output_description: Print the number of triples that satisfy the condition.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      H W
      s_{11}...s_{1W}
      :
      s_{H1}...s_{HW}
attempt: def distance(a, b):
      return abs(a[0] - b[0]) + abs(a[1] - b[1])
  
  
  n = 0
  
  H, W = input().split()
  H = int(H)
  W = int(W)
  r = []
  for i in range(H):
      r.append(input().split())
  stones = []
  print(r)
  for i in range(H):
      for j in range(W):
          if r[i][0][j] == "#":
              stones.append([j, i])
  
  for i in range(len(stones)):
      for j in range(i + 1, len(stones)):
          d = distance(stones[i], stones[j])
          for k in range(j + 1, len(stones)):
              if distance(stones[i], stones[k]) == distance(stones[j], stones[k]) == d:
                  n += 1
                  print(stones[i], stones[j], stones[k])
  print(n)
  
problem_description: Statement
  
  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.
samples: [{"input": "5 4\n    #.##\n    .##.\n    #...\n    ..##\n    ...#", "output": "3\n    \n\n((1,1),(1,3),(2,2)),((1,1),(2,2),(3,1)) and ((1,3),(3,1),(4,4)) satisfy the\ncondition.\n\n* * *"}, {"input": "13 27\n    ......#.........#.......#..\n    #############...#.....###..\n    ..............#####...##...\n    ...#######......#...#######\n    ...#.....#.....###...#...#.\n    ...#######....#.#.#.#.###.#\n    ..............#.#.#...#.#..\n    #############.#.#.#...###..\n    #...........#...#...#######\n    #..#######..#...#...#.....#\n    #..#.....#..#...#...#.###.#\n    #..#######..#...#...#.#.#.#\n    #..........##...#...#.#####", "output": "870"}]