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 {
	static int N;
	static String s;
	static String[] sw;
	static String first;
	static String last;

	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		N=sc.nextInt();
		s=sc.next();
		sw=new String[N];
		int count=0;
		//i=0が羊と仮定
		first="S";
		sw[0]="S";
		//i=N-1が羊のとき
		last="S";
		sw[N-1]="S";
		if(solve()){
			for(int i=0;i<N;i++)System.out.print(sw[i]);
			return;
		}
		Arrays.fill(sw, null);
		//i=N-1が狼のとき
		sw[0]="S";
		last="W";
		sw[N-1]="W";
		if(solve()){
			for(int i=0;i<N;i++)System.out.print(sw[i]);
			return;
		}
		Arrays.fill(sw, null);
		//i=0が狼と仮定
		first="W";
		sw[0]="W";
		//i=N-1が羊の時
		last="S";
		sw[N-1]="S";
		if(solve()){
			for(int i=0;i<N;i++)System.out.print(sw[i]);
			return;
		}
		Arrays.fill(sw, null);
		//i=N-1が狼の時
		sw[0]="W";
		last="W";
		sw[N-1]="W";
		if(solve()){
			for(int i=0;i<N;i++)System.out.print(sw[i]);
			return;
		}
		System.out.println(-1);
	}
	static boolean solve(){
		for(int i=0;i<s.length()-1;i++){
			if((sw[i]=="S" && s.charAt(i)=='o')||(sw[i]=="W" && s.charAt(i)=='x')){
				sw[i+1]=sw[i];
			}else{
				if(sw[i]=="S")sw[i+1]="W";
				else sw[i+1]="S";
			}
		}
		if((sw[N-1]=="S" && s.charAt(N-1)=='o')||(sw[N-1]=="W" && s.charAt(N-1)=='x')){
			sw[0]=sw[N-1];
		}else{
			if(sw[N-1]=="S")sw[0]="W";
			else sw[0]="S";
		}
		if(sw[N-1]==last && sw[0]==first)return true;
		else return false;
	}

}