module Main where

import Control.Applicative ((<|>))
import Data.Function ((&))
import qualified Control.Monad
import qualified Data.Char
import qualified Data.Function
import qualified Data.List
import qualified Data.Map.Strict as Map
import qualified Data.Word
import qualified Data.Bits
import qualified Data.Vector
import Data.Vector ((!))

fixM :: (Eq t, Monad m) => (t -> m t) -> t -> m t
fixM f x = f x >>= \x' -> if x' == x then return x else fixM f x'

setBits :: Data.Word.Word16 -> [Data.Word.Word16] -> Data.Word.Word16
setBits = Data.List.foldl' (Data.Bits..|.)

data Cell = Fixed Data.Word.Word16
          | Possible Data.Word.Word16
          deriving (Show, Eq)

type Grid = Data.Vector.Vector Cell
type CellIxs = [Int]

isPossible :: Cell -> Bool
isPossible (Possible _) = True
isPossible _            = False

readGrid :: String -> Maybe Grid
readGrid s
  | length s == 81 = Data.Vector.fromList <$> traverse readCell s
  | otherwise      = Nothing
  where
    allBitsSet = 1022

    readCell '.' = Just $ Possible allBitsSet
    readCell c
      | Data.Char.isDigit c && c > '0' = Just . Fixed . Data.Bits.bit . Data.Char.digitToInt $ c
      | otherwise = Nothing

fromXY :: (Int, Int) -> Int
fromXY (x, y) = x * 9 + y

allRowIxs, allColIxs, allSubGridIxs :: [CellIxs]
allRowIxs = [getRow i | i <- [0..8]]
  where getRow n = [ fromXY (n, i) | i <- [0..8] ]

allColIxs = [getCol i | i <- [0..8]]
  where getCol n = [ fromXY (i, n) | i <- [0..8] ]

allSubGridIxs = [getSubGrid i | i <- [0..8]]
  where getSubGrid n = let (r, c) = (n `quot` 3, n `mod` 3)
                       in [ fromXY (3 * r + i, 3 * c + j) | i <- [0..2], j <- [0..2] ]

replaceCell :: Int -> Cell -> Grid -> Grid
replaceCell i c g = g Data.Vector.// [(i, c)]

showGrid :: Grid -> String
showGrid grid = unlines . map (unwords . map (showCell . (grid !))) $ allRowIxs
  where
    showCell (Fixed x) = show . Data.Bits.countTrailingZeros $ x
    showCell _         = "."

showGridWithPossibilities :: Grid -> String
showGridWithPossibilities grid = unlines . map (unwords . map (showCell . (grid !))) $ allRowIxs
  where
    showCell (Fixed x)     = (show . Data.Bits.countTrailingZeros $ x) ++ "          "
    showCell (Possible xs) =
      "[" ++ map (\i -> if Data.Bits.testBit xs i then Data.Char.intToDigit i else ' ') [1..9] ++ "]"

exclusivePossibilities :: [Cell] -> [Data.Word.Word16]
exclusivePossibilities row =
  row
  & zip [1..9]
  & filter (isPossible . snd)
  & Data.List.foldl'
      (\acc ~(i, Possible xs) ->
        Data.List.foldl'
          (\acc' n -> if Data.Bits.testBit xs n then Map.insertWith prepend n [i] acc' else acc')
          acc
          [1..9])
      Map.empty
  & Map.filter ((< 4) . length)
  & Map.foldlWithKey'(\acc x is -> Map.insertWith prepend is [x] acc) Map.empty
  & Map.filterWithKey (\is xs -> length is == length xs)
  & Map.elems
  & map (Data.List.foldl' Data.Bits.setBit Data.Bits.zeroBits)
  where
    prepend ~[y] ys = y:ys

makeCell :: Data.Word.Word16 -> Maybe Cell
makeCell ys
  | ys == Data.Bits.zeroBits   = Nothing
  | Data.Bits.popCount ys == 1 = Just $ Fixed ys
  | otherwise                  = Just $ Possible ys

