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.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
//using static System.Globalization.CultureInfo;

class Program
{
    private static int num;
    static void Main(string[] args)
    {
        num = Input.num;
        var str = ReadLine();
        var res = new string[num];
        var sw = new[] { "S", "W" };
        res[0] = "S";
        if (str[0] == 'o')
            for(var i=0;i<2;i++)
            {
                res[num - 1] = sw[i];
                if (ss(res, str, 1, sw[i]))
                {
                    WriteLine(string.Join("", res));
                    return;
                }
            }
        else for(var i = 0; i < 2; i++)
            {
                res[num - 1] = sw[i];
                if (ss(res, str, 1, sw[1 - i]))
                {
                    WriteLine(string.Join("", res));
                    return;
                }
            }
        WriteLine(-1);
    }
    private static bool ss(string[] res, string str, int index, string state)
    {
        if (!string.IsNullOrEmpty(res[index]) && res[index] != state)
            return false;
        if (index == 0) return true;
        res[index] = state;
        if (state == "S")
        {
            if (str[index] == 'o')
               return ss(res, str, (index + 1) % num, res[index - 1]);
            else return ss(res, str, (index + 1) % num, res[index - 1] == "S" ? "W" : "S");
        }
        else
        {
            if (str[index] == 'o')
                return ss(res, str, (index + 1) % num, res[index - 1] == "S" ? "W" : "S");
            else return ss(res, str, (index + 1) % num, res[index - 1]);
        }
    }
}

public class Input
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public static string[] gred(int h) 
        => Enumerable.Repeat(0, h).Select(v => read).ToArray();
    public static int[][] twodim(int num)
        => Enumerable.Repeat(0, num).Select(v => ar).ToArray();
    public static long[][] twodimL(int num)
        => Enumerable.Repeat(0, num).Select(v => arL).ToArray();
    public static Tuple<int, int, long> MakeEdge(int num1, int num2, long weight=Inf)
        => new Tuple<int, int, long>(num1, num2, weight);
    public const long Inf = (long)1e18;
    public const double eps = 1e-11;
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}