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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int N;

int check(const char *s, char *t, int flag) {
    int i;

    if (flag & 1) t[0] = 'W';
    else t[0] = 'S';
    i = 0;
    if (((flag & 1) && s[0] == 'o') || (!(flag & 1) && s[0] == 'x')) {
        if (flag & 2) { t[1] = 'S'; t[N-1] = 'W'; }
        else { t[1] = 'W'; t[N-1] = 'S'; }
    } else if (((flag & 1) && s[0] == 'x') || (!(flag & 1) && s[0] == 'o')) {
        if (flag & 2) { t[1] = 'W'; t[N-1] = 'W'; }
        else { t[1] = 'S'; t[N-1] = 'S'; }
    }
    if (N == 3) {
        if (((t[2] == t[0] && t[1] == 'S' && s[1] == 'o') || 
             (t[2] != t[0] && t[1] == 'S' && s[1] == 'x') ||
             (t[2] == t[0] && t[1] == 'W' && s[1] == 'x') ||
             (t[2] != t[0] && t[1] == 'W' && s[1] == 'o')) && 
            ((t[1] == t[0] && t[2] == 'S' && s[2] == 'o') || 
             (t[1] != t[0] && t[2] == 'S' && s[2] == 'x') ||
             (t[1] == t[0] && t[2] == 'W' && s[2] == 'x') ||
             (t[1] != t[0] && t[2] == 'W' && s[2] == 'o'))) {
            t[N] = '\0';
            return 0;
        } else {
    //        printf("%s\n", t);
            return 1;
        }
    } else {
        while (++i < N-2) {
            if (t[i] == 'S') {
                if (s[i] == 'o') t[i+1] = t[i-1];
                else if (t[i-1] == 'S') t[i+1] = 'W';
                else t[i+1] = 'S';
            } else {
                if (s[i] == 'o') {
                    if (t[i-1] == 'W') t[i+1] = 'S';
                    else t[i+1] = 'W';
                } else t[i+1] = t[i-1];
            }
        }
        if ((t[N-2] == t[0] && t[N-1] == 'S' && s[N-1] == 'o') || 
            (t[N-2] != t[0] && t[N-1] == 'S' && s[N-1] == 'x') ||
            (t[N-2] == t[0] && t[N-1] == 'W' && s[N-1] == 'x') ||
            (t[N-2] != t[0] && t[N-1] == 'W' && s[N-1] == 'o')) {
            t[N] = '\0';
            return 0;
        } else {
    //        printf("%s\n", t);
            return 1;
        }
    }
}

int main(void) {
    int i, res;
    char S[100010], T[100010];
    scanf("%d%s", &N, &S);
    memset(T,0,100010);

    memset(T,0,100010);
    res = check(S, T, 0);
    while (res && ++i<4) {
        memset(T,0,100010);
        res = check(S, T, i);
    }
    if (!res) printf("%s\n", T);
    else printf("-1\n");
    return 0;
}