Score : 700 points
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:
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.
#
or .
.Input is given from Standard Input in the following format:
H W s_{11}...s_{1W} : s_{H1}...s_{HW}
Print the number of triples that satisfy the condition.
5 4 #.## .##. #... ..## ...#
3
((1,1),(1,3),(2,2)),((1,1),(2,2),(3,1)) and ((1,3),(3,1),(4,4)) satisfy the condition.
13 27 ......#.........#.......#.. #############...#.....###.. ..............#####...##... ...#######......#...####### ...#.....#.....###...#...#. ...#######....#.#.#.#.###.# ..............#.#.#...#.#.. #############.#.#.#...###.. #...........#...#...####### #..#######..#...#...#.....# #..#.....#..#...#...#.###.# #..#######..#...#...#.#.#.# #..........##...#...#.#####
870