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<set>
#include <bitset>
#include<queue>
#include<vector>
#include<map>
#include<stack>
#include <cstdio>
#include<algorithm>
#include <sstream>
#include<string>
#include<string.h>
#include <cmath>
#include <iomanip>
#include <string>
#include<list>
#include <limits>
#include <numeric>
#include <type_traits>
#include<bitset>
#define int long long
#define ll long long
#define mod  1000000007
#define inf 1e17
#define rep(i,j,n) for(int i=j;i<n;i++)
#define P pair<int,int>
double pi = 3.141592653589793;
using namespace std;
//ここから始めよう
signed main(){
    int n;string s;cin>>n>>s;
    s+=s;
    //cout<<s<<endl;
    int animal[114514]={};
    rep(i,0,1<<2){
        rep(j,0,2){
            if(i&(1<<j))animal[j]=1;
        }
        rep(j,1,n+1){
            if((animal[j]==1&&s[j]=='o')||(animal[j]==0&&s[j]=='x'))animal[j+1]=animal[j-1];
            else animal[j+1]=animal[j-1]*-1+1;
        }
       // rep(j,0,n+1)cout<<animal[j];cout<<endl;
        if(animal[n]==animal[0]&&animal[n+1]==animal[1]){
            rep(j,0,n){if(animal[j]==0)cout<<'W';else cout<<'S';}cout<<endl;return 0;
        }
    }cout<<-1<<endl;return 0;
}