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: Accepted)

#include <bits/stdc++.h>

using namespace std;
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define MIN(a,b) ((a)>(b)? (b): (a))
#define MAX(a,b) ((a)<(b)? (b): (a))

const long long INF = 1LL << 60;
typedef unsigned long long ll;
const long long MOD = 1000000000 + 7;

int main(){
    int n;
    cin >> n;
    string s;
    cin >> s;
    rep(i,4){
        char res[n+2];    
        if(i%2 == 0) res[0] = 'S';
        else res[0] = 'W';
        if(i/2 == 0) res[1] = 'S';
        else res[1] = 'W';
        rep(j,n){
            char bs = res[j];
            char ns = res[j+1];
            if(bs == 'S' && ns == 'S' ){
                if(s[j] == 'o') res[j+2] = 'S';
                else res[j+2] = 'W'; 
            }else if(bs == 'S' && ns == 'W'){
                if(s[j] == 'o') res[j+2] = 'W';
                else res[j+2] = 'S';                 
            }else if(bs == 'W' && ns == 'S'){
                if(s[j] == 'o') res[j+2] = 'W';
                else res[j+2] = 'S'; 
            }else if(bs == 'W' && ns == 'W'){
                if(s[j] == 'o') res[j+2] = 'S';
                else res[j+2] = 'W'; 
            }    
        }
        if (res[n] == res[0] && res[n+1] == res[1]){
            for(int j = 1; j< n+1; j++) cout << res[j] ;
            cout << endl;
            return 0;
        }
    }
    cout << -1 << endl;
    return 0;
}