시간 제한메모리 제한제출정답맞힌 사람정답 비율
2 초 128 MB7281609517.658%

문제

N×M 크기의 감옥이 있다. 감옥은 스코필드가 미리 뚫어 놓은 탈출구, 벽, 그리고 빈 칸으로 이루어져 있는데 각각의 모든 빈 칸에는 사람이 한 명씩 있다. 감옥 안에 있는 모든 사람들은 탈출구를 통해 탈옥을 해 내야 한다. 물론, 최대한 빨리 모든 사람이 탈출하도록 하고 싶다.

각 사람이 한 칸을 이동하는 데에는 1초가 걸리며, 하나의 탈출구를 통해서는 1초에 한 사람만 탈출을 할 수 있다. 그리고 사람들이 탈출하는 동안에는 하나의 빈 칸에 여러 명의 사람들이 있어도 된다. 감옥의 정보가 주어져 있을 때, 사람들이 모두 탈출하려면 모두 몇 초의 시간이 걸리는지 구하는 프로그램을 작성하시오.

감옥의 가장자리는 반드시 벽 또는 탈출구이며, 안쪽에는 탈출구가 없다. 탈출구가 없을 수도 있고, 감옥에는 빈 칸이 하나 이상 있다.

입력

첫째 줄에 감옥의 행의 수와 열의 수, N, M이 공백을 사이에 두고 주어진다. 그리고 N개의 줄에 걸쳐서 감옥의 정보가 주어진다. ‘X'는 벽을 의미하고 '.'은 빈 칸, 'D'는 스코필드가 미리 뚫어 놓은 탈출구 위치를 의미한다.

출력

첫째 줄에 모든 사람이 탈출을 하는 최소시간을 출력한다. 만약에 모두 탈출하는 것이 불가능하다면 “impossible"을 출력한다.

제한

  • 3 ≤ N, M ≤ 12

예제 입력 1

5 5
XXDXX
X...X
D...X
X...D
XXXXX

예제 출력 1

3

예제 입력 2

5 5
XDXXX
X.X.D
XX.XX
D.X.X
XXXDX

예제 출력 2

impossible
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