Description

The pasture contains a small, contiguous grove of trees that has no 'holes' in the middle of the it. Bessie wonders: how far is it to walk around that grove and get back to my starting position? She's just sure there is a way to do it by going from her start location to successive locations by walking horizontally, vertically, or diagonally and counting each move as a single step. Just looking at it, she doesn't think you could pass 'through' the grove on a tricky diagonal. Your job is to calculate the minimum number of steps she must take. Happily, Bessie lives on a simple world where the pasture is represented by a grid with R rows and C columns (1 <= R <= 50, 1 <= C <= 50). Here's a typical example where '.' is pasture (which Bessie may traverse), 'X' is the grove of trees, '' represents Bessie's start and end position, and '+' marks one shortest path she can walk to circumnavigate the grove (i.e., the answer): ...+... ..+X+.. .+XXX+. ..+XXX+ ..+X..+ ...+++ The path shown is not the only possible shortest path; Bessie might have taken a diagonal step from her start position and achieved a similar length solution. Bessie is happy that she's starting 'outside' the grove instead of in a sort of 'harbor' that could complicate finding the best path.

牧场里有一片树林，林子里没有坑．

贝茜很想知道，最少需要多少步能围绕树林走一圈，最后回到起点．她能上下左右走，也能走对角线格子．牧场被分成R行C列(1≤R≤50，1≤C≤50)．下面是一张样例的地图，其中“．”表示贝茜可以走的空地，  “X”表示树林，  “*”表示起点．而贝茜走的最近的路已经特别地用“+”表示出来．

题目保证，最短的路径一定可以找到．

Format

Input

• Line 1: Two space-separated integers: R and C

• Lines 2..R+1: Line i+1 describes row i with C characters (with no spaces between them).

  第1行输入R和C，接下来R行C列表示一张地图．地图中的符号如题干所述．

Output

• Line 1: The single line contains a single integer which is the smallest number of steps required to circumnavigate the grove.

  输出最少的步数．

Samples

6 7
.......
...X...
..XXX..
...XXX.
...X...
......*

13