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: Wrong Answer)

import java.util.* ;
import java.io.* ;
public class Main
{
		static BufferedReader reader;
        static StringTokenizer tokenizer;
        static void init(InputStream input)
        {
            reader = new BufferedReader( new InputStreamReader(input) );
            tokenizer = new StringTokenizer("");
        }
        static String next() throws IOException
        {
            while ( ! tokenizer.hasMoreTokens() )
            {
                tokenizer = new StringTokenizer(reader.readLine() );
            }
            return tokenizer.nextToken();
        }
     
        static long nextInt() throws IOException
        {
            return Long.parseLong( next() );
        }
        public static int ri() throws IOException
        {
        	return (int)nextInt() ;
        }
        public static long rl() throws IOException
        {
        	return nextInt() ;
        }
        public static double rd() throws NumberFormatException, IOException
        {
        	return Double.parseDouble(next()) ;
        }
        static void print_a(int [] arr)
        {
        	for(int i = 0 ;i<arr.length ; i++)
        	{
        		print(arr[i]+" ") ;
        	}
        	println() ;
        }
        public static int [] ria() throws IOException
        {
        	int n = ri() ;
        	int [] a = new int[n] ;
        	for(int i = 0 ; i<n ; i++)
        	{
        		a[i] = ri() ;
        	}
        	return a ;
        }
        public static long [] rla() throws IOException
        {
        	int n = ri() ;
        	long [] a = new long[n] ;
        	for(int i =0 ; i<n ; i++)
        	{
        		a[i] = rl() ;
        	}
        	return a ;
        }
        public static int p(int i)
        {
        	return (int)Math.pow(2,i) ;
        }
        static PrintWriter writer;
        static void outit(OutputStream outputStream)
        {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }
        static void print(Object...objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0)
                    writer.print(' ');
                writer.print(objects[i]);
            }
        }
     
        static void println(Object...objects) {
            print(objects);
            writer.println();
        }
     
        static void close() {
            writer.close();
        }
     
        static void flush() {
            writer.flush();
        }
        public static void main(String [] args) throws IOException
        {
            init(System.in) ;
            outit(System.out) ;
    //    	int t = (int)nextInt() ;
    //    	for(int i =0 ; i<t ; i++)
            output() ;
            flush();
            close();
        }
        static int n ;
        static String s1 ;
        static String s2 ;
        static long [][] cache ;
        static long mod = 1000000007 ;
        public static void output() throws IOException
        {
        	n = ri();
        	s1 = next() ;
        	s2 = next() ;
        	cache = new long[n][2] ;
        	for(int i = 0 ;i<n ; i++)
        	{
        		cache[i][0] =-1 ;
        		cache[i][1] =-1 ;
        	}
        	if(n==1)
        	{
        		println(3) ;
        		return ;
        	}
        	if(check2(0))
        	{
        		println(((long)6*dp(2,1))%mod) ;
        	}
        	else
        	{
        		println(((long)3*dp(1,0))%mod) ;
        	}
        }
        public static long dp(int ind,int state)
        {
        	if(ind==n)
        	{
        		return (long)0 ;
        	}
        	if(ind==n-1)
        	{
        		if(state==0)
        		{
        			return (long)2 ;
        		}
        		else
        		{
        			return (long)1 ;
        		}
        	}
        	if(cache[ind][state]!=-1)
        	{
        		return cache[ind][state] ;
        	}
        	long ret = 1 ;
        	if(check2(ind))
        	{
        		if(state==0)
        		{
        			ret = ((long)2*dp(ind+2,1))%mod ;
        		}
        		else
        		{
        			ret = ((long)3*dp(ind+2,1))%mod ;
        		}
        	}
        	else
        	{
        		if(state==0)
        		{
        			ret =  ((long)2*dp(ind+1,0))%mod ;
        		}
        		else
        		{
        			ret =  dp(ind+1,0) ;
        		}
        	}
        	return ret ;
        }
        static boolean check2(int i)
        {
        	if(s1.charAt(i)==s1.charAt(i+1)&&s2.charAt(i)==s2.charAt(i+1))
        	{
        		return true ;
        	}
        	else
        	{
        		return false ;
        	}
        }
}