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# (.NET Core 3.1.201) (judge verdict: Accepted)

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

namespace ConsoleApp15
{
    class Class403
    {
        static char[][] pattern = new char[4][]
        {
            new char[2]{'S','S'},
            new char[2]{'S','W'},
            new char[2]{'W','S'},
            new char[2]{'W','W'}
        };
        static void Main()
        {
            int N = int.Parse(Console.ReadLine());
            string s = Console.ReadLine();
            for (int j = 0; j < 4; j++)
            {
                char[] ans = new char[N + 2];
                ans[0] = pattern[j][0];
                ans[1] = pattern[j][1];

                for (int i = 1; i < N+1; i++)
                {
                    int num = i % N;

                    if (ans[i] == 'S')
                    {
                        if (s[num] == 'o') ans[i + 1] = ans[i - 1];
                        else ans[i + 1] = Swap(ans[i - 1]);
                    }
                    else
                    {
                        if (s[num] == 'o') ans[i + 1] = Swap(ans[i - 1]);
                        else ans[i + 1] = ans[i - 1];
                    }
                }

                if (ans[0] == ans[N] && ans[1] == ans[N + 1])
                {

                    Console.WriteLine(string.Join("", ans.Take(N)));
                    return;

                }
            }

            Console.WriteLine(-1);
            
        }
        static char Swap(char c)
        {
            if (c == 'S') return 'W';
            else return 'S';
        }
    }
}