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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
public class Aprob {
    public static void Main() {
        int N = int.Parse(Console.ReadLine());
        string s = Console.ReadLine();
        char[] outp = new char[N];
        bool judge = false;
        char[] test = { 'S', 'S', 'S', 'W', 'W', 'W', 'W', 'S' };


        for (int k = 0; k < 4;k++) {
            outp[0] = test[2*k];
            outp[1] = test[2 * k + 1];
            for (int i = 1; i < N; i++) {
                if (s.Substring(i, 1) == "o") {
                    if (outp[i] == 'S') {
                        if (i != N - 1) {
                            outp[i + 1] = outp[i - 1];
                        } else {
                            outp[0] = outp[i - 1];
                        }
                    } else {
                        if (outp[i-1] == 'S') {
                            if (i != N - 1) {
                                outp[i + 1] = 'W';
                            } else {
                                outp[0] = 'W';
                            }
                        } else {
                            if (i != N - 1) {
                                outp[i + 1] = 'S';
                            } else {
                                outp[0] = 'S';
                            }
                        }
                    }
                } else {
                    if (outp[i] == 'S') {
                        if (outp[i-1] == 'S') {
                            if (i != N - 1) {
                                outp[i + 1] = 'W';
                            } else {
                                outp[0] = 'W';
                            }
                        } else {
                            if (i != N - 1) {
                                outp[i + 1] = 'S';
                            } else {
                                outp[0] = 'S';
                            }
                        }
                    } else {
                        if (i != N - 1) {
                            outp[i + 1] = outp[i - 1];
                        } else {
                            outp[0] = outp[i - 1];
                        }
                    }
                }
            }
            if (s.Substring(0, 1) == "o") {
                if (outp[0] == 'S') {
                    judge = (outp[N-1] == outp[1]);
                } else {
                    judge = (outp[N - 1] != outp[1]);
                }
            } else {
                if (outp[0] == 'S') {
                    judge = (outp[N - 1] != outp[1]);
                } else {
                    judge = (outp[N - 1] == outp[1]);
                }
            }
            if (judge) {
                break;
            }
            outp[0] = '0';

        }
        string outs = "";
        if (outp[0] == '0') {
            outs = "-1";
        } else {
            for (int i = 0; i < N; i++) {
                outs += outp[i];
            }
        }
        Console.WriteLine(outs);


    }
}