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 <bits/stdc++.h>

using namespace std;

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

typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<ll> vl;

ll N;
string s;

void solve() {
    cin >> N >> s;
    rep(mask,4) {
        int ani[N];
        ani[0] = mask & 1;
        ani[1] = (mask >> 1) & 1;
        REP(i,2,N) {
            if (s[i-1] == 'o') {
                ani[i] = (ani[i-1]) ? (!ani[i-2]) : (ani[i-2]);
            } else {
                ani[i] = (ani[i-1]) ? (ani[i-2]) : (!ani[i-2]);
            }
        }
        bool flag = 0;
        if (s[N-1] == 'o') {
            flag = ani[0] == (ani[N-1]) ? (!ani[N-2]) : (ani[N-2]);
        } else {
            flag = ani[0] == (ani[N-1]) ? (ani[N-2]) : (!ani[N-2]);
        }
        if (flag) {
            rep(i,N) cout << (ani[i] ? "W" : "S");
            cout << endl;
            return;
        }
    }
    cout << -1 << endl;
}

int main() {
    cin.tie(0);
   	ios::sync_with_stdio(false);
    solve();
    return 0;
}