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: Accepted)

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

namespace AtCoder
{
    class Program
    {
        private const char SHEEP = 'S';
        private const char WOLF = 'W';
        private const char ROUND = 'o';

        static void Main(string[] args)
        {
            var sr = new InputReader(Console.In);
            //var sr = new InputReader(new StreamReader("input.txt"));
            using (var sw = Console.Out)
            {
                Solve(sr, sw);
            }
        }

        internal static void Solve(InputReader sr, TextWriter sw)
        {
            var animalCount = sr.NextInt32();
            var remarks = sr.NextString();
            for (var i = 0; i < 2; i++)
            {
                for (var j = 0; j < 2; j++)
                {
                    for (var k = 0; k < 2; k++)
                    {
                        var ch1 = i == 0 ? SHEEP : WOLF;
                        var ch2 = j == 0 ? SHEEP : WOLF;
                        var ch3 = k == 0 ? SHEEP : WOLF;
                        var answ = new char[animalCount];
                        if (CanSheep(remarks, ch1, ch2, ch3, answ))
                        {
                            sw.WriteLine(answ);
                            return;
                        }
                    }
                }
            }
            sw.WriteLine(-1);
        }
        private static bool CanSheep(string str, char ch1, char ch2, char ch3, char[] answ)
        {
            answ[0] = ch1;
            answ[1] = ch2;
            answ[2] = ch3;
            for (var i = 2; i < str.Length - 1; i++)
            {
                if (answ[i] == SHEEP)
                {
                    if (str[i] == ROUND)
                    {
                        if (i + 1 < str.Length)
                        {
                            if (answ[i - 1] == SHEEP)
                            {
                                answ[i + 1] = SHEEP;
                            }
                            else
                            {
                                answ[i + 1] = WOLF;
                            }
                        }
                    }
                    else
                    {
                        if (i + 1 < str.Length)
                        {
                            if (answ[i - 1] == SHEEP)
                            {
                                answ[i + 1] = WOLF;
                            }
                            else
                            {
                                answ[i + 1] = SHEEP;
                            }
                        }
                    }
                }
                else
                {
                    if (str[i] == ROUND)
                    {
                        if (i + 1 < str.Length)
                        {
                            if (answ[i - 1] == SHEEP)
                            {
                                answ[i + 1] = WOLF;
                            }
                            else
                            {
                                answ[i + 1] = SHEEP;
                            }
                        }
                    }
                    else
                    {
                        if (i + 1 < str.Length)
                        {
                            if (answ[i - 1] == SHEEP)
                            {
                                answ[i + 1] = SHEEP;
                            }
                            else
                            {
                                answ[i + 1] = WOLF;
                            }
                        }
                    }
                }
            }


            for (var i = 0; i < str.Length; i++)
            {
                char prev;
                if (i - 1 >= 0)
                {
                    prev = answ[i - 1];
                }
                else
                {
                    prev = answ[answ.Length - 1];
                }
                char next;
                if (i + 1 < str.Length)
                {
                    next = answ[i + 1];
                }
                else
                {
                    next = answ[0];
                }
                if (answ[i] == SHEEP)
                {
                    if (str[i] == ROUND)
                    {
                        if (prev != next)
                            return false;
                    }
                    else
                    {
                        if (prev == next)
                            return false;
                    }
                }
                else
                {
                    if (str[i] == ROUND)
                    {
                        if (prev == next)
                            return false;
                    }
                    else
                    {
                        if (prev != next)
                            return false;
                    }
                }
            }

            return true;
        }
    }

    internal class InputReader : IDisposable
    {
        private bool isDispose;
        private readonly TextReader sr;

        public InputReader(TextReader stream)
        {
            sr = stream;
        }

        public void Dispose()
        {
            Dispose(true);
            GC.SuppressFinalize(this);
        }

        public string NextString()
        {
            var result = sr.ReadLine();
            return result;
        }

        public int NextInt32()
        {
            return Int32.Parse(NextString());
        }

        public long NextInt64()
        {
            return Int64.Parse(NextString());
        }

        public string[] NextSplitStrings()
        {
            return NextString()
                .Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
        }

        public T[] ReadArray<T>(Func<string, CultureInfo, T> func)
        {
            return NextSplitStrings()
                .Select(s => func(s, CultureInfo.InvariantCulture))
                .ToArray();
        }

        public T[] ReadArrayFromString<T>(Func<string, CultureInfo, T> func, string str)
        {
            return
                str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries)
                    .Select(s => func(s, CultureInfo.InvariantCulture))
                    .ToArray();
        }

        protected void Dispose(bool dispose)
        {
            if (isDispose) return;
            if (dispose)
                sr.Close();
            isDispose = true;
        }

        ~InputReader()
        {
            Dispose(false);
        }
    }
}