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)

import Control.Applicative

getNext :: Bool -> Bool -> Bool -> Bool
getNext x y z = if (y && z) || (not $ y || z) then x else not x

oxToBool :: String -> [Bool]
oxToBool [] = []
oxToBool (x:xs) = (if (x == 'o') then True
                                else False)
                                : oxToBool xs

typeChange :: [Bool] -> [Bool] -> ([(Bool,Bool)],[Bool],[Bool])
typeChange (p:q:rs) (x:y:_) = ([(p,x),(q,y)],(p:q:rs),[x,y])

lastToHead :: [a] -> [a]
lastToHead xs = last xs : (init xs)

sortResult :: [Bool] -> [Bool]
sortResult = lastToHead . lastToHead

forCycle :: ([(Bool,Bool)], [Bool], [Bool]) -> Maybe [Bool]
forCycle ([(s,t),(u,v)],[x],[p,q])   = if getNext q s t == v then Just [(getNext q s t)] else Nothing
forCycle ([(s,t),(u,v)],[x,y],[p,q]) = if getNext p y q == t then (:) <$> (Just (getNext p y q)) <*> forCycle ([(s,t),(u,v)],[x],[q,getNext p y q]) else Nothing
forCycle ([(s,t),(u,v)],(_:y:xs),[p,q]) = (:) <$> (Just h) <*> forCycle ([(s,t),(u,v)],(y:xs),[q,h])
  where h = getNext p y q

judgeResult :: [Maybe [Bool]] -> String
judgeResult [] = "-1"
judgeResult (x:xs) = case x of Just i -> (returnSW.sortResult) i
                               Nothing -> judgeResult xs

returnSW :: [Bool] -> String
returnSW [] = []
returnSW (x:xs) = h : returnSW xs
  where h = if x == True then 'S' else 'W'

returnResult :: [Bool] -> String
returnResult xs = judgeResult $ map (forCycle.typeChange xs) $ (:) <$> [True, False] <*> [[True], [False]]

main = do
  num <- fmap read getLine :: IO Int
  nums <- fmap oxToBool getLine :: IO [Bool]
  putStrLn $ returnResult nums