{"raw_statement":[{"iden":"problem statement","content":"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.\nThere 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.\nFind the number of triples of different coins that satisfy the following condition:\n\n*   Choosing any two of the three coins would result in the same Manhattan distance between the points where they exist.\n\nHere, 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."},{"iden":"constraints","content":"*   $1 \\leq H,W \\leq 300$\n*   $s_{ij}$ is `#` or `.`."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$H$ $W$\n$s_{11}...s_{1W}$\n$:$\n$s_{H1}...s_{HW}$"},{"iden":"sample input 1","content":"5 4\n#.##\n.##.\n#...\n..##\n...#"},{"iden":"sample output 1","content":"3\n\n$((1,1),(1,3),(2,2)),((1,1),(2,2),(3,1))$ and $((1,3),(3,1),(4,4))$ satisfy the condition."},{"iden":"sample input 2","content":"13 27\n......#.........#.......#..\n#############...#.....###..\n..............#####...##...\n...#######......#...#######\n...#.....#.....###...#...#.\n...#######....#.#.#.#.###.#\n..............#.#.#...#.#..\n#############.#.#.#...###..\n#...........#...#...#######\n#..#######..#...#...#.....#\n#..#.....#..#...#...#.###.#\n#..#######..#...#...#.#.#.#\n#..........##...#...#.#####"},{"iden":"sample output 2","content":"870"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}