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 Ruby (2.3.3) (judge verdict: Runtime Error)

#include <stdio.h>

#define MAX(X,Y) ((X)>(Y)?(X):(Y))
#define MIN(X,Y) ((X)<(Y)?(X):(Y))

int main(void){
    int n;
    char s[100001];
    int animals[100001];
    
    scanf("%d %s", &n, s);
    for (int initial = 0; initial <= 3; initial++){
        animals[0] = initial & 1; // sheep:0, wolf:1
        animals[1] = initial >> 1;
        for (int i=2; i<n; i++){
            animals[i] = animals[i-2] ^ (s[i-1]=='x');
            if (animals[i-1] == 1){
                animals[i] = 1-animals[i];
            }
        }
        if (animals[n-2] ^ animals[n-1] ^ (s[n-1]=='x') == animals[0] &&
            animals[n-1] ^ animals[0] ^ (s[0] == 'x') == animals[1]){
//        if (1){
            for (int i=0; i<n; i++){
                putchar("SW"[animals[i]]);
            }
            puts("");
            return 0;
        }
    }
    puts("-1");
    return 0;
}