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 {

	public static char[] assign;
	public static char[] ans;
	public static int n;

	public static boolean check() {
		for(int i = 0; i < n; i++) {
			int next = (i + 1) % n;
			int back = (i + n - 1) % n;

			if(assign[i] == 'o' && ans[i] == 'S') {
				if(ans[back] == 'S' && ans[next] == 'W') {
					return false;
				}else if(ans[back] == 'W' && ans[next] == 'S') {
					return false;
				}
			}
			else if(assign[i] == 'o' && ans[i] == 'W') {
				if(ans[back] == 'S' && ans[next] == 'S') {
					return false;
				}else if(ans[back] == 'W' && ans[next] == 'W') {
					return false;
				}
			}
			else if(assign[i] == 'x' && ans[i] == 'S') {
				if(ans[back] == 'S' && ans[next] == 'S') {
					return false;
				}else if(ans[back] == 'W' && ans[next] == 'W') {
					return false;
				}
			}
			else if(assign[i] == 'x' && ans[i] == 'W') {
				if(ans[back] == 'S' && ans[next] == 'W') {
					return false;
				}else if(ans[back] == 'W' && ans[next] == 'S') {
					return false;
				}
			}
		}

		return true;
	}

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

		n = sc.nextInt();
		assign = sc.next().toCharArray();
		ans = new char[n];

		for(int cnt = 0; cnt < 2; cnt++) {
			for(int i = 0; i < n; i++) {
				ans[i] = '0';
			}

			if(cnt == 0) {
				ans[0] = 'S';
			}
			else if(cnt == 1) {
				ans[0] = 'W';
			}

			for (int i = 0; i < n; i++) {

				int next = (i + 1) % n;
				int back = (i + n - 1) % n;

				if(assign[i] == 'o') {
					if(ans[i] == 'S') {
						if(ans[back] == 'S') {
							ans[next] = 'S';
						}
						else if(ans[back] == 'W') {
							ans[next] = 'W';
						}
						else if(ans[back] == '0') {
							ans[back] = 'S';
							ans[next] = 'S';
						}
					}
					else if(ans[i] == 'W') {
						if(ans[back] == 'S') {
							ans[next] = 'W';
						}
						else if(ans[back] == 'W') {
							ans[next] = 'S';
						}
						else if(ans[back] == '0') {
							ans[back] = 'W';
							ans[next] = 'S';
						}
					}
				}
				else if(assign[i] == 'x') {
					if(ans[i] == 'S') {
						if(ans[back] == 'S') {
							ans[next] = 'W';
						}
						else if(ans[back] == 'W') {
							ans[next] = 'S';
						}
						else if(ans[back] == '0') {
							ans[back] = 'W';
							ans[next] = 'S';
						}
					}
					else if(ans[i] == 'W') {
						if(ans[back] == 'S') {
							ans[next] = 'S';
						}
						else if(ans[back] == 'W') {
							ans[next] = 'W';
						}
						else if(ans[back] == '0') {
							ans[back] = 'S';
							ans[next] = 'S';
						}
					}
				}
			}

			if(check()) {
				String str = String.valueOf(ans);
				System.out.println(str);
				return;
			}
		}
		System.out.println(-1);
	}
}