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 Data.Array

type Z_2 = Bool

addz2::Z_2 -> Z_2 -> Z_2
addz2 True True = False
addz2 False False = False
addz2 True False = True
addz2 False True = True

addz2_3::Z_2 -> Z_2 -> Z_2 -> Z_2
addz2_3 x y z = addz2 (addz2 x y) z

convert::String->[Z_2]
convert []    = []
convert (x:xs)= (if x=='o' then False else True):(convert xs)

deconv::[Z_2]->String
deconv []     = []
deconv (x:xs) = (if x then 'W' else 'S'):(deconv xs)


genline::Array Int Z_2-> Int -> (Z_2,Z_2)->Array Int Z_2
genline b n (init_1,init_2) = let a = listArray (0,n+1) (init_1:init_2:[addz2_3 (a!(i-1)) (a!(i-2)) (b!(mod (i-1) n)) |i<-[2..(n+1)]])  in a

check::Int -> Array Int Z_2 -> Bool
check n a =((a!0) == (a!n))&&((a!1) == (a!(n+1)))

solver::Array Int Z_2 -> Int ->String
solver b n = let pat = map (genline b n) [(False,False),(False,True),(True,False),(False,False)] in
              let ok = filter (check n) pat in
              if ok==[] then "-1" else deconv ( take n (elems (head ok)))

main::IO()
main= do
  nc<-getLine
  let n = read nc::Int
  dat<-getLine
  let b = listArray (0,n-1) (convert dat)
  putStr ((solver b n)++"\n")