import Data.List

main :: IO ()
main = do
  input <- readFile "input"
  let grid = lines input
  let antennas = getAntennas grid
  let nodes = filter (isInBounds (gridBounds grid) ) .
              nub .
              flatten .
              map (getAntinodes (gridBounds grid)) .
              groupAntennas $ antennas
  print $ length nodes

isInBounds (h,w) (y,x) = y >= 0 && y < h && x >= 0 && x < w

getAntinodes bounds coords =
  let n = length coords
  in flatten [drawLine bounds (coords!!j) (coords!!i) | i <- [0..n-1], j <- [0..i-1]]

drawLine bounds (y1,x1) (y2,x2) =
  let (dy,dx) = reduce (y2-y1,x2-x1)
  in (takeWhile (isInBounds bounds) [(y1+i*dy,x1+i*dx) | i <- [0..]])
     ++
     (takeWhile (isInBounds bounds) [(y1-i*dy,x1-i*dx) | i <- [0..]])

groupAntennas =
  map (map snd) .
  groupBy (\a b -> fst a == fst b) .
  sortOn fst

flatten l = foldl (++) [] l

gridBounds grid = (length grid, length (head grid))

getAntennas grid =
  let (n,m) = gridBounds grid
  in [(grid!!i!!j, (i,j)) | i <- [0..n-1], j <- [0..m-1], grid!!i!!j /= '.']

reduce (n,d) =
  let g = gcd (abs n) (abs d)
  in (n `div` g, d `div` g)