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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;

class Myon
{
    public Myon() { }
    public static int Main()
    {
        cin = new Scanner();
        new Myon().calc();
        return 0;
    }


    static Scanner cin;
    int N;
    string S;
    bool[] isWolf;

    void calc()
    {
        N = cin.nextInt();
        S = cin.next();
        // 4パターン試して矛盾がないことを見る
        if (loop())
        {
            isWolf.ToList().ForEach(i => Console.Write(i ? "W" : "S"));
            Console.Write("\n");
        }
        else
        {
            Console.WriteLine(-1);
        }
        Console.ReadLine();
    }

    bool loop()
    {
        bool[] loop = new bool[] { false, true };
        bool result = false;
        foreach (var i in loop)
        {
            foreach (var j in loop)
            {
                result = check(i, j);
                if (result) return true;
            }
        }
        return false;
    }

    bool check(bool j1, bool j2)
    {
        List<bool> isWolfList = new bool[S.Length + 1].ToList();
        isWolfList[0] = j1;
        isWolfList[1] = j2;
        for (int i = 0; i < S.Length; i++)
        {
            if (i == 0)
            {
                if ((isWolfList[i] && S[i] == 'o') || (!isWolfList[i] && S[i] == 'x'))
                {
                    // 両隣が異なる場合
                    isWolfList[S.Length - 1] = !isWolfList[i + 1];
                }
                else
                {
                    // 両隣が一致する場合
                    isWolfList[S.Length - 1] = isWolfList[i + 1];
                }
            }
            else
            {
                if ((isWolfList[i] && S[i] == 'o') || (!isWolfList[i] && S[i] == 'x'))
                {
                    // 両隣が異なる場合
                    isWolfList[i + 1] = !isWolfList[i - 1];
                }
                else
                {
                    // 両隣が一致する場合
                    isWolfList[i + 1] = isWolfList[i - 1];
                }
            }
        }
        isWolf = new bool[S.Length];
        for(int i = 0; i < S.Length; i++)
        {
            isWolf[i] = isWolfList[i];
        }

        return isWolfList.Last() == isWolfList[0];
    }


    class Scanner
    {
        string[] s;
        int i;

        char[] cs = new char[] { ' ' };

        public Scanner()
        {
            s = new string[0];
            i = 0;
        }

        public string next()
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            if (s.Length == 0) return next();
            i = 0;
            return s[i++];
        }

        public int nextInt()
        {
            return int.Parse(next());
        }
        public int[] ArrayInt(int N, int add = 0)
        {
            int[] Array = new int[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextInt() + add;
            }
            return Array;
        }

        public long nextLong()
        {
            return long.Parse(next());
        }

        public long[] ArrayLong(int N, long add = 0)
        {
            long[] Array = new long[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextLong() + add;
            }
            return Array;
        }

        public double nextDouble()
        {
            return double.Parse(next());
        }


        public double[] ArrayDouble(int N, double add = 0)
        {
            double[] Array = new double[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextDouble() + add;
            }
            return Array;
        }
    }
}