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.Collections.Generic;
using System;
class Program
    {
        static void Main(string[] args)
        {
            //var sr = new System.IO.StreamReader(@"test.txt", Encoding.UTF8);
            //string line = sr.ReadLine();
            string line = System.Console.ReadLine().Trim();

            int N = int.Parse(line);


            line = System.Console.ReadLine().Trim();
            //line = sr.ReadLine();
            string[] s = new string[line.Length];

            for (int i = 0; i < line.Length; i++)
            {
                s[i] = line[i].ToString();
            }


            int index = (int)Math.Pow(2, N);

            List<string> list = new List<string>();

            for (int i = 0; i < index; i++)
            {
                string binaryNum = Convert.ToString((i), 2);

                if (binaryNum.Length < N)
                {
                    int leng = binaryNum.Length;

                    for (int j = 0; j < N - leng ; j++)
                    {
                        binaryNum = binaryNum.Insert(0, "0");
                    }
                }

                list.Add(binaryNum);
            }


            for (int i = 0; i < list.Count; i++)
            {
                string str = list[i];

                bool flag = true;


                for (int j = 0; j < N; j++)
                {
                    if (str[j] == '0')
                    {
                        if (s[j] == "o")
                        {
                            if (j == 0)
                            {
                                if (str[N - 1] == str[j + 1])
                                {
                                    ///OK
                                }
                                else
                                {
                                    flag = false;
                                    break;
                                }
                            }
                            else if (j == N-1)
                            {
                                if (str[0] == str[j - 1])
                                {
                                    ///OK
                                }
                                else
                                {
                                    flag = false;
                                    break;
                                }
                            }
                            else
                            {
                                if (str[j - 1] == str[j + 1])
                                {
                                    ///OK
                                }
                                else
                                {
                                    flag = false;
                                    break;
                                }
                            }

                        }
                        else if (s[j] == "x")
                        {
                            if (j == 0)
                            {
                                if (str[N - 1] != str[j + 1])
                                {
                                    ///OK
                                }
                                else
                                {
                                    flag = false;
                                    break;
                                }
                            }
                            else if (j == N - 1)
                            {
                                if (str[0] != str[j - 1])
                                {
                                    ///OK
                                }
                                else
                                {
                                    flag = false;
                                    break;
                                }
                            }
                            else
                            {
                                if (str[j - 1] != str[j + 1])
                                {
                                    ///OK
                                }
                                else
                                {
                                    flag = false;
                                    break;
                                }
                            }
                        }
                    }
                    else if (str[j] == '1')
                    {
                        if (s[j] == "o")
                        {
                            if (j == 0)
                            {
                                if (str[N - 1] != str[j + 1])
                                {
                                    ///OK
                                }
                                else
                                {
                                    flag = false;
                                    break;
                                }
                            }
                            else if (j == N - 1)
                            {
                                if (str[0] != str[j - 1])
                                {
                                    ///OK
                                }
                                else
                                {
                                    flag = false;
                                    break;
                                }
                            }
                            else
                            {
                                if (str[j - 1] != str[j + 1])
                                {
                                    ///OK
                                }
                                else
                                {
                                    flag = false;
                                    break;
                                }
                            }

                        }
                        else if (s[j] == "x")
                        {
                            if (j == 0)
                            {
                                if (str[N - 1] == str[j + 1])
                                {
                                    ///OK
                                }
                                else
                                {
                                    flag = false;
                                    break;
                                }
                            }
                            else if (j == N - 1)
                            {
                                if (str[0] == str[j - 1])
                                {
                                    ///OK
                                }
                                else
                                {
                                    flag = false;
                                    break;
                                }
                            }
                            else
                            {
                                if (str[j - 1] == str[j + 1])
                                {
                                    ///OK
                                }
                                else
                                {
                                    flag = false;
                                    break;
                                }
                            }
                        }
                    }

                }


                if(flag == true)
                {
                    for (int j= 0; j < str.Length; j++)
                    {
                        if(str[j] =='0')
                        {
                            System.Console.Write("S");
                        }
                        else
                        {
                            System.Console.Write("W");
                        }
                    }

                    System.Console.WriteLine();
                    return;
                }
            }
            System.Console.WriteLine("-1");
        }
    }