#include <bits/stdc++.h>
using namespace std;


int main(void){
    int n;
    cin>>n;
    string ox;
    cin>>ox;
    ox+=ox;
    vector <int> ss(n+2);
    ss[0]= 1;ss[1]= 1;
    
    for(int j=0;j<4;j++){
        for(int i=2;i<=n+1;i++){
            if(ss[i-1]==1){
                if(ox[i-1]=='o'){
                    ss[i]=ss[i-2];
                }else{
                    ss[i]=ss[i-2]*(-1);
                }
            }else{
                if(ox[i-1]=='o'){
                    ss[i]=ss[i-2]*(-1);
                }else{
                    ss[i]=ss[i-2];
                }
            }
        }
    
        if(ss[0]==ss[n] and ss[1]==ss[n+1])
        {
            for(int i=0;i<n;i++){
                if(ss[i]==1) cout<<'S';
                else cout<<'W';
            }
            cout<<endl;
            return 0;
        }
        
        if(j%2==0) ss[0]*=(-1);
        else ss[1]*=(-1);
    
    }
    cout<<-1<<endl;
    return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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.

Examples

Input

6
ooxoox


Output

SSSWWS


Input

3
oox


Output

-1


Input

10
oxooxoxoox


Output

SSWWSSSWWS

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;


int main(void){
    int n;
    cin>>n;
    string ox;
    cin>>ox;
    ox+=ox;
    vector <int> ss(n+2);
    ss[0]= 1;ss[1]= 1;
    
    for(int j=0;j<4;j++){
        for(int i=2;i<=n+1;i++){
            if(ss[i-1]==1){
                if(ox[i-1]=='o'){
                    ss[i]=ss[i-2];
                }else{
                    ss[i]=ss[i-2]*(-1);
                }
            }else{
                if(ox[i-1]=='o'){
                    ss[i]=ss[i-2]*(-1);
                }else{
                    ss[i]=ss[i-2];
                }
            }
        }
    
        if(ss[0]==ss[n] and ss[1]==ss[n+1])
        {
            for(int i=0;i<n;i++){
                if(ss[i]==1) cout<<'S';
                else cout<<'W';
            }
            cout<<endl;
            return 0;
        }
        
        if(j%2==0) ss[0]*=(-1);
        else ss[1]*=(-1);
    
    }
    cout<<-1<<endl;
    return 0;
}

```