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>
#define sinv(X) ((X) == 'o' ? 'x' : 'o')
#define ainv(X) ((X) == 'S' ? 'W' : 'S')

int n;
char s[100005];
char a[100005];
char ch[] = {'S', 'W'};

int f(void);

int main()
{
    scanf("%d", &n);
    scanf("%s", s);

    for (int i = 0; i < 2; i++) {
        for (int j = 0; j < 2; j++) {
            a[0] = ch[i];
            a[1] = ch[j];

            if (f()) {
                printf("%s\n", a);
                return 0;
            }
        }
    }

    printf("-1\n");
    
    return 0;
}

int f(void)
{
    char op;
    
    for (int i = 1; i < n; i++) {
        op = s[i];

        if (a[i] == 'W') {
            op = sinv(op);
        }

        if (op == 'o') {
            a[i + 1] = a[i - 1];
        }
        else {
            a[i + 1] = ainv(a[i - 1]);
        }
    }

    if (a[n] == a[0]) {
        a[n] = 0;
        return 1;
    }

    return 0;
}