The heroes and the White Demon play a game on an n×m grid. Some cells are initially filled and cannot be used. Players take turns placing a yogurt-bread in an empty cell so that, except for the very first yogurt-bread, each placement must be in a cell adjacent (sharing a side) to the opponent’s immediately previous move. The heroes (Team 1) move first. If a player cannot move on their turn, they lose.

Call an empty cell a Chef cell if, by placing the first yogurt-bread there, the heroes can force a win regardless of how the opponent plays. Given the current board, count the number of Chef cells.

Input

• The first line contains two integers n and m: the board dimensions.
• The next n lines each contain a string of length m describing the board.
• Each character is either '.' (empty) or '#' (filled/blocked).
• The heroes place the first yogurt-bread on any empty cell.
• After the first move, each move must be to a cell that shares a side with the cell chosen by the opposing team on the immediately preceding turn.
• Adjacent means sharing a side (up, down, left, or right).

Output

• Single integer: the number of Chef cells on the given board.

Notes

• You cannot place a yogurt-bread on a filled cell ('#').
• If there are no empty cells, the answer is 0.
• A move is legal if and only if the chosen cell is empty and (except for the very first move) is adjacent to the opponent’s immediately previous move.

Example 1 Input

3 3
#.#
...
#.#

Example 1 Output

4

Example 2 Input

3 3
..#
...
...

Example 2 Output

0

Example 3 Input

1 4
...#

Example 3 Output

2