The Shortest Fence

Limits: 1 sec., 128 MiB

Equestrian competitions ended at the Olympic Games in Tokyo. And while the athletes are exchanging contacts on social networks, the main groom of the Olympics has an important task — to make sure that the horses do not run away from the competition venue all over the island of Honshu.

The field on which the competition is held has the shape of a rectangle with the length of L jō (unit of length) and the width of W jō. The groom has already divided the field into 1x1 jō cells, which are parallel to the sides of the field. Also, he found locations of all the horses using a drone and marked which cells are occupied by horses. Now he wants to build a solid closed fence that would fence off all the horses in the field so that they do not run away. The groom will build a fence on the sides of the cells of the field. Help him to determine the minimal possible length of the fence. Note that only one fence must be built which should not overlap and should have no self-intersections.

It is guaranteed that at least one cell is occupied by horses.

Input

The first line contains two integers L and W — the length and the width of the field.

The following L lines contain W characters each. The i-th character of the j-th line is # if cell (i,j) is occupied by horses, or . if the cell is empty.

Output

Print one integer — the minimum length of the fence.

Constraints

\(1 \le L, W \le 100.\)

Samples