Problem Statement

There is an $N×M$ grid. Each cell is either '.' or 'x'. When two 'x' cells share a vertex of a cell, they are said to be "linked".
Also, when a cycle of 3 or more cells can be formed by connecting 'x' cells through their 8-neighborhoods, it is called a ring.

Every 'x' is always linked with exactly 2 other 'x' cells, forming a ring. Each ring has a strength, defined as the number of 'x' cells that make it up.

For each ring, you can choose either to "use" it or "not use" it. The sum of the strengths of the used rings is the strength of the grid.
You cannot use both a ring and the ring immediately outside it.

For example, in the figures below, used rings are recolored red and unused rings are recolored blue.




In this case, the following 5 ways of using rings are allowed.



Find the maximum strength of the grid when the rings to use are chosen appropriately.

Input

$N$ $M$
$grid_0$
$grid_1$
...
$grid_{N-1}$

• $1 ≤ N, M ≤ 10^3$
• $grid_i$ $(0 ≤ i ≤ N-1)$ is a string with $M$ elements, consisting only of '.' and 'x'.
• It is guaranteed that each "linkage" forms a unique ring (you may assume that it cannot be interpreted as multiple rings).
• There is no 'x' that does not form part of a ring.

Output

Output the maximum strength of the grid.

Sample

5 10
..........
..xx...xx.
.x..x.x..x
..xx...xx.
..........

12

2 2
xx
x.

3

1 1
.

0

12 23
..xxxxxxxxxxxxxxxxxxxx.
.x....................x
.x..xxxxxx...xxxxxxx..x
.x.x......x.x.......x.x
.x.x..xx..x.x..xx...x.x
.x.x.x..x.x.x.x..x..x.x
.x.x..xx..x.x.x..x.x..x
.x.x......x.x..xx..x..x
.x..xxxxxx...x....x...x
.x............xxxx....x
.x....................x
..xxxxxxxxxxxxxxxxxxxx.

74