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: Accepted)

using System;

using System.Collections;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.Text;
using System.Text.RegularExpressions;
using System.Linq;
using System.IO;

class Program
{
    static void Main(string[] args)
    {
        new Magatro().Solve();
    }
}

public class Scanner
{
    private StreamReader Sr;

    private string[] S;
    private int Index;
    private const char Separator = ' ';

    public Scanner(Stream source)
    {
        Index = 0;
        S = new string[0];
        Sr = new StreamReader(source);
    }

    private string[] Line()
    {
        return Sr.ReadLine().Split(Separator);
    }

    public string Next()
    {
        string result;
        if (Index >= S.Length)
        {
            S = Line();
            Index = 0;
        }
        result = S[Index];
        Index++;
        return result;
    }
    public int NextInt()
    {
        return int.Parse(Next());
    }
    public double NextDouble()
    {
        return double.Parse(Next());
    }
    public long NextLong()
    {
        return long.Parse(Next());
    }
    public decimal NextDecimal()
    {
        return decimal.Parse(Next());
    }
    public string[] StringArray(int index = 0)
    {
        Next();
        Index = S.Length;
        return S.Skip(index).ToArray();
    }
    public int[] IntArray(int index = 0)
    {
        return StringArray(index).Select(int.Parse).ToArray();
    }
    public long[] LongArray(int index = 0)
    {
        return StringArray(index).Select(long.Parse).ToArray();
    }
    public bool EndOfStream
    {
        get { return Sr.EndOfStream; }
    }
}

public class Magatro
{
    private Scanner Cin;
    private int N;
    private string s;

    private void Scan()
    {
        Cin = new Scanner(Console.OpenStandardInput());
        N = Cin.NextInt();
        s = Cin.Next();
    }
    public void Solve()
    {
        Scan();
        int[] ar = new int[N];
        ar[0] = 1;
        ar[1] = 1;
        if (Ans(ar))
        {
            Console.WriteLine(string.Join("", ar.Select(S).ToArray()));
            return;
        }
        ar = new int[N];
        ar[0] = -1;
        ar[1] = 1;
        if (Ans(ar))
        {
            Console.WriteLine(string.Join("", ar.Select(S).ToArray()));
            return;
        }
        ar = new int[N];
        ar[0] = -1;
        ar[1] = -1;
        if (Ans(ar))
        {
            Console.WriteLine(string.Join("", ar.Select(S).ToArray()));
            return;
        }
        ar = new int[N];
        ar[0] = 1;
        ar[1] = -1;
        if (Ans(ar))
        {
            Console.WriteLine(string.Join("", ar.Select(S).ToArray()));
            return;
        }
        Console.WriteLine(-1);
    }

    private string S(int i)
    {
        if (i == 1) return "S";
        else return "W";
    }
    private bool Ans(int[] arr)
    {
        for (int i = 1; i <= N; i++)
        {
            int p = i % N;
            int before = i - 1;
            int next = (i + 1) % N;
            switch (s[p])
            {
                case 'o':
                    if (arr[p] == 1)
                    {
                        arr[next] = arr[before];
                    }
                    else
                    {
                        arr[next] = arr[before] * -1;
                    }
                    break;
                case 'x':
                    if (arr[p] == -1)
                    {
                        arr[next] = arr[before];
                    }
                    else
                    {
                        arr[next] = arr[before] * -1;
                    }
                    break;
            }
        }
        for (int i = 0; i < N; i++)
        {
            int b = (N + i - 1) % N;
            int n = (i + 1) % N;
            if (arr[i] == 1)
            {
                if (s[i] == 'o')
                {
                    if (arr[n] != arr[b])
                    {
                        return false;
                    }
                }
                else
                {
                    if (arr[b] == arr[n])
                    {
                        return false;
                    }
                }
            }
            else
            {
                if (s[i] != 'o')
                {
                    if (arr[n] != arr[b])
                    {
                        return false;
                    }
                }
                else
                {
                    if (arr[b] == arr[n])
                    {
                        return false;
                    }
                }
            }
        }
        return true;
    }
}