module Gauss ( gaussianReduce ) where
type Row = [Double]
type Column = [Double]
type RMatrix = [Row] 
type CMatrix = [Column] 
stringToDouble = read :: String -> Double

stringsToDoubles :: [String] -> [Double]
stringsToDoubles = map stringToDouble 
gaussianReduce :: RMatrix -> RMatrix
gaussianReduce matrix = foldl reducerow matrix [0..length matrix-1] where
  reducerow :: RMatrix -> Int -> RMatrix
  reducerow m r = let 
    row = m !! r
    p = row !! r  
    row' = map (/ p) row  
    reduceonerow nrow = let nr = nrow !! r in zipWith (\a b -> nr*a - b) row' nrow
    nextrows = map reduceonerow (drop (r+1) m)
    in take r m ++ [row'] ++ nextrows
-- gaussianSolve :: RMatrix -> [Double]
-- Your code goes here

main :: IO () 
main = do
  raw <- getContents
  let rows = lines raw
  let rows' = map words rows
  let matrix = map stringsToDoubles rows'
  print $ gaussianReduce matrix