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;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            string Si = Console.ReadLine();
            string test1 = "";
            string test2 = "";
            if (Si.Substring(0,1)=="o")
            {
                for (int cnt =1;cnt<=4; cnt++)
                {
                    switch (cnt)
                    {
                        case 1:
                            test1 = "sss";
                            test2 = "ss";
                            break;
                        case 2:
                            test1 = "wsw";
                            test2 = "sw";
                            break;
                        case 3:
                            test1 = "sww";
                            test2 = "ww";
                            break;
                        case 4:
                            test1 = "wws";
                            test2 = "ws";
                            break;
                    }
                    for (int i = 1; i < Si.Length - 2; i++)
                    {
                        test1 = test1 + Ans(Si.Substring(i, 1), test1.Substring(test1.Length - 2, 1), test1.Substring(test1.Length - 1, 1));
                    }
                    for (int i = 1; i < Si.Length - 1; i++)
                    {
                        test2 = test2 + Ans(Si.Substring(i, 1), test2.Substring(test2.Length - 2, 1), test2.Substring(test2.Length - 1, 1));
                    }
                    test1 = test1.Substring(1, test1.Length - 1) + test1.Substring(0, 1);
                    if (test1 == test2)
                    {
                        Console.WriteLine(test2);
                        return;
                    }
                }
            }
            else
            {
                for (int cnt = 1; cnt <= 4; cnt++)
                {
                    switch (cnt)
                    {
                        case 1:
                            test1 = "ssw";
                            test2 = "sw";
                            break;
                        case 2:
                            test1 = "wss";
                            test2 = "ss";
                            break;
                        case 3:
                            test1 = "sws";
                            test2 = "ws";
                            break;
                        case 4:
                            test1 = "www";
                            test2 = "ww";
                            break;
                    }
                    for (int i = 1; i < Si.Length - 2; i++)
                    {
                        test1 = test1 + Ans(Si.Substring(i, 1), test1.Substring(test1.Length - 2, 1), test1.Substring(test1.Length - 1, 1));
                    }
                    for (int i = 1; i < Si.Length - 1; i++)
                    {
                        test2 = test2 + Ans(Si.Substring(i, 1), test2.Substring(test2.Length - 2, 1), test2.Substring(test2.Length - 1, 1));
                    }
                    test1 = test1.Substring(1, test1.Length - 1) + test1.Substring(0, 1);
                    if (test1 == test2)
                    {
                        Console.WriteLine(test2); 
                        return;
                    }
                }
            }
            Console.WriteLine("-1");
        }

        static string Ans(string Si,string type1,string type2)
        {
            if (Si == "o" & type1 == "s" & type2 == "s")      { return "s"; }
            else if (Si == "o" & type1 == "w" & type2 == "s") { return "w"; }
            else if (Si == "o" & type1 == "w" & type2 == "w") { return "s"; }
            else if (Si == "o" & type1 == "s" & type2 == "w") { return "w"; }
            else if (Si == "x" & type1 == "s" & type2 == "s") { return "w"; }
            else if (Si == "x" & type1 == "w" & type2 == "s") { return "s"; }
            else if (Si == "x" & type1 == "w" & type2 == "w") { return "w"; }
            else                                              { return "s"; }
        }

    }
}