Problem Statement

There are some goats on a grid with H rows and W columns.
Alice wants to put some fences at some cells where goats do not exist so that no goat can get outside the grid.
Goats can move in the four directions, that is, up, down, right and left.
Goats can not move onto the cells where fences are placed.
If a goat exists at one of the outermost cells in the grid, it can move outside.
Goats do not move until all fences are placed.
Find the minimum number of fences to be placed.

Input

The input is given from the Standart Input in the following format:

H W
S_1
:
S_H

The $j-th (1 \leq j \leq W)$ character in $S_i (1 \leq i \leq H)$ represents
whether a goat exists at the cell located at row i and column j.
Character . represents there is no goat, and X represents there is one goat at the cell.

Output

Print the minimun number of fences to be placed. If there is no way to keep all the goats inside the grid, print -1.

Constraints

• $1 \leq H \leq 100$
• $1 \leq W \leq 100$
• There is at least one goat on the given grid.

Sample Input 1

4 5
.....
.....
..X..
.....

Sample Output 1

4

The optimum answer is to put fences at the cells located at
row 3 and column 2,
row 2 and column 3,
row 3 and column 4,
and row 4 and column 3.

Sample Input 2

2 2
..
.X

Sample Output 2

-1

In this case, there is no way to keep the goats inside the grid.

Sample Input 3

6 6
......
......
..X...
.X..X.
..X...
......

Sample Output 3

10

见题面 Input 部分

见题面 Output 部分