Problem:
Score : 500 points

Problem Statement

Snuke, who loves animals, built a zoo.

There are N animals in this zoo. They are conveniently numbered 1 through N, and arranged in a circle.
The animal numbered i (2≤i≤N-1) is adjacent to the animals numbered i-1 and i+1. Also, the animal numbered 1 is adjacent to the animals numbered 2 and N, and the animal numbered N is adjacent to the animals numbered N-1 and 1.

There are two kinds of animals in this zoo: honest sheep that only speak the truth, and lying wolves that only tell lies.

Snuke cannot tell the difference between these two species, and asked each animal the following question: "Are your neighbors of the same species?" The animal numbered i answered s_i. Here, if s_i is o, the animal said that the two neighboring animals are of the same species, and if s_i is x, the animal said that the two neighboring animals are of different species.

More formally, a sheep answered o if the two neighboring animals are both sheep or both wolves, and answered x otherwise.
Similarly, a wolf answered x if the two neighboring animals are both sheep or both wolves, and answered o otherwise.

Snuke is wondering whether there is a valid assignment of species to the animals that is consistent with these responses. If there is such an assignment, show one such assignment. Otherwise, print -1.

Constraints

3 ≤ N ≤ 10^{5}

s is a string of length N consisting of o and x.

Input

The input is given from Standard Input in the following format:

N
s

Output

If there does not exist an valid assignment that is consistent with s, print -1.
Otherwise, print an string t in the following format. The output is considered correct if the assignment described by t is consistent with s.

t is a string of length N consisting of S and W.

If t_i is S, it indicates that the animal numbered i is a sheep. If t_i is W, it indicates that the animal numbered i is a wolf.

Sample Input 1

6
ooxoox

Sample Output 1

SSSWWS

For example, if the animals numbered 1, 2, 3, 4, 5 and 6 are respectively a sheep, sheep, sheep, wolf, wolf, and sheep, it is consistent with their responses. Besides, there is another valid assignment of species: a wolf, sheep, wolf, sheep, wolf and wolf.

Let us remind you: if the neiboring animals are of the same species, a sheep answers o and a wolf answers x. If the neiboring animals are of different species, a sheep answers x and a wolf answers o.

Sample Input 2

3
oox

Sample Output 2

-1

Print -1 if there is no valid assignment of species.

Sample Input 3

10
oxooxoxoox

Sample Output 3

SSWWSSSWWS

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

main :: IO ()
main = do
  n <- (read :: String -> Int) <$> getLine
  strs <- getLine
  let answers = solve n $ encode strs
  if null answers then print $ -1
                  else putStrLn.decode.drop 1 $ reverse.drop 1 $head answers
encode :: String -> [Bool]
encode str = map (== 'o') str
 
decode :: [Bool] -> String
decode [] = "-1"
decode bs = map (\b -> if b then 'S' else 'W') bs
 
 
xor :: Bool -> Bool -> Bool
xor a b = (not a && b) || (not b && a)
 
solve :: Int -> [Bool] -> [[Bool]]
solve n input = filter check $ search input [[True, True]
                     ,[True, False]
                     ,[False, True]
                     ,[False, False]]
  where
    search :: [Bool] -> [[Bool]] -> [[Bool]]
    search [] result = result
    search (x:xs) result = search xs $ map next result 
      where
        next :: [Bool] -> [Bool]
        next (s1:s2:s3) = if xor x s1
                          then not s2:s1:s2:s3
                          else s2:s1:s2:s3 
    check :: [Bool] -> Bool
    check bs = and $ zipWith (==) (take 2 bs) (drop n bs)