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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#define rep(i, n) for (i = 0; i < n; i++)
#define rrep(i, n) for (i = n; i >= 0; i--)
#define max(a, b) (a > b ? a : b)
#define min(a, b) (a < b ? a : b)

#define O 1
#define X 0
#define S 1
#define W 0

int next(int p, int c, int a) {
    if (c == S) return a ? p : !p;
    if (c == W) return a ? !p : p;
}

int collect(int p, int c, int n, int a) {
    if (c == S) return a ? p == n : p != n;
    if (c == W) return a ? p != n : p == n;
}

int main() {
    static int n, s[114514], i, j;
    scanf("%d", &n);
    getchar();
    rep(i, n) s[i] = getchar() == 'o' ? O : X;

    static int p[4][114514] = { { S, S }, { S, W }, { W, S }, { W, W } };
    rep(i, 4) rep(j, n) {
        if (j < 2) continue;
        p[i][j] = next(p[i][j - 2], p[i][j - 1], s[j - 1]);
    }

    rep(i, 4) {
        if (collect(p[i][n - 1], p[i][0], p[i][1], s[0]) &&
            collect(p[i][n - 2], p[i][n - 1], p[i][0], s[n - 1])) {
            rep(j, n) putchar(p[i][j] ? 'S' : 'W');
            printf("\n");
            return 0;
        }
    }
    puts("-1");
    return 0;
}