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

class Main {
	public static void main(String args[]) throws IOException {
		@SuppressWarnings("resource")
		Scanner cin = new Scanner(System.in);
		ArrayList<String> inLines = new ArrayList<String>();
		for (; cin.hasNext();) {
			inLines.add(cin.nextLine());
		}
		Solver solver = new Solver();
		solver.solve(inLines);
	}
}

class Solver {
	int N;
	String str;

	public void solve(ArrayList<String> inLines) {
		N = Integer.parseInt(inLines.get(0));
		str = inLines.get(1);

		animals = new char[N];
		animals[0] = 'S';
		animals[1] = 'S';
		if (check()) {
			System.out.println(animals);
			return;
		}
		animals[0] = 'S';
		animals[1] = 'W';
		if (check()) {
			System.out.println(animals);
			return;
		}
		animals[0] = 'W';
		animals[1] = 'S';
		if (check()) {
			System.out.println(animals);
			return;
		}
		animals[0] = 'W';
		animals[1] = 'W';
		if (check()) {
			System.out.println(animals);
			return;
		}
		System.out.println(-1);
	}

	char[] animals;

	private boolean check() {
		for (int i = 1; i < N - 1; i++) {
			if (animals[i] == 'S') {
				if (str.charAt(i) == 'o') {
					animals[i + 1] = animals[i - 1];
				} else {
					animals[i + 1] = animals[i - 1] == 'S' ? 'W' : 'S';
				}
			}
			if (animals[i] == 'W') {
				if (str.charAt(i) == 'x') {
					animals[i + 1] = animals[i - 1];
				} else {
					animals[i + 1] = animals[i - 1] == 'S' ? 'W' : 'S';
				}
			}
		}

		if (animals[N - 1] == 'S') {
			if (str.charAt(N - 1) == 'o' && animals[N - 2] != animals[0]) {
				return false;
			}
			if (str.charAt(N - 1) == 'x' && animals[N - 2] == animals[0]) {
				return false;
			}
		}
		if (animals[N - 1] == 'W') {
			if (str.charAt(N - 1) == 'o' && animals[N - 2] == animals[0]) {
				return false;
			}
			if (str.charAt(N - 1) == 'x' && animals[N - 2] != animals[0]) {
				return false;
			}
		}
		if (animals[0] == 'S') {
			if (str.charAt(0) == 'o' && animals[N - 1] != animals[1]) {
				return false;
			}
			if (str.charAt(0) == 'x' && animals[N - 1] == animals[1]) {
				return false;
			}
		}
		if (animals[0] == 'W') {
			if (str.charAt(0) == 'o' && animals[N - 1] == animals[1]) {
				return false;
			}
			if (str.charAt(0) == 'x' && animals[N - 1] != animals[1]) {
				return false;
			}
		}
		return true;
	}
}