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.Generic;
using System.Text;
using System.Linq;

class Program
{
    void solve()
    {
        int N = int.Parse(Console.ReadLine());
        string s = Console.ReadLine();

        byte[] said = new byte[N];
        byte[,] who = new byte[4, N];

        who[0, 0] = 0; who[0, N - 1] = 0;
        who[1, 0] = 0; who[1, N - 1] = 1;
        who[2, 0] = 1; who[2, N - 1] = 0;
        who[3, 0] = 1; who[3, N - 1] = 1;


        for (int i = 0; i < N; ++i)
            said[i] = (byte)(s[i] == 'o' ? 0 : 1);

        for (int i = 0; i < N; ++i)
        {
            for (int j = 0; j < 4; ++j)
            {
                who[j, (i + 1) % N] = (byte)(said[i] ^ who[j, (N + i - 1) % N] ^ who[j, i]);
            }
        }

        int k = -1;
        if (who[0, 0] == 0 && who[0, N - 1] == 0)
            k = 0;
        else if (who[1, 0] == 0 && who[1, N - 1] == 1)
            k = 1;
        else if (who[2, 0] == 1 && who[2, N - 1] == 0)
            k = 2;
        else if (who[3, 0] == 1 && who[3, N - 1] == 1)
            k = 3;

        string ans = string.Empty;
        if (k == -1)
        {
            ans = "-1";
        }
        else
        {
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < N; ++i)
            {
                sb.Append(who[k, i] == 1 ? 'W' : 'S');
                //ans += who[k, i] == 1 ? "W" : "S";
            }
            ans = sb.ToString();
        }
        Console.WriteLine(ans);
    }
    public static int Main()
    {
        bool loop = false;
#if ES_DEBUG
        loop = true;
#endif
        do
        {
            new Program().solve();
        } while (loop);
        return 0;
    }
}