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: Time Limit Exceeded)


import java.util.*;

public class Main {
	public static void main(String[] args){
		Scanner scanner = new Scanner(System.in);
		int num = scanner.nextInt();
		String remark = scanner.next();
		
		for(int i = 0; i < 4; i++){
			String ans = "";
			if(i == 0){
				ans += "SS";
			}else if(i == 1){
				ans += "SW";
			}else if(i == 2){
				ans += "WS";
			}else if(i == 3){
				ans += "WW";
			}
			
			
			
			int j = 1;
			char c;
			char ind;
			while(j < remark.length() - 1){
				c = remark.charAt(j);
				ind = ans.charAt(j);
				if(ind == 'S'){
					if(c == 'o'){
						ans += ans.charAt(j - 1);
					} else {
						if(ans.charAt(j - 1) == 'S'){
							ans += "W";
						} else {
							ans += "S";
						}
					}
				} else {
					if(c == 'o'){
						if(ans.charAt(j - 1) == 'S'){
							ans += "W";
						} else {
							ans += "S";
						}
					} else {
						ans += ans.charAt(j - 1);
					}
				}
				
				j++;
			}
			
			c = remark.charAt(j);
			if(ans.charAt(j) == 'S'){
				if(c == 'o'){
					if(ans.charAt(0) == ans.charAt(j - 1)){
						System.out.println(ans);
						return;
					}
				} else {
					if(ans.charAt(0) != ans.charAt(j - 1)){
						System.out.println(ans);
						return;
					}
				}
			} else {
				if(c == 'o'){
					if(ans.charAt(0) != ans.charAt(j - 1)){
						System.out.println(ans);
						return;
					}
				} else {
					if(ans.charAt(0) == ans.charAt(j - 1)){
						System.out.println(ans);
						return;
					}
				}
			}	
		}
		
		System.out.println(-1);
		return;
	}
}