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: Accepted)

using System;
using System.Text;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            string Si = Console.ReadLine();
            for (int cnt = 1; cnt <= 4; cnt++)
            {
                char[] SW = new char[N+2];
                switch (cnt)
                {
                    case 1:
                        SW[0] = 'S';
                        SW[1] = 'S';
                        break;
                    case 2:
                        SW[0] = 'W';
                        SW[1] = 'S';
                        break;
                    case 3:
                        SW[0] = 'S';
                        SW[1] = 'W';
                        break;
                    case 4:
                        SW[0] = 'W';
                        SW[1] = 'W';
                        break;
                }
                for (int i = 0; i < N; i++)
                {
                    SW[i+2] = Ans(Si.Substring(i, 1), SW[i],SW[i+1]);
                }
                if (SW[0] == SW[N] & SW[1] == SW[N+1])
                {
                    string output = new String(SW);
                    Console.WriteLine(output.Substring(1,N));
                    Console.ReadKey();
                    return;
                }
            }
            Console.WriteLine("-1");
            Console.ReadKey();
        }

        static char Ans(string Si, char type1,char 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'; }
        }

    }
}