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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
    int n;
    int[] s;

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

    void run() {
        FastReader sc = new FastReader();
        n = sc.nextInt();
        char[] cs = sc.next().toCharArray();
        s = new int[n + 1];
        for (int i = 0; i < n; i++) {
            s[i] = cs[i] == 'o' ? 1 : 0;
        }
        s[n] = s[0];
        solve();
    }

    void solve() {
        // n: sheep, 1: sheep
        boolean[] ss = new boolean[n + 2];
        ss[0] = true;
        ss[1] = true;
        for (int i = 2; i <= n + 1; i++) {
            if (ss[i - 1] && s[i - 2] == 1 || !ss[i - 1] && s[i - 2] == 0) {
                ss[i] = ss[i - 2];
            } else {
                ss[i] = !ss[i - 2];
            }
        }
        if (ss[n] == ss[0] && ss[n + 1] == ss[1]) {
            for (int i = 1; i <= n; i++) {
                System.out.print(ss[i] ? 'S' : 'W');
            }
            System.out.println();
            return;
        }
        // n: sheep, 1: wolf
        Arrays.fill(ss, false);
        ss[0] = true;
        ss[1] = false;
        for (int i = 2; i <= n + 1; i++) {
            if (ss[i - 1] && s[i - 2] == 1 || !ss[i - 1] && s[i - 2] == 0) {
                ss[i] = ss[i - 2];
            } else {
                ss[i] = !ss[i - 2];
            }
        }
        if (ss[n] == ss[0] && ss[n + 1] == ss[1]) {
            for (int i = 1; i <= n; i++) {
                System.out.print(ss[i] ? 'S' : 'W');
            }
            System.out.println();
            return;
        }
        // n: wolf, 1: sheep
        Arrays.fill(ss, false);
        ss[0] = false;
        ss[1] = true;
        for (int i = 2; i <= n + 1; i++) {
            if (ss[i - 1] && s[i - 2] == 1 || !ss[i - 1] && s[i - 2] == 0) {
                ss[i] = ss[i - 2];
            } else {
                ss[i] = !ss[i - 2];
            }
        }
        if (ss[n] == ss[0] && ss[n + 1] == ss[1]) {
            for (int i = 1; i <= n; i++) {
                System.out.print(ss[i] ? 'S' : 'W');
            }
            System.out.println();
            return;
        }
        // n: wolf, 1: wolf
        Arrays.fill(ss, false);
        ss[0] = false;
        ss[1] = false;
        for (int i = 2; i <= n + 1; i++) {
            if (ss[i - 1] && s[i - 2] == 1 || !ss[i - 1] && s[i - 2] == 0) {
                ss[i] = ss[i - 2];
            } else {
                ss[i] = !ss[i - 2];
            }
        }
        if (ss[n] == ss[0] && ss[n + 1] == ss[1]) {
            for (int i = 1; i <= n; i++) {
                System.out.print(ss[i] ? 'S' : 'W');
            }
            System.out.println();
            return;
        }
        System.out.println(-1);
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}