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();
        String s = sc.next();
        sc.close();

        boolean[] ans = new boolean[n];
        boolean[] ani = new boolean[n];
        for(int i=0; i<n; i++){
            ans[i] = s.charAt(i) == 'o';
        }

        ani[0] = true;
        ani[1] = true;
        if(setAndCheck(n, ans, ani)){
            print(n, ani);
            return;
        }

        ani[0] = true;
        ani[1] = false;
        if(setAndCheck(n, ans, ani)){
            print(n, ani);
            return;
        }

        ani[0] = false;
        ani[1] = true;
        if(setAndCheck(n, ans, ani)){
            print(n, ani);
            return;
        }

        ani[0] = false;
        ani[1] = false;
        if(setAndCheck(n, ans, ani)){
            print(n, ani);
            return;
        }

        System.out.println(-1);
    }

    static boolean setAndCheck(int n, boolean[] ans, boolean[] ani){
        boolean ret = true;
        for(int i=1; i<n-1; i++){
            if(ani[i] == ans[i]){
                ani[i+1] = ani[i-1];
            }else{
                ani[i+1] = !ani[i-1];
            }
        }

        if(ani[0] == ans[0]){
            ret = ani[1] == ani[n-1];
        }else{
            ret = ani[1] != ani[n-1];
        }
        if(!ret) return false;

        if(ani[n-1] == ans[n-1]){
            ret = ani[n-2] == ani[0];
        }else{
            ret = ani[n-2] != ani[0];
        }

        return ret;
    }

    static void print(int n, boolean[] ani){
        StringBuilder sb = new StringBuilder();
        for(int i=0; i<n; i++){
            if(ani[i]){
                sb.append('S');
            }else{
                sb.append('W');
            }
        }
        System.out.println(sb.toString());
    }
}