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문제

오늘은 직사각형 모양의 방을 로봇 청소기를 이용해 청소하려고 한다. 이 로봇 청소기는 유저가 직접 경로를 설정할 수 있다.

방은 크기가 1×1인 정사각형 칸으로 나누어져 있으며, 로봇 청소기의 크기도 1×1이다. 칸은 깨끗한 칸과 더러운 칸으로 나누어져 있으며, 로봇 청소기는 더러운 칸을 방문해서 깨끗한 칸으로 바꿀 수 있다.

일부 칸에는 가구가 놓여져 있고, 가구의 크기도 1×1이다. 로봇 청소기는 가구가 놓여진 칸으로 이동할 수 없다. 

로봇은 한 번 움직일 때, 인접한 칸으로 이동할 수 있다. 또, 로봇은 같은 칸을 여러 번 방문할 수 있다.

방의 정보가 주어졌을 때, 더러운 칸을 모두 깨끗한 칸으로 만드는데 필요한 이동 횟수의 최솟값을 구하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트케이스로 이루어져 있다.

각 테스트 케이스의 첫째 줄에는 방의 가로 크기 w와 세로 크기 h가 주어진다. (1 ≤ w, h ≤ 20) 둘째 줄부터 h개의 줄에는 방의 정보가 주어진다. 방의 정보는 4가지 문자로만 이루어져 있으며, 각 문자의 의미는 다음과 같다.

  • .: 깨끗한 칸
  • *: 더러운 칸
  • x: 가구
  • o: 로봇 청소기의 시작 위치

더러운 칸의 개수는 10개를 넘지 않으며, 로봇 청소기의 개수는 항상 하나이다.

입력의 마지막 줄에는 0이 두 개 주어진다.

출력

각각의 테스트 케이스마다 더러운 칸을 모두 깨끗한 칸으로 바꾸는 이동 횟수의 최솟값을 한 줄에 하나씩 출력한다. 만약, 방문할 수 없는 더러운 칸이 존재하는 경우에는 -1을 출력한다.

예제 입력 1

7 5
.......
.o...*.
.......
.*...*.
.......
15 13
.......x.......
...o...x....*..
.......x.......
.......x.......
.......x.......
...............
xxxxx.....xxxxx
...............
.......x.......
.......x.......
.......x.......
..*....x....*..
.......x.......
10 10
..........
..o.......
..........
..........
..........
.....xxxxx
.....x....
.....x.*..
.....x....
.....x....
0 0

예제 출력 1

8
49
-1
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