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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        char[] s = sc.next().toCharArray();
        char m = 'o';
        char b = 'x';
        boolean[] ans = null;
        for (int i = 0; i < 4; i++) {
            boolean[] a = new boolean[n];
            if((i&1) == 1) a[0] = true;
            else a[0] = false;
            if((i>>1 & 1) == 1) a[n-1] = true;
            else a[n-1] = false;
            if(a[0] && s[0] == m) a[1] = a[n-1];
            else if(a[0] && s[0] == b) a[1] = !a[n-1];
            else if(!a[0] && s[0] == m) a[1] = !a[n-1];
            else if(!a[0] && s[0] == b) a[1] = a[n-1];
            for (int j = 1; j < n-2; j++) {
                if(a[j] && s[j] == m) a[j+1] = a[j-1];
                else if(a[j] && s[j] == b) a[j+1] = !a[j-1];
                else if(!a[j] && s[j] == m) a[j+1] = !a[j-1];
                else if(!a[j] && s[j] == b) a[j+1] = a[j-1];
            }
            if(((a[n-2] && s[n-2] == m) || (!a[n-2] && s[n-2] == b)) && a[n-3] != a[n-1]) continue;
            if(((a[n-2] && s[n-2] == b) || (!a[n-2] && s[n-2] == m)) && a[n-3] == a[n-1]) continue;
            if(((a[n-1] && s[n-1] == m) || (!a[n-1] && s[n-1] == b)) && a[n-2] != a[0]) continue;
            if(((a[n-1] && s[n-1] == b) || (!a[n-1] && s[n-1] == m)) && a[n-2] == a[0]) continue;
            ans = a;
            break;
        }
        if(ans == null) System.out.println(-1);
        else{
            StringBuilder sb = new StringBuilder();
            for(boolean c : ans){
                if(c) sb.append("S");
                else sb.append("W");
            }
            System.out.println(sb.toString());
        }
        sc.close();

    }

}