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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
typedef pair<int,int>pa;
map<int,int>mp;
const int N=2e5+100;
int dp[50][500][500];///前n个a有i，b有j的最小花费
int a[50],b[50],c[50];
int inf=0x3f3f3f3f;
string s;
int n;
bool slove(int a,int b)
{
    vector<int>ve;
    ve.push_back(a);ve.push_back(b);
    for(int i=1;i<n;i++){
        if(s[i]=='o'){
           if(ve[i]==1) ve.push_back(ve[i-1]);
           else ve.push_back(3-ve[i-1]);
        }
        else {
            if(ve[i]==1) ve.push_back(3-ve[i-1]);
            else ve.push_back(ve[i-1]);
        }
    }
    if(ve[n]==ve[0]) {
        for(int i=0;i<ve.size()-1;i++){
            if(ve[i]==1) cout<<'S';
            else cout<<'W';
        }
        return true;
    }
    return false;
}
int main()
{
    ios::sync_with_stdio(0);cin.tie(0);
    cin>>n>>s;
    int f=0;
    for(int i=1;i<=2;i++){
        for(int j=1;j<=2;j++){
            f=slove(i,j);
            if(f) break;
        }
        if(f) break;
    }
    if(!f) cout<<-1<<endl;
    return 0;
}