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;

namespace AtCoder
{
    class Program
    {
        private const string SHEEP = "S";
        private const string WOLF = "W";
        private const string ROUND = "o";

        static void Main(string[] args)
        {
            var animalCount = int.Parse(Console.ReadLine());
            var remarks = Console.ReadLine().Select(x => x.ToString()).ToList();

            //var randam = new Random();
            //var animalCount = randam.Next(10) + 3;
            //var remarks = CreateRandamData(animalCount);
            var answer = Enumerable.Repeat<string>(null, animalCount).ToList();
            Func<int, int> nextIndex = (int index) => index + 1 == animalCount ? 0 : index + 1;
            Func<int, int> previewIndex = (int index) => index == 0 ? animalCount - 1 : index - 1;
            Action<int, string> rightInsert = (int index, string animal) => answer[nextIndex(index)] = animal;
            Action<int, string> leftInsert = (int index, string animal) => answer[previewIndex(index)] = animal;
            Action<int> insertSheepOrWolf = (int index) =>
            {
                var previewAnimal = answer[previewIndex(index)];
                if (answer[index] == SHEEP)
                {
                    if (remarks[index] == ROUND)
                    {
                        rightInsert(index, previewAnimal == SHEEP ? SHEEP : WOLF);
                    }
                    else
                    {
                        rightInsert(index, previewAnimal == SHEEP ? WOLF : SHEEP);
                    }
                }
                else
                {
                    if (remarks[index] == ROUND)
                    {
                        rightInsert(index, previewAnimal == SHEEP ? WOLF : SHEEP);
                    }
                    else
                    {
                        rightInsert(index, previewAnimal == SHEEP ? SHEEP : WOLF);
                    }
                }
            };

            var initializePaterns = new List<Tuple<string, string, string>>
            {
                Tuple.Create(SHEEP,SHEEP,SHEEP),
                Tuple.Create(WOLF,SHEEP,WOLF),
                Tuple.Create(SHEEP,WOLF,WOLF),
                Tuple.Create(WOLF,WOLF,SHEEP),
            };
            //最初の発言を基準とする
            foreach (var initializePatern in initializePaterns)
            {
                answer[0] = initializePatern.Item2;
                rightInsert(0, initializePatern.Item3);
                leftInsert(0, initializePatern.Item1);

                for (var i = 1; i < animalCount - 2; ++i)
                {
                    insertSheepOrWolf(i);
                }

                var isConfirm = ResultCheck(remarks, answer);
                if (isConfirm)
                {
                    Console.WriteLine(answer.Aggregate((x, next) => x + next));
                    return;
                }
            }
            Console.WriteLine(-1);
        }

        private static List<string> CreateRandamData(int count)
        {
            var randam = new Random();
            var test = new List<string>(count);
            for (var i = 0; i < count; ++i)
            {
                var ran = randam.Next();
                test.Add(ran % 2 == 0 ? "o" : "x");
            }
            return test;
        }

        private static bool ResultCheck(List<string> remarks, List<string> answer)
        {
            for (var i = 0; i < answer.Count; ++i)
            {
                var previewIndex = i == 0 ? remarks.Count - 1 : i - 1;
                var nextIndex = i + 1 == remarks.Count ? 0 : i + 1;

                if (answer[i] == SHEEP)
                {
                    if (remarks[i] == ROUND)
                    {
                        if (answer[previewIndex] != answer[nextIndex]) return false;
                    }
                    else
                    {
                        if (answer[previewIndex] == answer[nextIndex]) return false;
                    }
                }
                else
                {
                    if (remarks[i] == ROUND)
                    {
                        if (answer[previewIndex] == answer[nextIndex]) return false;
                    }
                    else
                    {
                        if (answer[previewIndex] != answer[nextIndex]) return false;
                    }
                }
            }
            return true;
        }
    }
}