"Z" Matrix

Problem Description

For a matrix containing only . and z, it is called a Z matrix when all of the following hold:

1. The matrix has equal numbers of rows and columns.
2. The first row and the last row are entirely z.
3. The diagonal from the top-right corner to the bottom-left corner is entirely z.

Now given an $n \times m$ matrix, count how many of its submatrices are Z matrices.

Input Format

The first line contains two integers $n, m$, the number of rows and columns of the matrix respectively ($1 \le n, m \le 3 \times 10^3$).

The next $n$ lines each contain $m$ characters, describing the matrix.

Output Format

Output one integer: the number of Z matrices.

Sample Input

4 4
zzzz
z.z.
.zz.
zzzz

Sample Output

14