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.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner reader = new Scanner(System.in);
		int N = reader.nextInt();
		String str = reader.next();
		String[] arr = str.split("");
		String ans = "-1";
		String[] answers = new String[4];
		answers[0] = "SW";
		answers[1] = "WS";
		answers[2] = "SS";
		answers[3] = "WW";
		for (int k = 0; k < 4; k++) {
			for (int i = 2; i < N; i++) {
				char sw = ' ';
				char pre_a = arr[i-1].charAt(0);
				char pre_sw = answers[k].charAt(i-1);
				char pre_pre_sw = answers[k].charAt(i-2);
				boolean same = isSame(pre_pre_sw, pre_sw, sw, pre_a);
				boolean dif = isDif(pre_pre_sw, pre_sw, sw, pre_a);
				if (same) {
					sw = pre_pre_sw;
				} else if (dif && pre_pre_sw == 'W') {
					sw = 'S';
				} else if (dif && pre_pre_sw == 'S') {
					sw = 'W';
				} else {
					answers[k] = "";
					break;
				}
				answers[k] += sw;
				if (!(isSame(pre_pre_sw, pre_sw, sw, pre_a) || isDif(pre_pre_sw, pre_sw, sw, pre_a))) {
					answers[k] = "";
					break;
				}
			}
		}
		for (int k = 0; k < 4 ;k++) {
			if (answers[k].length() > 0) {
				char sw = answers[k].charAt(0);
				char pre_a = arr[N-1].charAt(0);
				char pre_sw = answers[k].charAt(N-1);
				char pre_pre_sw = answers[k].charAt(N-2);
				boolean same = isSame(pre_pre_sw, pre_sw, sw, pre_a);
				boolean dif = isDif(pre_pre_sw, pre_sw, sw, pre_a);
				boolean isValid = same || dif;
				if (isValid) {
					ans = answers[k];
					break;
				}
			}
		}
		System.out.println(ans);
		reader.close();

	}
	public static boolean isSame(char first_sw, char second_sw, char third_sw,
							char second_ox) {
		return ((second_sw == 'S' && second_ox == 'o') ||
				(second_sw == 'W' && second_ox == 'x')) && (first_sw == third_sw || third_sw == ' ');

	}

	public static boolean isDif(char first_sw, char second_sw, char third_sw,
				char second_ox) {
		return ((second_sw == 'S' && second_ox == 'x') ||
		(second_sw == 'W' && second_ox == 'o')) && (first_sw != third_sw || third_sw == ' ');
	}


}