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;
const int maxn = 1e5 + 100;
const int mod = 1e9 + 7;
int n, s[maxn];
char str[maxn];

bool fun(int a, int b) {
    s[0] = a, s[1] = b;
    for (int i = 1; i < n; i++) {
        if (s[i]) {
            if (str[i] == 'o') {
                s[i + 1] = s[i - 1];
            } else {
                s[i + 1] = s[i - 1] ^ 1;
            }
        } else {
            if (str[i] == 'o') {
                s[i + 1] = s[i - 1] ^ 1;
            } else {
                s[i + 1] = s[i - 1];
            }
        }
    }
    if (((s[1] == s[n - 1] && str[0] == 'o') || (s[1] != s[n - 1] && str[0] == 'x')) &&
        ((s[0] == s[n - 2] && str[n - 1] == 'o') || (s[1] != s[n - 2] && str[n - 1] == 'x'))) {
        for (int i = 0; i < n; i++) {
            if (s[i]) cout << "S";
            else cout << "W";
        }
        cout << endl;
        //cout<<a<<" "<<b<<endl;
        return 1;
    }
    return 0;
}

int main() {
    cin >> n;
    cin >> str;
    if (fun(0, 1));
    else if (fun(0, 0));
    else if (fun(1, 1));
    else if (fun(1, 0));
    else cout << -1 << endl;
    return 0;
}