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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.Scanner;
class Main {
	public static void main(String[] args){
		try(Scanner sc = new Scanner(System.in)){
			int N = Integer.parseInt(sc.next());
			char[] S = sc.next().toCharArray();
			int[] isSheep = new int[N];
			
			StringBuilder answer= new StringBuilder();
			boolean isAnsExists=false;
			int[][] isSheepInitial= {{1,1},{0,0},{0,1},{1,0}};
			for(int ini=0; ini<4;ini++){
				isSheep[0]=isSheepInitial[ini][0];
				isSheep[1]=isSheepInitial[ini][1];
				for(int i=1;i<N-1;i++){
					isSheep[i+1]=succ(isSheep[i-1],isSheep[i],S[i]);
				}
				if((succ(isSheep[N-2],isSheep[N-1],S[N-1])==isSheep[0])&&(succ(isSheep[N-1],isSheep[0],S[0])==isSheep[1])&&!isAnsExists){
					for(int k=0;k<N;k++){answer.append((isSheep[k]==1)?"S":"W");
					isAnsExists=true;
					}
				}
			}
			if(isAnsExists){
				System.out.println(answer.toString());
			}else{
				System.out.println(-1);
			}
			
			
		}
	}
	static int succ(int back,int now, char ox){
		int answer=0;
		int[][] succMato={{1,0},{0,1}};
		int[][] succMatx={{0,1},{1,0}};
		if(ox=='o')answer=succMato[back][now];
		if(ox=='x')answer=succMatx[back][now];
		return answer;
	}
	
}