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;

#define rep(i, a) for (int i = 0; i < (a); i++ )

 
typedef pair<int,int> P;
typedef long long ll;
 
const int INF = 1001001001;
const int MOD = 1000000007;
const double PI=acos(-1);

char next_char(char now, char pre, string s, int k) {
    if (s[k]=='o') {
        if (now=='S') return pre;
        else if (pre=='W') return 'S';
        else return 'W';
    }
    else {
        if (now=='W') return pre;
        else if (pre=='W') return 'S';
        else return 'W';
    }
}

int main(){
    int N;
    cin >> N;
    string s;
    cin >> s;
    
    map<int,string> mp;
    mp[0] = "S";
    mp[1] = "W";

    rep(i,2) rep(j,2) {
        string ans = mp[i] + mp[j];
        rep(k,N-1) {
            char now = ans[k+1];
            char pre = ans[k];
            char next = next_char(now,pre,s,k+1);
            if (k==N-2) {
                if (next==ans[0]) {
                    now = ans[0];
                    pre = ans[-1];
                    next = next_char(now,pre,s,0);
                    if (next==ans[1]) {
                        cout << ans << endl;

                        return 0;
                    }
                }
            }
            else {
                ans += next;
            }
        }
    }
    cout << -1 << endl;
    return 0;
}