Grid Repainting

Constraints

• H is an integer between 2 and 50 (inclusive).
• W is an integer between 2 and 50 (inclusive).
• s_{i, j} is . or # (1 \leq i \leq H, 1 \leq j \leq W).
• s_{1, 1} and s_{H, W} are ..

Input

Input is given from Standard Input in the following format:

H W s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W} s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W} : : s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}

Output

Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.

Examples

Input

3 3 ..# #.. ...

Output

2

Input

3 3 ..# .. ...

Output

2

Input

10 37 ..................................... ...#...####...####..###...###...###.. ..#.#..#...#.##....#...#.#...#.#...#. ..#.#..#...#.#.....#...#.#...#.#...#. .#...#.#..##.#.....#...#.#.###.#.###. .#####.####..#.....#...#..##....##... .#...#.#...#.#.....#...#.#...#.#...#. .#...#.#...#.##....#...#.#...#.#...#. .#...#.####...####..###...###...###.. .....................................

Output

209

inputFormat

Input

Input is given from Standard Input in the following format:

H W s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W} s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W} : : s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}

outputFormat

Output

Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.

Examples

Input

3 3 ..# #.. ...

Output

2

Input

3 3 ..# .. ...

Output

2

Input

10 37 ..................................... ...#...####...####..###...###...###.. ..#.#..#...#.##....#...#.#...#.#...#. ..#.#..#...#.#.....#...#.#...#.#...#. .#...#.#..##.#.....#...#.#.###.#.###. .#####.####..#.....#...#..##....##... .#...#.#...#.#.....#...#.#...#.#...#. .#...#.#...#.##....#...#.#...#.#...#. .#...#.####...####..###...###...###.. .....................................

Output

209

样例

10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................

209