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;

public class Main {
	int f(int lAnimal, int cAnimal, char cAnswer) {
		if (cAnswer == 'o') {
			if (cAnimal == 0) {
				return (lAnimal + 1) % 2;
			} else {
				return lAnimal;
			}
		} else {
			if (cAnimal == 0) {
				return lAnimal;
			} else {
				return (lAnimal + 1) % 2;
			}
		}
	}

	void g(int[] ret) {
		int n = ret.length;
		for (int i = 0; i < n; i++) {
			if (ret[i] == 0) {
				System.out.print('W');
			} else {
				System.out.print('S');
			}
		}
		System.out.println();
	}

	boolean h(int n, char[] s, int a0, int a1) {
		int[] ret = new int[n];
		ret[0] = a0;
		ret[1] = a1;
		for (int i = 2; i < n; i++) {
			ret[i] = f(ret[i - 2], ret[i - 1], s[i - 1]);
		}
		if (f(ret[n - 2], ret[n - 1], s[n - 1]) == ret[0] && f(ret[n - 1], ret[0], s[0]) == ret[1]) {
			g(ret);
			return true;
		}
		return false;
	}

	void run() {
		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();
		char[] s = sc.next().toCharArray();
		if (h(n, s, 1, 1)) return;
		if (h(n, s, 1, 0)) return;
		if (h(n, s, 0, 1)) return;
		if (h(n, s, 0, 0)) return;
		System.out.println(-1);
}

	public static void main(String[] args) {
		new Main().run();
	}
}