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;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace Tasks
{
    public class D
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var N = int.Parse(Console.ReadLine());
            var S = Console.ReadLine();


            var answer = Enumerable.Repeat('-', N).ToArray();

            Func<char[], int, bool> check = (char[] array, int current) =>
            {
                var left = (current - 1 + N) % N;
                var right = (current + 1) % N;
                var isEmpty = array[right] == '-';

                if (array[current] == 'S')
                {
                    if (isEmpty)
                    {
                        if (S[current] == 'o') array[right] = array[left];
                        else array[right] = array[left] == 'S' ? 'W' : 'S';
                        return true;
                    }
                    else
                    {
                        var same = array[left] == array[right];
                        if (S[current] == 'o') return same;
                        else return !same;
                    }
                }
                else
                {
                    if (isEmpty)
                    {
                        if (S[current] == 'o') array[right] = array[left] == 'S' ? 'W' : 'S';
                        else array[right] = array[left];
                        return true;
                    }
                    else
                    {
                        var same = array[left] == array[right];
                        if (S[current] == 'o') return !same;
                        else return same;
                    }
                }
            };

            var ok = true;
            for (var bit = 0; bit < 1 << 3; bit++)
            {
                answer = Enumerable.Repeat('-', N).ToArray();
                answer[0] = (bit >> 1 & 1) == 1 ? 'S' : 'W';
                answer[1] = (bit >> 0 & 1) == 1 ? 'S' : 'W';
                answer[N - 1] = (bit >> 2 & 1) == 1 ? 'S' : 'W';
                ok = true;
                for (var i = 0; i < N; i++)
                {
                    ok = check(answer, i);
                    if (!ok) break;
                }
                if (ok) break;
            }

            Console.WriteLine(ok ? new string(answer) : "-1");
        }
    }
}