You are given an $n \times m$ grid whose each square is either black or white.

Count the number of rectangles whose each corner square is black.

Input

The first input line contains two integer $n$ and $m$: the size of the grid.

Then, there are $n$ lines of length $m$ that describe the grid. Each line consists of characters 0 (white) and 1 (black).

Output

Print the number of rectangles whose each corner square is black.

Constraints

• $1 \le n,m \le 3000$

Example

Input:

3 4
0111
0011
0101

Output:

2