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.Scanner;

public class Main {

	static int N;
	static int[][] yosou = new int[4][100000];
	static int[] input_array = new int[100000];

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

		N = sc.nextInt();
		String line = sc.next();
		for(int i = 0;i < line.length();i++){
			char ch = line.charAt(i);
			if(ch == 'x')input_array[i] = 1;
		}

		//羊、羊...
		yosou[0][0] =  1;
		yosou[0][1] =  1;
		//羊、狼...
		yosou[1][0] =  1;
		yosou[1][1] = -1;
		//狼、羊...
		yosou[2][0] = -1;
		yosou[2][1] =  1;
		//狼、狼...
		yosou[3][0] = -1;
		yosou[3][1] = -1;

		int yosou_id = -1;
		for(int i = 0;i < 4;i++){
			for(int j = 2;j < N;j++){
				int left1_animal = yosou[i][j-1];
				int left2_animal = yosou[i][j-2];


				if(input_array[j-1] == 0){
					yosou[i][j] = left1_animal * left2_animal;
				}else{
					yosou[i][j] = -left1_animal * left2_animal;
				}
			}
			if(yosou[i][0] == 1){
				if(input_array[0] == 0){
					if(yosou[i][N-1] == yosou[i][1]){
						yosou_id = i;
						break;
					}
				}else{
					if(yosou[i][N-1] != yosou[i][1]){
						yosou_id = i;
						break;
					}
				}
			}else{
				if(input_array[0] == 0){
					if(yosou[i][N-1] != yosou[i][1]){
						yosou_id = i;
						break;
					}
				}else{
					if(yosou[i][N-1] == yosou[i][1]){
						yosou_id = i;
						break;
					}
				}
			}
		}

		if(yosou_id < 0){
			System.out.println(-1);
		}else{
			for(int i = 0;i < N;i++){
				if(yosou[yosou_id][i] == 1){
					System.out.print("S");
				}else{
					System.out.print("W");
				}
			}
		}
		System.out.println();

		sc.close();
	}
}