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: Time Limit Exceeded)

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

namespace AtCoderRegularContest069
{
    public class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine(program1(new String[] { Console.ReadLine(), Console.ReadLine() }));
        }

        public static string program1(string[] args)
        {
            var n = int.Parse(args[0]);
            var s = args[1].ToCharArray();

            var animalPattern = new List<char>[] { new List<char>() { 'S', 'S' }, new List<char> { 'S', 'W' }, new List<char> { 'W', 'W' }, new List<char> { 'W', 'S' } };

            return string.Join("", animalPattern.Select(animals =>
            {
                var prevAnimal = animals.First();

                return s.Skip(1).Aggregate((IEnumerable<char>)animals, (ani, ans) =>
                {
                    if (ani.Last() == 'S' && ans == 'x' || ani.Last() == 'W' && ans == 'o')
                    {
                        return ani.Concat(new char[] { ani.ElementAt(ani.Count() - 2) == 'S' ? 'W' : 'S' });
                    }
                    else
                    {
                        return ani.Concat(new char[] { ani.ElementAt(ani.Count() - 2) });
                    }
                });
            })
            .Where(animals => animals.First() == animals.Last())
            .Select(animals => animals.Take(n))
            .FirstOrDefault(animals => {
                if (s.First() == 'o' && animals.First() == 'S' || s.First() == 'x' && animals.First() == 'W')
                {
                    return animals.ElementAt(1) == animals.Last();
                }
                else
                {
                    return animals.ElementAt(1) != animals.Last();
                }
            }) ?? new List<char>() { '-', '1' }) ;
        }
    }
}