1784 - [Usaco2010 Jan]island

一个字符矩阵,'.'为海洋,'A'为主岛,'x'为其它岛,保证所有'A'构成一个联通块,画一个圈,使得所有的'A'在圈内,所有的'x'在圈外,更具体的看样例,求这样的圈的最小周长

Input

Line 1: Two space-separated integers: H and W * Lines 2..H+1: Line i+1 contains contains W characters that are the elements of map row i (all '.' or 'x' or 'A')

Output

  • Line 1: The minimum length of a path that Farmer John's cruise ship can take

Examples

Input

12 19
...................
...................
.....A.............
.....A..x..........
..x..A.....AAAA....
.....A.....A..A....
.....AAAAAAAA.A....
........A.....A....
.xx...AAA...x.A....
......A............
...AAAAAAAAAAAAA...
...................

Output

62
Time Limit 1 second
Memory Limit 128 MB
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