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.*;
import java.math.BigInteger;
import java.util.*;

public class Main implements Runnable {


    private void solve() throws IOException {
        int N = nextInt();

        String s = reader.readLine();

        int[] q = new int[] { 1, 2 };

        for(int first = 0; first < 2; ++first) {
            for(int second = 0; second < 2; ++ second) {
                int[] ans = new int[s.length()];
                ans[0] = q[first];
                ans[1] = q[second];
                boolean isValid = true;
                for(int i = 1; i < s.length()-1; ++i) {
                    if(s.charAt(i) == 'o') {
                        if(ans[i] == 1) {
                            // sheep here
                            int leftId = ( i - 1 + s.length()) % s.length();
                            int rightId = (i + 1) % s.length();
                            if(ans[rightId] == 0) {
                                ans[rightId] = ans[leftId];
                            } else {
                                if(ans[leftId] != ans[rightId]) {
                                    isValid = false;
                                }
                            }
                        } else {
                            // is wolf here
                            int leftId = ( i - 1 + s.length()) % s.length();
                            int rightId = (i + 1) % s.length();
                            if(ans[rightId] == 0) {
                                if(ans[leftId] == 1) {
                                    ans[rightId] = 2;
                                } else {
                                    ans[rightId] = 1;
                                }
                            } else {
                                if(ans[leftId] == ans[rightId]) {
                                    isValid = false;
                                }
                            }
                        }
                    } else {
                        // x
                        if(ans[i] == 1) {
                            // is sheep here
                            int leftId = ( i - 1 + s.length()) % s.length();
                            int rightId = ( i + 1 ) % s.length();
                            if(ans[rightId] == 0) {
                                if(ans[leftId] == 1) {
                                    ans[rightId] = 2;
                                } else {
                                    ans[rightId] = 1;
                                }
                            } else {
                                if(ans[leftId] == ans[rightId]) {
                                    isValid = false;
                                }
                            }
                        } else {
                            // the wolf is here
                            int leftId = ( i - 1 + s.length()) % s.length();
                            int rightId = ( i + 1 ) % s.length();
                            if(ans[rightId] == 0) {
                                if(ans[leftId] == 1) {
                                    ans[rightId] = 1;
                                } else {
                                    ans[rightId] = 2;
                                }
                            } else {
                                if(ans[rightId] != ans[leftId]) {
                                    isValid = false;
                                }
                            }
                        }
                    }
                }

                for(int i = 0; i < s.length(); ++i) {
                    int leftId = ( i - 1 + s.length()) % s.length();
                    int rightId = ( i + 1 ) % s.length();
                    if(ans[i] == 1) {
                        if(s.charAt(i) == 'o') {
                            isValid &= ( ans[leftId] == ans[rightId]);
                        } else {
                            isValid &= (ans[leftId] != ans[rightId]);
                        }
                    } else {
                        if(s.charAt(i) == 'o') {
                            isValid &= (ans[leftId] != ans[rightId]);
                        } else {
                            isValid &= (ans[leftId] == ans[rightId]);
                        }
                    }
                }
                if(isValid) {
                    StringBuilder sb = new StringBuilder("");
                    for(int i = 0; i < ans.length; ++i) {
                        if(ans[i] == 1) sb.append("S");
                        else sb.append("W");
                    }
                    writer.println(sb.toString());
                    return;
                }
            }
        }
        writer.println(-1);

    }



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

    BufferedReader reader;
    //    BufferedReader reader2;
    StringTokenizer tokenizer;
    PrintWriter writer;
    //    BufferedWriter writer;

    public void run() {
        try {
            reader = new BufferedReader(new InputStreamReader(System.in));
//            reader = new BufferedReader(new FileReader("highcard.in"));
            //            reader2 = new BufferedReader(new FileReader("1.in"));
            tokenizer = null;
            writer = new PrintWriter(System.out);
//            writer = new     PrintWriter("highcard.out");
//                                                    writer = new BufferedWriter(System.out);
            //                        writer = new BufferedWriter(new OutputStreamWriter(System.out));
            solve();
            reader.close();
            //            reader2.close();
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    short nextShort() throws IOException {
        return Short.parseShort(nextToken());
    }

    String nextToken() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }

        return tokenizer.nextToken();
    }

}