import Data.List (permutations)
 
magicSquare = head . filter condition . map setTri . permutations . map (2^) $ [0..8]
  where
  setTri [] = []
  setTri (a:b:c:xs) = [[a, b, c]] ++ setTri xs
 
  condition xs = line xs && row xs && diagonal xs
    where
    line (x:[]) = True
    line (x:xs) = (product x) == (product . head $ xs) && (line xs)
 
    row ((x:[]):(y:[]):(z:[]):_) = True
    row (x:y:z:_) = (product . map head $ [x, y, z]) == (product . map middle $ [x, y, z]) && (row . map tail $ [x, y, z])
 
    diagonal (a:b:c:_) = product [head a, middle b, last c] == product [last a, middle b, head c]
 
    middle = head . tail
 
 
main = mapM_ print magicSquare

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