pruneCells :: Grid -> CellIxs -> Maybe Grid
pruneCells grid cellIxs = Control.Monad.foldM pruneCell grid cellIxs
  where
    cells         = map (grid !) cellIxs
    exclusives    = exclusivePossibilities cells
    allExclusives = setBits Data.Bits.zeroBits exclusives
    fixeds        = setBits Data.Bits.zeroBits [x | Fixed x <- cells]

    pruneCell g i =
      pruneCellByFixed g (i, g ! i) >>= \g' -> pruneCellByExclusives g' (i, g' ! i)

    pruneCellByFixed g (_, Fixed _) = Just g
    pruneCellByFixed g (i, Possible xs)
      | xs' == xs = Just g
      | otherwise = flip (replaceCell i) g <$> makeCell xs'
      where
        xs' = xs Data.Bits..&. Data.Bits.complement fixeds

    pruneCellByExclusives g (_, Fixed _) = Just g
    pruneCellByExclusives g (i, Possible xs)
      | null exclusives                = Just g
      | intersection == xs             = Just g
      | intersection `elem` exclusives =
          flip (replaceCell i) g <$> makeCell intersection
      | otherwise                      = Just g
      where
        intersection = xs Data.Bits..&. allExclusives

pruneGrid' :: Grid -> Maybe Grid
pruneGrid' grid =
  Control.Monad.foldM pruneCells grid allRowIxs
  >>= flip (Control.Monad.foldM pruneCells) allColIxs
  >>= flip (Control.Monad.foldM pruneCells) allSubGridIxs

pruneGrid :: Grid -> Maybe Grid
pruneGrid = fixM pruneGrid'

isGridFilled :: Grid -> Bool
isGridFilled = not . Data.Vector.any isPossible

isGridInvalid :: Grid -> Bool
isGridInvalid grid =
  any isInvalidRow (map (map (grid !)) allRowIxs)
  || any isInvalidRow (map (map (grid !)) allColIxs)
  || any isInvalidRow (map (map (grid !)) allSubGridIxs)
  where
    isInvalidRow row =
      let fixeds         = [x  | Fixed x <- row]
          emptyPossibles = [() | Possible x <- row, x == Data.Bits.zeroBits]
      in hasDups fixeds || not (null emptyPossibles)

    hasDups l = hasDups' l []

    hasDups' [] _ = False
    hasDups' (y:ys) xs
      | y `elem` xs = True
      | otherwise   = hasDups' ys (y:xs)

nextGrids :: Grid -> (Grid, Grid)
nextGrids grid =
  let (i, first@(Fixed _), rest) =
        fixCell
        . Data.Vector.minimumBy (compare `Data.Function.on` (possibilityCount . snd))
        . Data.Vector.imapMaybe (\j cell -> if isPossible cell then Just (j, cell) else Nothing)
        $ grid
  in (replaceCell i first grid, replaceCell i rest grid)
  where
    possibilityCount (Possible xs) = Data.Bits.popCount xs
    possibilityCount (Fixed _)     = 1

    fixCell ~(i, Possible xs) =
      let x = Data.Bits.countTrailingZeros xs
      in case makeCell (Data.Bits.clearBit xs x) of
        Nothing -> error "Impossible case"
        Just cell -> (i, Fixed (Data.Bits.bit x), cell)

solve :: Grid -> Maybe Grid
solve grid = pruneGrid grid >>= solve'
  where
    solve' g
      | isGridInvalid g = Nothing
      | isGridFilled g  = Just g
      | otherwise       =
          let (grid1, grid2) = nextGrids g
          in solve grid1 <|> solve grid2

main :: IO ()
main = do
  inputs <- lines <$> getContents
  Control.Monad.forM_ inputs $ \input ->
    case readGrid input of
      Nothing   -> putStrLn "Invalid input"
      Just grid -> case solve grid of
        Nothing    -> putStrLn "No solution found"
        Just grid' -> putStrLn $ showGrid grid'