Problem:
Score : 400 points

Problem Statement

We have a board with a 2 \times N grid.
Snuke covered the board with N dominoes without overlaps.
Here, a domino can cover a 1 \times 2 or 2 \times 1 square.

Then, Snuke decided to paint these dominoes using three colors: red, cyan and green.
Two dominoes that are adjacent by side should be painted by different colors.
Here, it is not always necessary to use all three colors.

Find the number of such ways to paint the dominoes, modulo 1000000007.

The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:

Each domino is represented by a different English letter (lowercase or uppercase).

The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.

Constraints

1 \leq N \leq 52

|S_1| = |S_2| = N

S_1 and S_2 consist of lowercase and uppercase English letters.

S_1 and S_2 represent a valid arrangement of dominoes.

Input

Input is given from Standard Input in the following format:

N
S_1
S_2

Output

Print the number of such ways to paint the dominoes, modulo 1000000007.

Sample Input 1

3
aab
ccb

Sample Output 1

6

There are six ways as shown below:

Sample Input 2

1
Z
Z

Sample Output 2

3

Note that it is not always necessary to use all the colors.

Sample Input 3

52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn

Sample Output 3

958681902

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Collections.ObjectModel;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

public sealed partial class Program
{
    int n;
    string[] ss;

    const long Mod = 1000000007L;

    void Consume(ref int x, out bool isPortrait)
    {
        if (ss[0][x] == ss[1][x])
        {
            isPortrait = true;
            x++;
        }
        else
        {
            isPortrait = false;
            x += 2;
        }
    }

    long Solve()
    {
        var x = 0;
        var isPortrait = default(bool);

        Consume(ref x, out isPortrait);

        var k = isPortrait ? 3L : 6L;
        var previousIsPortrait = isPortrait;

        while (x < n)
        {
            Consume(ref x, out isPortrait);

            if (isPortrait)
            {
                if (previousIsPortrait)
                {
                    k = (k * 2) % Mod;
                }
                else
                {
                    // 1x.
                }
            }
            else
            {
                if (previousIsPortrait)
                {
                    k = (k * 2) % Mod;
                }
                else
                {
                    k = (k * 3) % Mod;
                }
            }

            previousIsPortrait = isPortrait;
        }

        return k;
    }

    void Read()
    {
        var a = scanner;
        n = a.N();
        ss = 2.MakeArray(_ => input.ReadLine());
    }

    public void EntryPoint()
    {
        Read();
        WriteLine(Solve());
    }
}

#region Custom Library
public static class TemplateExtension
{
    public static X[] MakeArray<X>(this int count, Func<int, X> func)
    {
        var xs = new X[count];
        for (var i = 0; i < count; i++)
        {
            xs[i] = func(i);
        }
        return xs;
    }

    public static int[] Range(this int count, int start = 0)
    {
        return count.MakeArray(i => i + start);
    }

    public static string Intercalate<X>(this IEnumerable<X> @this, string separator)
    {
        return string.Join(separator, @this);
    }

    public static void ForEach<X>(this IEnumerable<X> @this, Action<X, int> action)
    {
        var list = @this as IReadOnlyList<X>;
        if (list != null)
        {
            var count = list.Count;
            for (var i = 0; i < count; i++)
            {
                action(list[i], i);
            }
        }
        else
        {
            var i = 0;
            foreach (var x in @this)
            {
                action(x, i);
                i++;
            }
        }
    }
}

public sealed class Scanner
{
    readonly TextReader reader;

    /// <summary>
    /// Reads next word separated by spaces.
    /// </summary>
    public string Word()
    {
        var sb = default(StringBuilder);
        var firstChar = default(char);
        var count = 0;

        while (true)
        {
            var r = reader.Read();

            if (r == '\r')
            {
                if (reader.Peek() == '\n') reader.Read();
                break;
            }
            else if (r == -1 || r == ' ' || r == '\n')
            {
                break;
            }
            else
            {
                var c = (char)r;

                switch (count)
                {
                    case 0:
                        firstChar = c;
                        count = 1;
                        break;
                    case 1:
                        sb = new StringBuilder();
                        sb.Append(firstChar).Append(c);
                        count = 2;
                        break;
                    default:
                        sb.Append(c);
                        break;
                }
            }
        }

        switch (count)
        {
            case 0:
                return "";
            case 1:
                return firstChar.ToString();
            default:
                return sb.ToString();
        }
    }

    /// <summary>
    /// Reads next word as <see cref="int"/>.
    /// </summary>
    public int N()
    {
        return int.Parse(Word());
    }

    /// <summary>
    /// Reads next word as <see cref="long"/>.
    /// </summary>
    public long L()
    {
        return long.Parse(Word());
    }

    /// <summary>
    /// Reads next word as <see cref="double"/>.
    /// </summary>
    public double F()
    {
        return double.Parse(Word());
    }

    public int[] Ns(int count)
    {
        return count.MakeArray(_ => N());
    }

    public long[] Ls(int count)
    {
        return count.MakeArray(_ => L());
    }

    public double[] Fs(int count)
    {
        return count.MakeArray(_ => F());
    }

    /// <summary>
    /// Reads next line and splits it by spaces.
    /// </summary>
    public X[] Words<X>(Func<string, X> func)
    {
        return reader.ReadLine().Split(' ').Select(func).ToArray();
    }

    public Scanner(TextReader reader)
    {
        this.reader = reader;
    }
}

public partial class Program
{
    readonly TextReader input;
    readonly TextWriter output;
    readonly Scanner scanner;

    void WriteLine(int value)
    {
        output.WriteLine(value);
    }

    void WriteLine(long value)
    {
        output.WriteLine(value);
    }

    void WriteLine(double value)
    {
        output.WriteLine(value);
    }

    void WriteLine(char value)
    {
        output.WriteLine(value);
    }

    void WriteLine(string value)
    {
        output.WriteLine(value);
    }

    public Program(TextReader input, TextWriter output)
    {
        this.input = input;
        this.output = output;
        scanner = new Scanner(input);
    }

    public static void Main(string[] args)
    {
#if DEBUG
        using (var writer = new VainZero.IO.DebugTextWriter(Console.Out))
#else
        var writer = Console.Out;
#endif
        {
            new Program(Console.In, writer).EntryPoint();
        }
    }
}
#endregion