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 {

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

    void compute() {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        String s = sc.next();
        boolean[] isO = new boolean[N];
        for (int i = 0; i < N; i++) {
            isO[i] = s.charAt(i) == 'o';
        }
        boolean[] first = {true, true, false, false};
        boolean[] second = {true, false, true, false};
        for (int i = 0; i < 4; i++) {
            boolean[] isS = new boolean[N];
            isS[0] = first[i];
            isS[1] = second[i];
            for (int j = 2; j < N; j++) {
                boolean tmp = isS[j - 1] ^ isO[j - 1];
                if (isS[j - 2]) {
                    tmp = !tmp;
                }
                isS[j] = tmp;
            }
            boolean tmp1 = isS[N - 1] ^ isO[N - 1];
            if (isS[N - 2]) {
                tmp1 = !tmp1;
            }
            boolean tmp2 = isS[0] ^ isO[0];
            if (isS[N - 1]) {
                tmp2 = !tmp2;
            }
            if (isS[0] == tmp1 && isS[1] == tmp2) {
                for (int j = 0; j < N; j++) {
                    System.out.print(isS[j] ? 'S' : 'W');
                }
                System.out.println();
                return;
            }
        }
        System.out.println(-1);
    }
}