The University of Texas Programming Club has lost track of where it is after staring at grid diagrams for too long. Fortunately, the club remembers one essential fact: Texas is shaped exactly like a size-$$$1$$$ plus sign. In this problem, a size-$$$1$$$ plus sign consists of five cells: a center cell and the four cells that share a side with it.
You are given an $$$n \times m$$$ map describing UTPC and its surroundings. Every cell is either open or blocked off. Count the number of ways to place a size-$$$1$$$ plus sign on the grid, lying on only open cells. Two placements are considered different if their center cells are different.
The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n, m \le 100$$$), the number of rows and columns of the map.
Each of the next $$$n$$$ lines contains a string of $$$m$$$ characters. A character "." represents an open cell, and a character "#" represents a blocked cell.
Print one integer: the number of valid placements of Texas.
3 3 ... ... ...
1
4 5 ..... ..#.. ..... .....
2
In the first example, the only valid placement is centered at row $$$2$$$, column $$$2$$$. It covers the center cell together with the cells directly above, below, to the left, and to the right.
In the second example, there are two valid placements. Their centers are at row $$$3$$$, column $$$2$$$ and row $$$3$$$, column $$$4$$$.
