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: Accepted)

#include <bits/stdc++.h>

using namespace std;

char s[100005];

int a[100005], n;

inline bool ok(int p) {
    int l = (p + n - 1) % n;
    int r = (p + 1) % n;
    if(a[p]) {
        if(s[p] == 'o')
            return a[l] != a[r];
        else
            return a[l] == a[r];
    } else {
        if(s[p] == 'o')
            return a[l] == a[r];
        else
            return a[l] != a[r];
    }
}

bool check() {
    for(int i = 2; i < n; ++ i) {
        if(a[i - 1]) {
            if(s[i - 1] == 'o')
                a[i] = a[i - 2] ^ 1;
            else
                a[i] = a[i - 2];
        } else {
            if(s[i - 1] == 'o')
                a[i] = a[i - 2];
            else
                a[i] = a[i - 2] ^ 1;
        }
    }
    return ok(0) && ok(n - 1);
}

void output() {
    for(int i = 0; i < n; ++ i)
        putchar(a[i] ? 'W' : 'S');
    exit(0);
}

int main() {
    scanf("%d%s", &n, s);
    for(a[0] = 0; a[0] < 2; ++ a[0]) {
        for(a[1] = 0; a[1] < 2; ++ a[1]) {
            if(check())
                output();
        }
    }
    puts("-1");
    return 0;
}