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)

#region using
using System;
using System.Collections.Generic;
using System.Linq;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using System.Text;
#endregion

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var N = consoleReader.Int;
            s = consoleReader.String;


            bool[] startWithSS = new bool[N];
            bool[] startWithSW = new bool[N];
            bool[] startWithWS = new bool[N];
            bool[] startWithWW = new bool[N];
            startWithSS[0] = startWithSS[1] = startWithSW[0] = startWithWS[1] = sheep;
            startWithWW[0] = startWithWW[1] = startWithWS[0] = startWithSW[1] = wolf;

            for (int i = 1; i < s.Length - 1; i++)
            {
                Set(startWithSS, i);
                Set(startWithSW, i);
                Set(startWithWS, i);
                Set(startWithWW, i);
            }
            var res = new[] {
            startWithSS,
            startWithSW,
            startWithWS,
            startWithWW,
            }.FirstOrDefault(IsValid);

            return new string(res?.Select(b => b ? 'S' : 'W')?.ToArray() ?? new[] { '-', '1' });
        }
        string s;

        const bool sheep = true;
        const bool wolf = false;

        bool IsValid(bool[] cur)
        {
            if (s[0] == 'o')
            {
                if (cur[0])
                {
                    if (cur[cur.Length - 1] != cur[1]) return false;
                }
                else if (cur[cur.Length - 1] == cur[1]) return false;
            }
            else
            {
                if (!cur[0])
                {
                    if (cur[cur.Length - 1] != cur[1]) return false;
                }
                else if (cur[cur.Length - 1] == cur[1]) return false;
            }

            if (s[s.Length - 1] == 'o')
            {
                if (cur[cur.Length - 1])
                {
                    if (cur[cur.Length - 2] != cur[0]) return false;
                }
                else if (cur[cur.Length - 2] == cur[0]) return false;
            }
            else
            {
                if (!cur[cur.Length - 1])
                {
                    if (cur[cur.Length - 2] != cur[0]) return false;
                }
                else if (cur[cur.Length - 2] == cur[0]) return false;
            }
            return true;
        }
        void Set(bool[] cur, int index)
        {
            if (cur[index] == sheep)
            {
                switch (s[index])
                {
                    case 'o':
                        cur[index + 1] = cur[index - 1];
                        break;
                    case 'x':
                        cur[index + 1] = !cur[index - 1];
                        break;
                }
            }
            else
            {
                switch (s[index])
                {
                    case 'o':
                        cur[index + 1] = !cur[index - 1];
                        break;
                    case 'x':
                        cur[index + 1] = cur[index - 1];
                        break;
                }
            }

        }


        #region いつもの
#pragma warning disable
        private ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
    }
    static class Ext
    {
        public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
        public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
    }
    public class ConsoleReader { private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries); private string[] line = Array.Empty<string>(); private int linePosition; private TextReader textReader; public ConsoleReader(TextReader tr) { textReader = tr; } public int Int => int.Parse(String); public long Long => long.Parse(String); public double Double => double.Parse(String); public string String { get { if (linePosition >= line.Length) { linePosition = 0; line = ReadLineSplit(); } return line[linePosition++]; } } public class SplitLine { private string[] splited; public SplitLine(ConsoleReader cr) { splited = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); } public int[] Int => String.Select(x => int.Parse(x)).ToArray(); public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray(); public long[] Long => String.Select(x => long.Parse(x)).ToArray(); public double[] Double => String.Select(x => double.Parse(x)).ToArray(); public string[] String => splited; } public SplitLine Split => new SplitLine(this); public class RepeatReader : IEnumerable<ConsoleReader> { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator(); System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator(); public IEnumerable<string> String => this.Select(cr => cr.String); public IEnumerable<int> Int => this.Select(cr => cr.Int); public IEnumerable<int> Int0 => this.Select(cr => cr.Int - 1); public IEnumerable<long> Long => this.Select(cr => cr.Long); public IEnumerable<double> Double => this.Select(cr => cr.Double); } public RepeatReader Repeat(int count) => new RepeatReader(this, count); }
    #endregion
}