The Inescapable Maze

Problem Description

There is a maze of $H$ rows and $W$ columns (rows are numbered $1$ to $H$ from top to bottom, columns $1$ to $W$ from left to right). The maze is given as an $H \times W$ matrix of . and #, where . is open ground you can pass through and # is a wall you cannot cross.

A person starts at $(1, 1)$ and at each step may move only one cell to the right or one cell down, without leaving the maze. He keeps walking until there is no legal move left, then stops.

What is the maximum number of cells he can pass through?

Input Format

The first line contains two integers $H$ and $W$: the maze has $H$ rows and $W$ columns.

Then follows an $H \times W$ matrix of . and # describing the maze.

Note: $(1, 1)$ is guaranteed to be ..

Output Format

Output one integer: the maximum number of cells that can be visited.

Sample Input 1

3 4
.#..
..#.
..##

Sample Output 1

4

Sample Input 2

1 1
.

Sample Output 2

1

Sample Input 3

5 5
.....
.....
.....
.....
.....

Sample Output 3

9

Constraints

$1 \leq H, W \leq 100$.