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 void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        char[] s = sc.next().toCharArray();
        char[] ans = new char[s.length];
        if (isCorrect('S', 'S', ans, s)) {
            System.out.println(String.valueOf(ans));
            return;
        }
        if (isCorrect('S', 'W', ans, s)) {
            System.out.println(String.valueOf(ans));
            return;
        }
        if (isCorrect('W', 'S', ans, s)) {
            System.out.println(String.valueOf(ans));
            return;
        }
        if (isCorrect('W', 'W', ans, s)) {
            System.out.println(String.valueOf(ans));
            return;
        }
        System.out.println(-1);
    }

    private static boolean isCorrect(char c1, char c2, char[] ans, char[] s) {
        ans[0] = c1;
        ans[1] = c2;
        boolean isOK = false;
        for (int i = 1; i < s.length; i++) {
            int idx = i + 1;
            if (i == s.length - 1) {
                idx = 0;
            }
            if (ans[i] == 'S') {
                if (s[i] == 'o' && ans[i - 1] == 'S') {
                    ans[idx] = 'S';
                } else if (s[i] == 'o' && ans[i - 1] == 'W') {
                    ans[idx] = 'W';
                } else if (s[i] == 'x' && ans[i - 1] == 'S') {
                    ans[idx] = 'W';
                } else if (s[i] == 'x' && ans[i - 1] == 'W') {
                    ans[idx] = 'S';
                }
            } else if (ans[i] == 'W') {
                if (s[i] == 'o' && ans[i - 1] == 'S') {
                    ans[idx] = 'W';
                } else if (s[i] == 'o' && ans[i - 1] == 'W') {
                    ans[idx] = 'S';
                } else if (s[i] == 'x' && ans[i - 1] == 'S') {
                    ans[idx] = 'S';
                } else if (s[i] == 'x' && ans[i - 1] == 'W') {
                    ans[idx] = 'W';
                }
            }
            if (idx == 0) {
                if (ans[0] == 'S') {
                    if (s[0] == 'o' && ans[i] == ans[1] && ans[0] == c1) {
                        isOK = true;
                    } else {
                        isOK = (s[0] == 'x' && ans[i] != ans[1] && ans[0] == c1);
                    }
                } else if (ans[i] == 'W') {
                    if (s[0] == 'o' && ans[i] != ans[1] && ans[0] == c1) {
                        isOK = true;
                    } else {
                        isOK = (s[0] == 'x' && ans[i] == ans[1] && ans[0] == c1);
                    }
                }
            }
        }
        return isOK;
    }
}