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;

int n;
string str;

int main() {
    cin >> n;
    cin >> str;

    vector<int> v(n), d(n,1), s(n), g(n, 1);
    s[n-1] = 1;
    g[n-1] = 0;
    for (int k = 0; k < n-1; k++) {
        int i = k % n;
        int r  = (i + 1) % n;
        int l = (n + i - 1) % n;

        if (str[i] == 'o') {
            if (v[i] == 0) {
                v[r] = v[l];
            } else {
                v[r] = !v[l];
            }
            if (d[i] == 0) {
                d[r] = d[l];
            } else {
                d[r] = !d[l];
            }
            if (s[i] == 0) {
                s[r] = s[l];
            } else {
                s[r] = !s[l];
            }
            if (g[i] == 0) {
                g[r] = g[l];
            } else {
                g[r] = !g[l];
            }
        } else {
            if (v[i] == 0) {
                v[r] = !v[l];
            } else {
                v[r] = v[l];
            }
            if (d[i] == 0) {
                d[r] = !d[l];
            } else {
                d[r] = d[l];
            }
            if (s[i] == 0) {
                s[r] = !s[l];
            } else {
                s[r] = s[l];
            }
            if (g[i] == 0) {
                g[r] = !g[l];
            } else {
                g[r] = g[l];
            }
        }
    }

    bool ans = true;
    if (str[n-1] == 'o') {
        if (v[n-1] == 0) {
            if (!(v[0] == v[n-2])) ans = false;
        } else {
            if (!(v[0] == !v[n-2])) ans = false;
        }
    } else {
        if (v[n-1] == 0) {
            if (!(v[0] == !v[n-2])) ans = false;
        } else {
            if (!(v[0] == v[n-2])) ans = false;
        }
    }
    bool ans1 = true;
    if (str[n-1] == 'o') {
        if (d[n-1] == 0) {
            if (!(d[0] == d[n-2])) ans1 = false;
        } else {
            if (!(d[0] == !d[n-2])) ans1 = false;
        }
    } else {
        if (d[n-1] == 0) {
            if (!(d[0] == !d[n-2])) ans1 = false;
        } else {
            if (!(d[0] == d[n-2])) ans1 = false;
        }
    }
    bool ans2 = true;
    if (str[n-1] == 'o') {
        if (s[n-1] == 0) {
            if (!(s[0] == s[n-2])) ans2 = false;
        } else {
            if (!(s[0] == !s[n-2])) ans2 = false;
        }
    } else {
        if (s[n-1] == 0) {
            if (!(s[0] == !s[n-2])) ans2 = false;
        } else {
            if (!(s[0] == s[n-2])) ans2 = false;
        }
    }
    bool ans3 = true;
    if (str[n-1] == 'o') {
        if (g[n-1] == 0) {
            if (!(g[0] == g[n-2])) ans3 = false;
        } else {
            if (!(g[0] == !g[n-2])) ans3 = false;
        }
    } else {
        if (g[n-1] == 0) {
            if (!(g[0] == !g[n-2])) ans3 = false;
        } else {
            if (!(g[0] == g[n-2])) ans3 = false;
        }
    }

    if (!ans && !ans1 && !ans2 && !ans3) {
        cout << -1 << endl;
        return 0;
    }

    if (ans) for (int i = 0; i < n; i++) cout << (v[i] ? 'W' : 'S');
    else if (ans1) for (int i = 0; i < n; i++) cout << (d[i] ? 'W' : 'S');
    else if (ans2) for (int i = 0; i < n; i++) cout << (s[i] ? 'W' : 'S');
    else if (ans3) for (int i = 0; i < n; i++) cout << (g[i] ? 'W' : 'S');
    cout << endl;

    return 0;
}