Problem Statement

There is a board with $N$ rows and $M$ columns. The information of this board is represented by $N$ strings $S_1,S_2,\\ldots,S_N$. Specifically, the state of the square at the $i$-th row from the top and the $j$-th column from the left is represented as follows:

• $S_{i,j}=$. : the square is empty.
• $S_{i,j}=$# : an obstacle is placed on the square.
• $S_{i,j}=$o : a piece is placed on the square.

Yosupo repeats the following operation:

• Choose a piece and move it to its right adjecent square or its down adjacent square. Moving a piece to squares with another piece or an obstacle is prohibited. Moving a piece out of the board is also prohibited.

Yosupo wants to perform the operation as many times as possible. Find the maximum possible number of operations.

Constraints

• $1 \\leq N \\leq 50$
• $1 \\leq M \\leq 50$
• $S_i$ is a string of length $M$ consisting of ., # and o.
• $1 \\leq ($ the number of pieces $)\\leq 100$. In other words, the number of pairs $(i, j)$ that satisfy $S_{i,j}=$o is between $1$ and $100$, both inclusive.

Input

Input is given from Standard Input in the following format:

$N$ $M$ $S_1$ $S_2$ $\\vdots$ $S_N$

Output

Print the maximum possible number of operations in a line.

Sample Input 1

3 3
o..
...
o.#

Sample Output 1

4

Yosupo can perform operations $4$ times as follows:

o..      .o.      ..o      ...      ...
...  ->  ...  ->  ...  ->  ..o  ->  ..o
o.#      o.#      o.#      o.#      .o#

Sample Input 2

9 10
.#....o#..
.#..#..##o
.....#o.##
.###.#o..o
#.#...##.#
..#..#.###
#o.....#..
....###..o
o.......o#

Sample Output 2

24