww
wrrrw
wwwww
3 3
2
LU

예제 출력 1

3
[{"problem_id":"3118","problem_lang":"0","title":"\uacfc\ud559\uc790","description":"<p>\uc0c1\uadfc\uc774\ub294 \uc2e4\ud5d8\uc6a9 \uc950\ub97c \uc774\uc6a9\ud574\uc11c \uc2e4\ud5d8\uc744 \ud558\uace0 \uc788\ub2e4. \uc0c1\uadfc\uc774\ub294 \uc950\ub97c N&times;N\uac1c\uc758 \uc815\uc0ac\uac01\ud615 \uce78\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc6b0\ub9ac\uc5d0 \uac00\ub450\uc5c8\ub2e4. \uac01\uac01\uc758 \uce78\uc740 \ube68\uac04\uc0c9\uc774\uac70\ub098 \ud770\uc0c9\uc774\ub2e4. \ud589\uc740 \uc704\uc5d0\uc11c\ubd80\ud130 1\ubc88\ubd80\ud130 N\ubc88\uc774\uba70, \uc5f4\uc740 \uc67c\ucabd\uc5d0\uc11c\ubd80\ud130 1\ubc88\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc950\ub294 \ub124 \ubc29\ud5a5(\uc67c\ucabd, \uc624\ub978\ucabd, \uc704, \uc544\ub798)\uc73c\ub85c \uc774\ub3d9\ud55c\ub2e4. \ud558\uc9c0\ub9cc, \ube68\uac04\uc0c9\uc744 \ubb34\uc11c\uc6cc\ud558\uae30 \ub54c\ubb38\uc5d0, \uc808\ub300\ub85c \ube68\uac04 \uce78\uc5d0\ub294 \ub4e4\uc5b4\uac00\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uc774\uc81c \uc950\ub97c \ud06c\uae30\uac00 K&times;K\uc778 \ubc15\uc2a4\uc548\uc5d0 \uac00\ub454\ub2e4. \ubc15\uc2a4\uc758 \ubcc0\uc740 \ubaa8\ub450 \uc6b0\ub9ac\uc758 \ubcc0\uc5d0 \ud3c9\ud589\ud558\ub2e4. \ubc15\uc2a4 \uc548\uc740 \ub9e4\uc6b0 \uc5b4\ub461\uc9c0\ub9cc \uc950\ub294 \uc5b4\ub514\uac00 \ube68\uac04\uc0c9 \uce78\uc778\uc9c0 \uc815\ud655\ud558\uac8c \uc54c\uace0 \uc788\uae30 \ub54c\ubb38\uc5d0 \ube68\uac04 \uce78\uc5d0 \ub4e4\uc5b4\uac00\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\ub294 \ubc15\uc2a4 \uc548\uc5d0 \uc788\ub294 \uc950\uc758 \uc704\uce58\ub97c \ubcfc \uc218 \uc5c6\uace0, \ubc15\uc2a4\uc758 \uc6c0\uc9c1\uc784\ub9cc \ubc16\uc5d0\uc11c \ubcfc \uc218 \uc788\ub2e4. \uc950\uac00 \ubc15\uc2a4\uc758 \uac00\uc7a5\uc790\ub9ac\ub97c \ubbf8\ub294 \uacbd\uc6b0\uc5d0 \ubc15\uc2a4\uac00 \uadf8 \ubc29\ud5a5\uc73c\ub85c \uc6c0\uc9c1\uc774\uac8c \ub41c\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/rat.png\" style=\"height:133px; width:524px\" \/><\/p>\r\n\r\n<p>\uc704\uc758 \uadf8\ub9bc\uc740 \uc608\uc81c\ub97c \ub098\ud0c0\ub0b8 \uac83\uc774\ub2e4. \uac80\uc815 \ub3d9\uadf8\ub77c\ubbf8\ub294 \uc950, \ud68c\uc0c9 \uc9c1\uc0ac\uac01\ud615\uc740 \ubc15\uc2a4\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p>\ubc15\uc2a4\uc758 \ucc98\uc74c \uc704\uce58\uc640 \ubc15\uc2a4\uac00 \uc6c0\uc9c1\uc778 \ubc29\ud5a5\uc774 \ubaa8\ub450 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uadf8\ub7ec\ud55c \uc6c0\uc9c1\uc784\uc744 \ub9cc\ub4dc\ub824\uba74 \uc950\uac00 \ucd5c\uc18c \uba87 \ubc88 \uc774\ub3d9\ud574\uc57c \ud558\ub294\uc9c0 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc6b0\ub9ac\uc758 \ud06c\uae30 N\uacfc \ubc15\uc2a4\uc758 \ud06c\uae30 K\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (2 &le; K &le; 10, K &lt; N &le; 100)<\/p>\r\n\r\n<p>\ub2e4\uc74c N\uac1c \uc904\uc5d0\ub294 \uc6b0\ub9ac\uc758 \uac01 \uce78\uc774 \ube68\uac04 \uce78(&#39;r&#39;)\uc778\uc9c0 \ud770 \uce78(&#39;w&#39;)\uc778\uc9c0 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc904\uc5d0\ub294 \ubc15\uc2a4\uc758 \ucc98\uc74c \uc704\uce58 R\uacfc C\uac00 \uc8fc\uc5b4\uc9c0\uba70, \uc774 \uc88c\ud45c\ub294 \ubc15\uc2a4\uc758 \uc67c\ucabd \uc704 \uaf2d\uc9d3\uc810\uc774\ub2e4. (1 &le; R, C &le; N-K+1)<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc904\uc5d0\ub294 \ubc15\uc2a4\uac00 \uc6c0\uc9c1\uc778 \ud69f\uc218 M (1 &le; M &le; 1,00,000)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 \ubc15\uc2a4\uac00 \uc6c0\uc9c1\uc778 \ubc29\ud5a5\uc774 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. (L, R, U, D)<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc950\uac00 \ucd5c\uc18c \uba87 \ubc88 \uc6c0\uc9c1\uc774\uba74 \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \ubc29\ud5a5\ub300\ub85c \uc6c0\uc9c1\uc774\ub294\uc9c0 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3118","problem_lang":"1","title":"STAKOR","description":"<p>Mad scientist Matija is experimenting with lab rats. He put one lab rat into a cage, the bottom of which is a grid of N&times;N square cells. Each square is coloured white or red. The rows are numbered 1 through N from top to bottom; columns are numbered left to right.&nbsp;<\/p>\r\n\r\n<p>The rat can move in the four basic directions (left, right, up and down), but is afraid of red, so it will never step into a red cell.&nbsp;<\/p>\r\n\r\n<p>After having spent some time in the cage and learned where it can move, Matija covered the rat in a box of size K&times;K, with sides of the box parallel to the sides of the cage. Even though it is now walking in the dark, thanks to its astounding memory, the rat still only enters white cells.&nbsp;<\/p>\r\n\r\n<p>While the rat moves under the box, it is not possible to see it. From outside you can only see when the box moves, which happens when the rat pushes against an edge of the box. When that happens, the box moves in the direction in which the rat pushes.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/rat.png\" style=\"height:133px; width:524px\" \/><\/p>\r\n\r\n<p>The solution to the example. The black circle is the rat, while the grey rectangle represents the box.&nbsp;<\/p>\r\n\r\n<p>Matija made note of the initial position of the box and the directions in which it moved. Write a program that calculates the smallest number of times the rat might have moved to cause the box to move like it did.&nbsp;<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","input":"<p>The first line contains two integers N and K (2 &le; K &le; 10, K &lt; N &le; 100) &ndash; the dimensions of the cage and of the box.&nbsp;<\/p>\r\n\r\n<p>Each of the following N lines contains a string of N characters, each of them either &#39;w&#39; or &#39;r&#39;, the colour of one cell.&nbsp;<\/p>\r\n\r\n<p>The next line contains two integers R and C (1 &le; R, C &le; N&minus;K+1), the row and column of the upper-left corner of the box in its initial position.&nbsp;<\/p>\r\n\r\n<p>The next line contains an integer M (1 &le; M &le; 1 000 000), the number of times the box moves.&nbsp;<\/p>\r\n\r\n<p>The next line contains a string of P letters, the directions in which the box moved. Each letter is one of &#39;L&#39;, &#39;R&#39;, &#39;U&#39; and &#39;D&#39;.&nbsp;<\/p>\r\n","output":"<p>Output the smallest possible number of times the rat might have moved.&nbsp;<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]