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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;
using System.Numerics;

namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
        }

        public void Solve(ConsoleInput cin)
        {
            var N = cin.ReadInt;
            var s = cin.ReadLine.ToArray();

            var animals1 = new char[N]; 
            animals1[N - 1] = 'S';
            animals1[0] = 'S';

            var animals2 = new char[N]; 
            animals2[N - 1] = 'S';
            animals2[0] = 'W';

            var animals3 = new char[N]; 
            animals3[N - 1] = 'W';
            animals3[0] = 'S';

            var animals4 = new char[N]; 
            animals4[N - 1] = 'W';
            animals4[0] = 'W';

            var ans = "-1";

            ans = this.GetAnimals(animals1, s, N);
            if (ans != "-1") 
            {
                WriteLine(ans);
                return;
            }
            ans = this.GetAnimals(animals2, s, N);
            if (ans != "-1") 
            {
                WriteLine(ans);
                return;
            }
            ans = this.GetAnimals(animals3, s, N);
            if (ans != "-1") 
            {
                WriteLine(ans);
                return;
            }
            ans = this.GetAnimals(animals4, s, N);
            WriteLine(ans);
            return;
        }

        private string GetAnimals(char[] animals,char[] s,int N) 
        {
            var lastAnimal = animals[N - 1];
            for (int i = 0; i < N; i++)
            {
                var pre = i - 1 < 0 ? N - 1 : i - 1;
                var next = i + 1 > N - 1 ? 1 : i + 1;
                var shouldEqual = true;

                if (animals[i] == 'S' ^ s[i] == 'o') shouldEqual = false;

                if (shouldEqual)
                {
                    animals[next] = animals[pre];
                }
                else
                {
                    animals[next] = animals[pre] == 'S' ? 'W' : 'S';
                }

                // WriteLine("pre {0} next {1} {3} : {2}", pre, next, new string(animals), shouldEqual);
            }
            return lastAnimal == animals[N - 1] ? new string(animals) : "-1";
        }

        private BigInteger Lcm(BigInteger a, BigInteger b) 
        {
            return (a * b) / Gcd(a, b);
        }

        /// <summary>
        /// 最大公約数計算
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        private BigInteger Gcd(BigInteger a, BigInteger b) 
        {
            if (a < b) return Gcd(b, a);
            
            while (b != 0) 
            {
                var mod = a % b;
                a = b;
                b = mod;
            }
            return a;
        }
    }

    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }

        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; i++)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }

        public string ReadLine { get { return _stream.ReadLine(); } }
        public int ReadInt { get { return int.Parse(Read); } }
        public long ReadLong { get { return long.Parse(Read); } }
        public double ReadDouble { get { return double.Parse(Read); } }
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
    }

    /// <summary>
    /// Mod計算用クラス
    /// </summary>
    struct ModInt
    {
        const int M = 1000000007;
        public long V;
        public ModInt(long v) { V = (v %= M) < 0 ? v + M : v; }

        public static implicit operator ModInt(long v) => new ModInt(v);
        public static ModInt operator +(ModInt x) => x;
        public static ModInt operator -(ModInt x) => -x.V;
        public static ModInt operator +(ModInt x, ModInt y) => x.V + y.V;
        public static ModInt operator -(ModInt x, ModInt y) => x.V - y.V;
        public static ModInt operator *(ModInt x, ModInt y) => x.V * y.V;
        public static ModInt operator /(ModInt x, ModInt y) => x.V * y.Inv();

        public ModInt Pow(int i) => MPow(V, i);
        public ModInt Inv() => MPow(V, M - 2);
        public override string ToString() => $"{V}";

        static long MPow(long b, int i)
        {
            for (var r = 1L; ; b = b * b % M)
            {
                if (i % 2 > 0) r = r * b % M;
                if ((i /= 2) < 1) return r;
            }
        }

        public static long MFactorial(int n) { for (long x = 1, i = 1; ; x = x * ++i % M) if (i >= n) return x; }
        public static long MNpr(int n, int r)
        {
            if (n < r) return 0;
            for (long x = 1, i = n - r; ; x = x * ++i % M) if (i >= n) return x;
        }
        public static ModInt MNcr(int n, int r) => n < r ? 0 : n - r < r ? MNcr(n, n - r) : (ModInt)MNpr(n, r) / MFactorial(r);
    }
}