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.util.Scanner;

/**
 * https://abc055.contest.atcoder.jp/tasks/arc069_b
 */
public class Main {

	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		char[] s = sc.next().toCharArray();
		sc.close();
		
		boolean[] ans = check(true, true, s);
		if(ans==null) ans = check(true, false, s);
		if(ans==null) ans = check(false, true, s);
		if(ans==null) ans = check(false, false, s);
		StringBuilder sb = new StringBuilder();
		if(ans!=null){
			for(boolean a:ans) sb.append( a ? 'S' : 'W');
		}else{
			sb.append("-1");
		}
		System.out.println(sb.toString());
	}
	
	static boolean[] check(boolean s1, boolean s2, char[] s){
		boolean[] ans = new boolean[s.length];
		ans[0] = s1; ans[1] = s2;
		for(int i=2; i<s.length; i++){
			if(s[i-1]=='o'){
				ans[i] = ans[i-1] ? ans[i-2] : !ans[i-2]; 
			}else{
				ans[i] = ans[i-1] ? !ans[i-2] : ans[i-2]; 
			}
		}	
		if(s[s.length-1] == 'o'){
			if((ans[s.length-1] && ans[s.length-2] != ans[0])||(!ans[s.length-1] && ans[s.length-2] == ans[0]))
				return null;
		}else{
			if((ans[s.length-1] && ans[s.length-2] == ans[0])||(!ans[s.length-1] && ans[s.length-2] != ans[0]))
				return null;
		}
		if(s[0] == 'o'){
			if((ans[0] && ans[s.length-1] != ans[1])||(!ans[0] && ans[s.length-1] == ans[1]))
				return null;
		}else{
			if((ans[0] && ans[s.length-1] == ans[1])||(!ans[0] && ans[s.length-1] != ans[1]))
				return null;
		}
		return ans;
		
	}

}