After finishing one task at work, Bob is getting bored. So he decides to count some patterns in the ~N~-pixel-high by ~M~-pixel-wide computer screen his employer gave him. Each pixel is either yellow (lit) or black (unlit).

Bob thinks a rectangle of pixels, with both dimensions at least ~2~, is ugly if its first and last rows are identical and its first and last columns are identical. (Note: this definition is the same as the one in Problem 5.) For example, the following rectangles are ugly:

Please help Bob count the number of ugly sub-rectangles in the ~N \times M~ screen!

Constraints

~2 \le N, M~

~4 \le N \times M \le 200\,000~

Subtask 1 [10%]

~4 \le N \times M \le 500~

Subtask 2 [20%]

~4 \le N \times M \le 8000~

Subtask 3 [70%]

No additional constraints.

Input Specification

The first line contains two space-separated integers, ~N~ and ~M~.
The next ~N~ lines each contain a string of ~M~ characters—Y for yellow and B for black—representing the colours of the pixels on the screen.

Output Specification

Output one integer, the number of ugly sub-rectangles.

Sample Input

3 3
BYB
YYY
BYB

Sample Output

1