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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
#define rep(i,N) for(int (i)=0;(i) < (N); (i)++)

string animals(string res, int& N, string& S){
    for(int i=1;i<N-1;i++){
        if(res[i] == 'S'){
            if(S[i] == 'o'){
                if(res[i-1] == 'S') res += 'S';
                else res += 'W';
            }
            else {
                if(res[i-1] == 'S') res += 'W';
                else res += 'S';
            }
        }
        else {
            if(S[i] == 'o'){
                if(res[i-1] == 'S') res += 'W';
                else res += 'S';
            }
            else{
                if(res[i-1] == 'S') res += 'S';
                res += 'W';
            }
        }
    }

    bool ok = true;
    if(res[0] == 'S'){
        if(S[0] == 'o' && res[N-1] != res[1]) ok = false;
        if(S[0] == 'x' && res[N-1] == res[1]) ok = false;
    }
    else {
        if(S[0] == 'o' && res[N-1] == res[1]) ok = false;
        if(S[0] == 'x' && res[N-1] != res[1]) ok = false;
    }
    for(int i=1;i<N;i++){
        if(res[i] == 'S'){
            if(S[i] == 'o' && res[i-1] != res[(i+1)%N]) ok = false;
            if(S[i] == 'x' && res[i-1] == res[(i+1)%N]) ok = false;
        }
        else {
            if(S[i] == 'o' && res[i-1] == res[(i+1)%N]) ok = false;
            if(S[i] == 'x' && res[i-1] != res[(i+1)%N]) ok = false;
        }
    }

    //cout << res << endl;

    if(!ok) return "-1";
    return res;
}

int main(){
    int N;
    string S;
    cin >> N >> S;

    string ans = "-1";

    if(ans == "-1") ans = animals("SS",N,S);
    if(ans == "-1") ans = animals("SW",N,S);
    if(ans == "-1") ans = animals("WS",N,S);
    if(ans == "-1") ans = animals("WW",N,S);

    cout << ans << endl;

}