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 <iostream>
#include <array>
#include <vector>
#include <iomanip>
#include <string>
#include <cmath>
#include <algorithm>
#include <queue>
#include <map>
#include <set>
using namespace std;

typedef  pair<int,int> P;
typedef long long LL;

const LL  INF=1<<31;
const LL MOD=1000000007;



int main(){
    LL n;
    string s;
    cin>>n>>s;
    
    string ans;
    bool answ=false;

    for(int j=0;j<4;j++){
        ans="";
        if(j=0)ans+="SS";
        if(j=1)ans+="SW";
        if(j=2)ans+="WS";
        if(j=3)ans+="WW";

    
    
    for(int i=1;i<n-1;++i){
        if(ans[i]=='S'){
            if(s[i]=='o')ans.push_back(ans[i-1]);
            else if(s[i]=='x'&&ans[i-1]=='S')ans.push_back('W');
            else ans.push_back('S');           
        }
        if(ans[i]=='W'){
            if(s[i]=='x')ans.push_back(ans[i-1]);
            else if(s[i]=='o'&&ans[i-1]=='S')ans.push_back('W');
            else ans.push_back('W');
        }
    }
    if(s[n-1]=='o'){
        if(ans[n-1]=='S'&&ans[0]==ans[n-2]){
            cout<<ans<<endl;
            return 0;
        }
        if(ans[n-1]=='W'&&ans[0]!=ans[n-2]){
            cout<<ans<<endl;
            return 0;

        }

    }
    if(s[n-1]=='x'){
        if(ans[n-1]=='S'&&ans[0]!=ans[n-2]){
            cout<<ans<<endl;
            return 0;
        }
        if(ans[n-1]=='W'&&ans[0]==ans[n-2]){
            cout<<ans<<endl;
            return 0;

        }
    }
}
    cout<<-1<<endl;
}