#include <iostream>
#include <string>
using namespace std;

int N; string S;
bool ani[100010];
bool greedy(bool f1, bool f2){
    ani[0]=f1;
    ani[1]=f2;
    for(int i=2; i<N; ++i){
        ani[i]=((S[i-1]=='o')^ani[i-1])^ani[i-2];
    }
    return (ani[1]^ani[N-1])^(S[0]=='o')==ani[0] && (ani[N-2]^ani[0])^(S[N-1]=='o')==ani[N-1];
}
int main() {
	cin >> N >> S;
	bool flag=false;
	for(int i=0; i<4; ++i){
	    if(greedy(i<2, i%2<1)){
	        flag=true;
	        break;
	    }
	}
	if(flag){
	    for(int i=0; i<N; ++i) cout << (ani[i] ? 'S' : 'W');
	    cout << endl;
	}
	else cout << -1 << endl;
	return 0;
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

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 <iostream>
#include <string>
using namespace std;

int N; string S;
bool ani[100010];
bool greedy(bool f1, bool f2){
    ani[0]=f1;
    ani[1]=f2;
    for(int i=2; i<N; ++i){
        ani[i]=((S[i-1]=='o')^ani[i-1])^ani[i-2];
    }
    return (ani[1]^ani[N-1])^(S[0]=='o')==ani[0] && (ani[N-2]^ani[0])^(S[N-1]=='o')==ani[N-1];
}
int main() {
	cin >> N >> S;
	bool flag=false;
	for(int i=0; i<4; ++i){
	    if(greedy(i<2, i%2<1)){
	        flag=true;
	        break;
	    }
	}
	if(flag){
	    for(int i=0; i<N; ++i) cout << (ani[i] ? 'S' : 'W');
	    cout << endl;
	}
	else cout << -1 << endl;
	return 0;
}

```