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

namespace ARC069
{
    public class D
    {
        private string F(int kind, string S)
        {
            bool isLastSheep = ((kind & 1) != 0);
            bool isFirstSheep = ((kind & 2) != 0);

            var builder = new StringBuilder();
            bool isPrevSheep = isLastSheep;
            bool isCurrentSheep = isFirstSheep;
            bool isNextSheep;
            for (int i = 0; i < S.Length - 2; ++i)
            {
                builder.Append(isCurrentSheep ? 'S' : 'W');
                if (isCurrentSheep)
                {
                    isNextSheep = ((S[i] == 'o') == isPrevSheep);
                }
                else
                {
                    isNextSheep = ((S[i] == 'o') != isPrevSheep);
                }
                isPrevSheep = isCurrentSheep;
                isCurrentSheep = isNextSheep;
            }

            if (isCurrentSheep != ((S[S.Length - 2] == 'o') == (isPrevSheep == isLastSheep))) { return null; }
            builder.Append(isCurrentSheep ? 'S' : 'W');

            if (isLastSheep != ((S[S.Length - 1] == '0') == (isCurrentSheep == isFirstSheep))) { return null; }
            builder.Append(isLastSheep ? 'S' : 'W');
            return builder.ToString();
        }

        private void Run()
        {
            var N = int.Parse(Console.ReadLine().Trim());
            var S = Console.ReadLine().Trim();

            Console.WriteLine(Enumerable.Range(0, 4).Select(i => F(i, S)).FirstOrDefault(s => s != null) ?? "-1");
        }

        public static void Main()
        {
            var old = Console.Out;
            using (var writer = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false })
            {
                Console.SetOut(writer);
                new D().Run();
                Console.Out.Flush();
                Console.SetOut(old);
            }
        }
    }
}