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 Java (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;
 
public class Main {
    public static void main(String[] args) throws Exception {
        FastScanner sc = new FastScanner(System.in);
        int n = sc.nextInt();
        char[] s = sc.next().toCharArray();
        char[] ans = new char[n];
        for(int i = 0; i < 4; i++){
            ans[0] = i / 2 <= 0 ? 'S' : 'W';
            ans[1] = i % 2 == 0 ? 'S' : 'W';
            String tmp = getAns(n,s,ans);
            if(!tmp.isEmpty()){
                System.out.println(tmp);
                return;
            }
        }
        System.out.println(-1);
    }
    
    public static String getAns(int n, char[] s, char[] ans){
        for(int i = 2; i < n; i++){
            if(ans[i-2] == 'S' && ans[i-1] == 'S'){
                if(s[i-1] == 'o'){
                    ans[i] = 'S';
                }else{
                    ans[i] = 'W';
                }
            }else if(ans[i-2] == 'S' && ans[i-1] == 'W'){
                if(s[i-1] != 'o'){
                    ans[i] = 'S';
                }else{
                    ans[i] = 'W';
                }
            }else if(ans[i-2] == 'W' && ans[i-1] == 'S'){
                if(s[i-1] != 'o'){
                    ans[i] = 'S';
                }else{
                    ans[i] = 'W';
                }
            }else{
                if(s[i-1] == 'o'){
                    ans[i] = 'S';
                }else{
                    ans[i] = 'W';
                }
            }
        }
        if(((((ans[0] == 'S' && s[0] == 'o') || (ans[0] == 'W' && s[0] == 'x')) && ans[n-1] == ans[1])
        || (((ans[0] == 'S' && s[0] == 'x') || (ans[0] == 'W' && s[0] == 'o')) && ans[n-1] != ans[1]))
        && 
        (((ans[n-1] == 'S' && s[n-1] == 'o') || (ans[n-1] == 'W' && s[n-1] == 'x')) && ans[0] == ans[n-2])
        || (((ans[n-1] == 'W' && s[n-1] == 'o') || (ans[n-1] == 'S' && s[n-1] == 'x')) && ans[0] != ans[n-2])){
            return new String(ans);
        }else{
            return "";
        }
    }
}

class FastScanner {
    private BufferedReader reader = null;
    private StringTokenizer tokenizer = null;
    public FastScanner(InputStream in) {
        reader = new BufferedReader(new InputStreamReader(in));
        tokenizer = null;
    }
    
    public void close() throws Exception{
        this.reader.close();
        return;
    }

    public String next() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public String nextLine() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken("\n");
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public double nextDouble() {
         return Double.parseDouble(next());
    }

    public int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        return a;
    }

    public long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nextLong();
        return a;
    } 
}