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 Java (OpenJDK 1.8.0) (judge verdict: Accepted)



import java.io.IOException;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();
		String str = sc.next();

		char[] result = new char[n + 1];

		String[] pre = {"SS","SW","WW","WS"};

		for(int i = 0; i < pre.length; i++){
			for(int j = 0; j < pre[i].length(); j++){
				result[j] = pre[i].charAt(j);
			}

			for(int j = pre[i].length() ; j < n + 1; j++){
				if(str.charAt(j - 1) == 'o'){
					if(result[j - 1] == 'S'){
						result[j] = result[j - 2];
					}
					else {
						result[j] = result[j - 2] == 'S' ? 'W' : 'S';
					}
				}
				else {
					if(result[j - 1] == 'W'){
						result[j] = result[j - 2];
					}
					else {
						result[j] = result[j - 2] == 'S' ? 'W' : 'S';
					}
				}
			}

			if(result[n] != result[0]){
				continue;
			}

			if(str.charAt(0) == 'o' && ((result[0] == 'S' && result[1] == result[n - 1]) ||
					(result[0] == 'W' && result[1] != result[n - 1]))){
				System.out.println(new String(result).substring(0, n));
				return;
			}
			if(str.charAt(0) == 'x' && ((result[0] == 'W' && result[1] == result[n - 1]) ||
					(result[0] == 'S' && result[1] != result[n - 1]))){
				System.out.println(new String(result).substring(0, n));
				return;
			}
		}

		System.out.println(-1);
	}

}