Lovro has a table of ~n~ rows and ~m~ columns, where each cell is either . or #. By rotating a square by ~45^\circ~ a diamond shape is formed in the table. For a part of the table to be considered a diamond, its edge must also consist only of the character #, while its inside must be completely filled with . and it must be nonempty. Outside of a diamond, any character is allowed. Diamonds come in different sizes, and the three smallest examples of a diamond are shown in the first sample.

Fabijan asked Lovro to tell him how many diamonds are there in the table, or else Lovro has to give him a cookie. Help Lovro by writing a program which counts the number of diamonds in his table.

Input Specification

The first line contains positive integers ~n~ and ~m~ ~(1 \le n, m \le 2\,000)~, the number of rows and columns.

Each of the next ~n~ lines contains ~m~ characters . or # which describe the table.

Output Specification

In the only line print the number of diamonds in the table.

Constraints

Subtask	Points	Constraints
~1~	~20~	~1 \le n, m \le 100~
~2~	~50~	No additional constraints.

Sample Input 1

7 25
.#...#....#....#.....#...
#.#..#...#.#...#....#.#..
.#...#..#...#..#...#...#.
.....#...#.#...#..#.....#
.....#....#....#...#...#.
.....#.........#....#.#..
.....#.........#.....#...

Sample Output 1

3

Sample Input 2

11 17
.....#........#..
....#.#........#.
...#...#....#...#
..#.....#....#.#.
.#....#..#....#..
#....#.#..#......
.#....#..#.......
..#.....#........
...#...#.........
....#.#..........
.....#...........

Sample Output 2

1

Explanation for Sample Output 2

There is only one diamond in the table (the one with the smallest possible size). There appears to be another diamond containing it, but it is not considered a diamond because its inside is not completely filled with .. The shape on the right side of the table is also not a diamond because it's missing a # character on its edge.

Sample Input 3

5 11
##.#.#.#.##
#.#.#.#.#.#
.#.#.#.#.#.
#.#.#.#.#.#
##.#.#.#.##

Sample Output 3

14