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: Wrong Answer)

main :: IO ()
main = do
  n <- readLn
  s <- getLine
  print $ solve n s

solve :: Int -> String -> String
solve n s
  | coresp ss s = ss
  | coresp sw s = sw
  | coresp ws s = ws
  | coresp ww s = ww
  | otherwise = "-1"
  where
    ss = "SS" ++ g 'S' 'S' s
    sw = "SW" ++ g 'S' 'W' s
    ws = "WS" ++ g 'W' 'S' s
    ww = "WW" ++ g 'W' 'W' s
    coresp (x:y:rest) (z:zx) =
      let
        l = last rest
        ll = last.init $ (y:rest)
        z' = last zx
      in
        c x z l y && c l z' ll x

g a b (x:y:[]) = []
g a b (x:y:rest) =
  c : g b c (y:rest)
  where
    not 'S' = 'W'
    not 'W' = 'S'
    c = case (b, y) of
          ('S', 'o') -> a
          ('S', 'x') -> not a
          ('W', 'o') -> not a
          ('W', 'x') -> a
g a b _ = []

c :: Char -> Char -> Char -> Char -> Bool
c sw xo l r =
  case (sw, xo) of
    ('S', 'o') -> l == r
    ('S', 'x') -> l /= r
    ('W', 'o') -> l /= r
    ('W', 'x') -> l == r