{"problem":{"name":"Equilateral","description":{"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_{i","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"tenka1_2018_e"},"statements":[{"statement_type":"Markdown","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.\n\n## Constraints\n\n*   $1 \\leq H,W \\leq 300$\n*   $s_{ij}$ is `#` or `.`.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$H$ $W$\n$s_{11}...s_{1W}$\n$:$\n$s_{H1}...s_{HW}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"tenka1_2018_e","tags":[],"sample_group":[["5 4\n#.##\n.##.\n#...\n..##\n...#","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."],["13 27\n......#.........#.......#..\n#############...#.....###..\n..............#####...##...\n...#######......#...#######\n...#.....#.....###...#...#.\n...#######....#.#.#.#.###.#\n..............#.#.#...#.#..\n#############.#.#.#...###..\n#...........#...#...#######\n#..#######..#...#...#.....#\n#..#.....#..#...#...#.###.#\n#..#######..#...#...#.#.#.#\n#..........##...#...#.#####","870"]],"created_at":"2026-03-03 11:01:14"}}