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: Wrong Answer)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
	int n;
	String s;
	String[] sw;
	
	public static void main(String[] args){
		new Main().solve();
	}
	
	public void solve(){
		Scanner sc=new Scanner(System.in);
		n=sc.nextInt();
		s=sc.next();
		sw=new String[n];
		
		
		//パターン１
		sw[0]="S";
		if(s.charAt(0)=='o'){
			sw[1]="S";
		}
		solve2();
		if(sw[n-1]=="S" && sw[0]=="S"){
			for(int i=0;i<n;i++)System.out.print(sw[i]);
			return;
		}
		Arrays.fill(sw, "");
		//パターン２
		sw[0]="S";
		if(s.charAt(0)=='o'){
			sw[1]="W";
		}
		solve2();
		if(sw[n-1]=="W"&& sw[0]=="S"){
			for(int i=0;i<n;i++)System.out.print(sw[i]);
			return;
		}
		Arrays.fill(sw, "");
		//パターン３
		sw[0]="S";
		if(s.charAt(0)=='x'){
			sw[1]="S";
		}
		solve2();
		if(sw[n-1]=="W" &&sw[0]=="S"){
			for(int i=0;i<n;i++)System.out.print(sw[i]);
			return;
		}
		Arrays.fill(sw, "");
		//パターン４
		sw[0]="S";
		if(s.charAt(0)=='x'){
			sw[1]="W";
		}
		solve2();
		if(sw[n-1]=="S"&&sw[0]=="S"){
			for(int i=0;i<n;i++)System.out.print(sw[i]);
			return;
		}
		Arrays.fill(sw,"");
		//パターン５
		sw[0]="W";
		if(s.charAt(0)=='o'){
			sw[1]="S";
		}
		solve2();
		if(sw[n-1]=="W"&&sw[0]=="W"){
			for(int i=0;i<n;i++)System.out.print(sw[i]);
			return;
		}
		Arrays.fill(sw, "");
		//パターン６
		sw[0]="W";
		if(s.charAt(0)=='o'){
			sw[1]="W";
		}
		solve2();
		if(sw[n-1]=="S"&&sw[0]=="W"){
			for(int i=0;i<n;i++)System.out.print(sw[i]);
			return;
		}
		Arrays.fill(sw, "");
		//パターン７
		sw[0]="W";
		if(s.charAt(0)=='x'){
			sw[1]="S";
		}
		solve2();
		if(sw[n-1]=="S"&&sw[0]=="W"){
			for(int i=0;i<n;i++)System.out.print(sw[i]);
			return;
		}
		Arrays.fill(sw, "");
		//パターン８
		sw[0]="W";
		if(s.charAt(0)=='x'){
			sw[1]="W";
		}
		solve2();
		if(sw[n-1]=="W"&&sw[0]=="W"){
			for(int i=0;i<n;i++)System.out.print(sw[i]);
			return;
		}
		Arrays.fill(sw, "");
		System.out.println("-1");
	}
	public void solve2(){
		if(n==3){
			for(int i=2;i<n;i++){
				if((sw[i]=="S"&&s.charAt(i)=='o')||(sw[i]=="W"&&s.charAt(i)=='x')){
					if(i!=n-1)
						sw[i+1]=sw[i-1];
					if(i==n-1)
						sw[0]=sw[i-1];
				}else{
					if(i!=n-1){
						if(sw[i-1]=="S")sw[i+1]="W";
						if(sw[i-1]=="W")sw[i+1]="S";
					}
					if(i==n-1){
						if(sw[i-1]=="S")sw[0]="W";
						if(sw[i-1]=="W")sw[0]="S";
					}
				}
			}
		}else{
		for(int i=1;i<n;i++){
			if((sw[i]=="S"&&s.charAt(i)=='o')||(sw[i]=="W"&&s.charAt(i)=='x')){
				if(i!=n-1)
					sw[i+1]=sw[i-1];
				if(i==n-1)
					sw[0]=sw[i-1];
			}else{
				if(i!=n-1){
					if(sw[i-1]=="S")sw[i+1]="W";
					if(sw[i-1]=="W")sw[i+1]="S";
				}
				if(i==n-1){
					if(sw[i-1]=="S")sw[0]="W";
					if(sw[i-1]=="W")sw[0]="S";
				}
			}
		}
		}
	}
}