Problem Statement

There is an $N \times M$ grid and a player standing on it.
Let (i,j) denote the square at the i-th row from the top and j-th column from the left of this grid.
Each square of this grid is ice or rock, which is represented by $N strings S_1,S_2,\dots,S_N$ of length M as follows:

• if the j-th character of S_i is ., square (i,j) is ice;
• if the j-th character of S_i is #, square (i,j) is rock.

The outer periphery of this grid (all squares in the 1-st row, N-th row, 1-st column, M-th column) is rock.
Initially, the player rests on the square (2,2), which is ice.
The player can make the following move zero or more times.

• First, specify the direction of movement: up, down, left, or right.
• Then, keep moving in that direction until the player bumps against a rock. Formally, keep doing the following:
• if the next square in the direction of movement is ice, go to that square and keep moving;
• if the next square in the direction of movement is rock, stay in the current square and stop moving.

Find the number of ice squares the player can touch (pass or rest on).

Input

The input is given from Standard Input in the following format:
N M
S_1
S_2
$\vdots$
S_N

Output

Print the answer as an integer.

Constraints

• $3 \le N,M \le 200$
• S_i is a string of length M consisting of # and ..
• Square (i, j) is rock if i=1, i=N, j=1, or j=M.
• Square (2,2) is ice.

Sample Input 1

6 6

....

.#..

..#.

....

Sample Output 1

12

For instance, the player can rest on (5,5) by moving as follows:

• $(2,2) \rightarrow (5,2) \rightarrow (5,5)$.

The player can pass (2,4) by moving as follows:

• $(2,2) \rightarrow (2,5), passing (2,4)$ in the process.

The player cannot pass or rest on (3,4).

Sample Input 2

21 25

..............###...

..............#..#...

........###...#...#...

........#..#..#........

...##...#..#..#...#....

..#..#..###...#..#.....

..#..#..#..#..###......

..####..#..#...........

..#..#..###............

..#..#.................

........##.............

.......#..#............

..........#....#.......

........###...##....#..

..........#..#.#...##..

.......#..#....#..#.#..

.......##.....#....#..

.............#....#..

.................#..

Sample Output 2

215

见题面 Input 部分

见题面 Output 部分