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 <iostream>
#include <vector>
#include <algorithm>
#define rep(i, n) for(int i = 0; i < (int)(n); ++i)
#define REP(i, n) for(int i = 1; i < (int)(n); ++i)
using namespace std;

int main() {
    int N;
    cin >> N;
    vector<char> S(N);
    rep(i, N) cin >> S[i];
    
    vector<char> animal = {'S', 'W'};
    vector<char> ans(N);
    rep(i, 4) {
        ans[0] = animal[i & (1 << 1)];
        ans[1] = animal[i & (1 << 2)];
        for (int j = 2; j < N; ++j) {
            if (ans[j - 1] == 'S') {
                if (S[j - 1] == 'o') ans[j] = ans[j - 2];
                else ans[j] = 'S' + 'W' - ans[j - 2];
            } else {
                if (S[j - 1] == 'o') ans[j] = 'S' + 'W' - ans[j - 2];
                else ans[j] = ans[j - 2];
            }
        }
        
        bool judge = true;
        if (ans[0] == 'S') {
            if (S[0] == 'o' && ans[1] != ans[N - 1]) judge = false;
            if (S[0] == 'x' && ans[1] == ans[N - 1]) judge = false;
        } else {
            if (S[0] == 'o' && ans[1] == ans[N - 1]) judge = false;
            if (S[0] == 'x' && ans[1] != ans[N - 1]) judge = false;
        }
        if (ans[N - 1] == 'S') {
            if (S[N - 1] == 'o' && ans[0] != ans[N - 2]) judge = false;
            if (S[N - 1] == 'x' && ans[0] == ans[N - 2]) judge = false;
        } else {
            if (S[N - 1] == 'o' && ans[0] == ans[N - 2]) judge = false;
            if (S[N - 1] == 'x' && ans[0] != ans[N - 2]) judge = false;
        }
        if (judge) {
            rep(j, N) cout << ans[j];
            cout << endl;
            return 0;
        }
    }
    cout << -1 << endl;
    return 0;
}