Equilateral

There are some coins in the xy-plane. The positions of the coins are represented by a grid of characters with H rows and W columns. If the character at the i-th row and j-th column, s_{ij}, is #, there is one coin at point (i,j); if that character is ., there is no coin at point (i,j). There are no other coins in the xy-plane.

There is no coin at point (x,y) where 1\leq i\leq H,1\leq j\leq W does not hold. There is also no coin at point (x,y) where x or y (or both) is not an integer. Additionally, two or more coins never exist at the same point.

Find the number of triples of different coins that satisfy the following condition:

• Choosing any two of the three coins would result in the same Manhattan distance between the points where they exist.

Here, the Manhattan distance between points (x,y) and (x',y') is |x-x'|+|y-y'|. Two triples are considered the same if the only difference between them is the order of the coins.

Constraints

• 1 \leq H,W \leq 300
• s_{ij} is # or ..

Input

Input is given from Standard Input in the following format:

H W s_{11}...s_{1W} : s_{H1}...s_{HW}

Output

Print the number of triples that satisfy the condition.

Examples

Input

5 4 #.## .##. #... ..## ...#

Output

3

Input

5 4 .## .##. ... ..## ...#

Output

3

Input

13 27 ......#.........#.......#.. ...#.....###.. ..............#####...##... ...#######......#...####### ...#.....#.....###...#...#. ...#######....#.#.#.#.###.# ..............#.#.#...#.#.. .#.#.#...###.. ...........#...#...####### ..#######..#...#...#.....# ..#.....#..#...#...#.###.# ..#######..#...#...#.#.#.# ..........##...#...#.#####

Output

870

inputFormat

Input

Input is given from Standard Input in the following format:

H W s_{11}...s_{1W} : s_{H1}...s_{HW}

outputFormat

Output

Print the number of triples that satisfy the condition.

Examples

Input

5 4 #.## .##. #... ..## ...#

Output

3

Input

5 4 .## .##. ... ..## ...#

Output

3

Input

13 27 ......#.........#.......#.. ...#.....###.. ..............#####...##... ...#######......#...####### ...#.....#.....###...#...#. ...#######....#.#.#.#.###.# ..............#.#.#...#.#.. .#.#.#...###.. ...........#...#...####### ..#######..#...#...#.....# ..#.....#..#...#...#.###.# ..#######..#...#...#.#.#.# ..........##...#...#.#####

Output

870

样例

5 4
#.##
.##.
#...
..##
...#

3