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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            string str = Console.ReadLine();
            string ex = string.Empty;
            wolfSheepArray ws = null;
            swString(N, "", str,ws,N,ref ex);
            
            if(ex.CompareTo(string.Empty)!=0)
            {
                Console.WriteLine(ex);
            }
            else
            {
                Console.WriteLine(-1);
            }
            Console.ReadLine();
        }

        static void swString(int N,string preset,string correct,wolfSheepArray ws,int amount,ref string ex)
        {
            string[] tmp = { "S", "W" };
            if (N != 0)
            {
                foreach (string s in tmp)
                {
                    if (ex != string.Empty) break;
                    swString(N - 1, preset + s,correct,ws,amount,ref ex);
                }
            }
            else
            {
                ws = new wolfSheepArray(amount, preset);
                if(correct.CompareTo(ws.judge())==0)
                { ex = preset; }
            }
        }

    }

    class wolfSheepArray
    {
        public int amount;
        public char[] arrange;

        public wolfSheepArray(int N, string str)
        {
            amount = N;
            arrange = new char[N];
            for(int i = 0;i<amount;i++)
            {
                arrange[i] = char.Parse(str.Substring(i, 1));
            }
        }

        public char this[int index]
        {
            set
            {
                arrange[index%amount] = value;
            }
            get
            {
                if (index == -1) return arrange[arrange.Length - 1];
                return arrange[index % amount];
            }
        }

        public string judge()
        {
            string ret = string.Empty;
            char c;
            for(int i = 0; i < amount;i++)
            {
                if(this[i] == 'W')
                {
                    if(this[i-1] == this[i+1])
                    {
                        c = 'x';
                    }
                    else { c = 'o'; }
                }
                else
                {
                    if (this[i - 1] == this[i + 1])
                    {
                        c = 'o';
                    }
                    else { c = 'x'; }

                }
                ret += c;
            }

            return ret;
        }

    }
}