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.io.*;
import java.util.*;
import java.util.Map.Entry;

public class Main {
	
	final boolean isDebug = false;
	String fileName = "input.txt";
	FastScanner sc;
	//PrintWriter out;
	final int MOD = 1000000007;
	
	int N;
	String s;
	boolean[] isSheep;
	
	/* solve */
	void solve(){
		N = sc.nextInt();
		s = sc.next();
		isSheep = new boolean[N];
		
		isSheep[0] = true;
		if(s.charAt(0) == 'o'){
			isSheep[1] = true; isSheep[N-1] = true;
			if(calc()) return;
			isSheep[1] = false; isSheep[N-1] = false;
			if(calc()) return;
		}else{
			isSheep[1] = true; isSheep[N-1] = false;
			if(calc()) return;
			isSheep[1] = false; isSheep[N-1] = true;
			if(calc()) return;
		}
		
		isSheep[0] = false;
		if(s.charAt(0) == 'o'){
			isSheep[1] = false; isSheep[N-1] = true;
			if(calc()) return;
			isSheep[1] = true; isSheep[N-1] = false;
			if(calc()) return;
		}else{
			isSheep[1] = true; isSheep[N-1] = true;
			if(calc()) return;
			isSheep[1] = false; isSheep[N-1] = false;
			if(calc()) return;
		}
		
		System.out.println(-1);
	}
	
	public boolean calc(){
		for(int i = 1; i < N; i++){
			if(i == N - 2){
				boolean tmp;
				if((isSheep[i] && s.charAt(i) == 'o') || (!isSheep[i] && s.charAt(i) == 'x')) tmp = isSheep[i-1];
				else tmp = !isSheep[i-1];
				
				if(tmp != isSheep[N-1]) return false;
			}else if(i == N - 1){
				boolean tmp;
				if((isSheep[i] && s.charAt(i) == 'o') || (!isSheep[i] && s.charAt(i) == 'x')) tmp = isSheep[i-1];
				else tmp = !isSheep[i-1];
				
				if(tmp == isSheep[0]){
					for(boolean is : isSheep) System.out.print(is ? "S" : "W");
					System.out.println();
					return true;
				}else{
					return false;
				}
			}else{
				if((isSheep[i] && s.charAt(i) == 'o') || (!isSheep[i] && s.charAt(i) == 'x')) isSheep[i+1] = isSheep[i-1];
				else isSheep[i+1] = !isSheep[i-1];
			}
		}
		
		return false;
	}
	/* end solve */
	
	/* main */
	public static void main(String[] args) throws IOException {
		new Main().m();
	}
	
	void m() throws IOException {
		long S = System.currentTimeMillis();
		sc = (isDebug) ? new FastScanner(new FileInputStream(fileName)) : new FastScanner(System.in);
		//out = new PrintWriter(System.out);
		solve();
		//out.flush();
		long G = System.currentTimeMillis();
		if(isDebug){
			System.out.println("---Debug---");
			System.out.printf("%7d ms", (G-S));
		}
	}
	/* end main */
}
/* end Main */

class FastScanner {
    private InputStream in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    public FastScanner(InputStream in) {
		this.in = in;
	}
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() {
    	if (hasNextByte()) return buffer[ptr++];
    	else return -1;
    }
    private static boolean isPrintableChar(int c){
    	return 33 <= c && c <= 126;
    }
    public boolean hasNext() {
    	while(hasNextByte() && !isPrintableChar(buffer[ptr]))
    		ptr++; return hasNextByte();
    }
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() {
    	return Double.parseDouble(next());
    }
}