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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author anand.oza
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DColoringDominoes solver = new DColoringDominoes();
        solver.solve(1, in, out);
        out.close();
    }

    static class DColoringDominoes {
        NumberTheory.Mod107 m = new NumberTheory.Mod107();

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            char[] s1 = in.next().toCharArray();
            char[] s2 = in.next().toCharArray();

            ArrayList<Boolean> vertical = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                if (s1[i] == s2[i]) {
                    vertical.add(true);
                } else {
                    vertical.add(false);
                    i++;
                }
            }

            NumberTheory.ModularNumber<NumberTheory.Mod107> answer = m.create(1);
            if (vertical.get(0)) {
                answer = answer.mult(3);
            } else {
                answer = answer.mult(6);
            }
            for (int i = 1; i < vertical.size(); i++) {
                boolean cur = vertical.get(i);
                boolean prev = vertical.get(i - 1);
                int ways = 0;
                if (cur) {
                    if (prev) {
                        ways = 2;
                    } else {
                        ways = 1;
                    }
                } else {
                    if (prev) {
                        ways = 2;
                    } else {
                        ways = 3;
                    }
                }
                answer = answer.mult(ways);
            }

            out.println(answer);
        }

    }

    static class NumberTheory {
        public abstract static class Modulus<M extends NumberTheory.Modulus<M>> {
            ArrayList<NumberTheory.ModularNumber<M>> factorial = new ArrayList<>();

            public abstract long modulus();

            public Modulus() {
                super();
                factorial.add(create(1));
            }

            public NumberTheory.ModularNumber<M> create(long value) {
                return new NumberTheory.ModularNumber(value, this);
            }

        }

        public static class Mod107 extends NumberTheory.Modulus<NumberTheory.Mod107> {
            public long modulus() {
                return 1_000_000_007L;
            }

        }

        public static class ModularNumber<M extends NumberTheory.Modulus<M>> {
            public final long value;
            public final M m;
            public final long MOD;

            public ModularNumber(long value, M m) {
                this.m = m;
                this.MOD = m.modulus();
                this.value = (value % MOD + MOD) % MOD;
            }

            public NumberTheory.ModularNumber<M> mult(long other) {
                return m.create(value * other);
            }

            public String toString() {
                return String.valueOf(value);
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}