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;

class program
{
    static void Main(string[] args)
    {
        int N = int.Parse(Console.ReadLine());
        string s = Console.ReadLine();
        //s は o と x のみからなる長さ N の文字列
        string temp = "";
        string ans = "-1";

        temp = "SS";
        
        for(int i = 2; i < N; i++)
        {
            if (temp[i - 1] == 'S')
            {
                if (s[i - 1] == 'o')
                {
                    if (temp[i - 2] == 'S') temp += 'S';
                    else temp += 'W';
                }
                else//x no baai
                {
                    if (temp[i - 2] == 'S') temp += 'W';
                    else temp += 'S';
                }
            }
            else // W
                if (s[i - 1] == 'o')
            {
                if (temp[i - 2] == 'S') temp += 'W';
                else temp += 'S';
            }
            else//x no baai
            {
                if (temp[i - 2] == 'S') temp += 'S';
                else temp += 'W';
            }

            if (i == N - 1)
            {
                i++;
                char t;
                if (temp[i - 1] == 'S')
                {
                    if (s[i - 1] == 'o')
                    {
                        if (temp[i - 2] == 'S') t= 'S';
                        else t= 'W';
                    }
                    else//x no baai
                    {
                        if (temp[i - 2] == 'S') t= 'W';
                        else t= 'S';
                    }
                }
                else // W
                    if (s[i - 1] == 'o')
                {
                    if (temp[i - 2] == 'S') t= 'W';
                    else t= 'S';
                }
                else//x no baai
                {
                    if (temp[i - 2] == 'S') t= 'S';
                    else t= 'W';
                }

                if (t == temp[0]) ans = temp;
            }

        }



        temp = "SW";
        for (int i = 2; i < N; i++)
        {
            if (temp[i - 1] == 'S')
            {
                if (s[i - 1] == 'o')
                {
                    if (temp[i - 2] == 'S') temp += 'S';
                    else temp += 'W';
                }
                else//x no baai
                {
                    if (temp[i - 2] == 'S') temp += 'W';
                    else temp += 'S';
                }
            }
            else // W
                if (s[i - 1] == 'o')
            {
                if (temp[i - 2] == 'S') temp += 'W';
                else temp += 'S';
            }
            else//x no baai
            {
                if (temp[i - 2] == 'S') temp += 'S';
                else temp += 'W';
            }

            if (i == N - 1)
            {
                i++;
                char t;
                if (temp[i - 1] == 'S')
                {
                    if (s[i - 1] == 'o')
                    {
                        if (temp[i - 2] == 'S') t = 'S';
                        else t = 'W';
                    }
                    else//x no baai
                    {
                        if (temp[i - 2] == 'S') t = 'W';
                        else t = 'S';
                    }
                }
                else // W
                    if (s[i - 1] == 'o')
                {
                    if (temp[i - 2] == 'S') t = 'W';
                    else t = 'S';
                }
                else//x no baai
                {
                    if (temp[i - 2] == 'S') t = 'S';
                    else t = 'W';
                }

                if (t == temp[0]) ans = temp;
            }

        }

        temp = "WS";
        for (int i = 2; i < N; i++)
        {
            if (temp[i - 1] == 'S')
            {
                if (s[i - 1] == 'o')
                {
                    if (temp[i - 2] == 'S') temp += 'S';
                    else temp += 'W';
                }
                else//x no baai
                {
                    if (temp[i - 2] == 'S') temp += 'W';
                    else temp += 'S';
                }
            }
            else // W
                if (s[i - 1] == 'o')
            {
                if (temp[i - 2] == 'S') temp += 'W';
                else temp += 'S';
            }
            else//x no baai
            {
                if (temp[i - 2] == 'S') temp += 'S';
                else temp += 'W';
            }

            if (i == N - 1)
            {
                i++;
                char t;
                if (temp[i - 1] == 'S')
                {
                    if (s[i - 1] == 'o')
                    {
                        if (temp[i - 2] == 'S') t = 'S';
                        else t = 'W';
                    }
                    else//x no baai
                    {
                        if (temp[i - 2] == 'S') t = 'W';
                        else t = 'S';
                    }
                }
                else // W
                    if (s[i - 1] == 'o')
                {
                    if (temp[i - 2] == 'S') t = 'W';
                    else t = 'S';
                }
                else//x no baai
                {
                    if (temp[i - 2] == 'S') t = 'S';
                    else t = 'W';
                }

                if (t == temp[0]) ans = temp;
            }

        }

        temp = "WW";

        for (int i = 2; i < N; i++)
        {
            if (temp[i - 1] == 'S')
            {
                if (s[i - 1] == 'o')
                {
                    if (temp[i - 2] == 'S') temp += 'S';
                    else temp += 'W';
                }
                else//x no baai
                {
                    if (temp[i - 2] == 'S') temp += 'W';
                    else temp += 'S';
                }
            }
            else // W
                if (s[i - 1] == 'o')
            {
                if (temp[i - 2] == 'S') temp += 'W';
                else temp += 'S';
            }
            else//x no baai
            {
                if (temp[i - 2] == 'S') temp += 'S';
                else temp += 'W';
            }

            if (i == N - 1)
            {
                i++;
                char t;
                if (temp[i - 1] == 'S')
                {
                    if (s[i - 1] == 'o')
                    {
                        if (temp[i - 2] == 'S') t = 'S';
                        else t = 'W';
                    }
                    else//x no baai
                    {
                        if (temp[i - 2] == 'S') t = 'W';
                        else t = 'S';
                    }
                }
                else // W
                    if (s[i - 1] == 'o')
                {
                    if (temp[i - 2] == 'S') t = 'W';
                    else t = 'S';
                }
                else//x no baai
                {
                    if (temp[i - 2] == 'S') t = 'S';
                    else t = 'W';
                }

                if (t == temp[0]) ans = temp;
            }

        }

        Console.WriteLine(ans);


    }
}