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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.UncheckedIOException;
import java.util.StringTokenizer;

public class Main {
	public static void main(String[] args) {
		SC sc = new SC(System.in);
		int N=sc.nextInt();
		String stat="";
		long MOD=1000000007L;
		StringBuilder sb=new StringBuilder();
		long[][] dp=new long[N][9];
		for(int i=0; i<N; i++) {
			for(int j=0; j<9; j++) {
				dp[i][j]=0;
			}
		}
		int mannaka=0;
		/*
		 * dp0  RR
		 * dp1  RG
		 * dp2  RB
		 * dp3  GG
		 * dp4  GR
		 * dp5  GB
		 * dp6  BB
		 * dp7  BR
		 * dp8  BG
		 */
		String ue=sc.next();
		String st=sc.next();
		for(int i=0; i<N; i++) {
			if(ue.charAt(i)==st.charAt(i)) {
				sb.append(1);
			}
			else {
				sb.append(2);
			}
		}
		stat=sb.toString();
		StringBuilder sbt=new StringBuilder(stat);
		String gyak=(sbt.reverse()).toString();

		if(N==1) {
			pl(3);
			System.exit(0);
		}
		else if(N==2) {
			pl(3);
			System.exit(0);
		}

		if(stat.equals(gyak)) {//パリンドロームのとき、ダブリを引かないといけない
			mannaka=0;
			//中心を決定する
			int tmp=0;
			int moji=stat.length();
			while(true) {
				if(stat.charAt(tmp)=='1') {
					if(tmp+1>(moji-1)/2) {
						//もしもこれを足して中心に到達するなら
						mannaka=tmp;
						break;
					}
					else {
						tmp++;
					}
				}
				else if(stat.charAt(tmp)=='2') {
					if(tmp+2>moji/2) {
						//もしもこれを足して中心に到達するなら
						mannaka=tmp;
						break;
					}
					else {
						tmp+=2;
					}
				}
			}
			int counter=0;
			if(stat.charAt(0)=='1') {
				dp[0][0]=1;
				dp[0][3]=1;
				dp[0][6]=1;
				counter++;
			}
			else if(stat.charAt(0)=='2'){
				dp[0][1]=1; dp[1][1]=dp[0][1];
				dp[0][2]=1; dp[1][2]=dp[0][2];
				dp[0][4]=1; dp[1][4]=dp[0][4];
				dp[0][5]=1; dp[1][5]=dp[0][5];
				dp[0][7]=1; dp[1][7]=dp[0][7];
				dp[0][8]=1; dp[1][8]=dp[0][8];
				counter+=2;
			}
			while(counter<N) {
				if(stat.charAt(counter)=='1') {
					if(stat.charAt(counter-1)=='1') {
						dp[counter][0]+=dp[counter-1][3]+dp[counter-1][6];
						dp[counter][3]+=dp[counter-1][0]+dp[counter-1][6];
						dp[counter][6]+=dp[counter-1][0]+dp[counter-1][3];
						for(int j=0; j<9; j++) {
							dp[counter][j]%=MOD;
						}
						counter++;
					}
					else if(stat.charAt(counter-1)=='2') {
						dp[counter][0]+=dp[counter-1][3]+dp[counter-1][5]+dp[counter-1][6]+dp[counter-1][8];
						dp[counter][3]+=dp[counter-1][0]+dp[counter-1][2]+dp[counter-1][6]+dp[counter-1][7];
						dp[counter][6]+=dp[counter-1][0]+dp[counter-1][1]+dp[counter-1][3]+dp[counter-1][4];
						for(int j=0; j<9; j++) {
							dp[counter][j]%=MOD;
						}
						counter++;
					}
				}
				else if(stat.charAt(counter)=='2') {
					if(stat.charAt(counter-1)=='1') {
						dp[counter][1]+=dp[counter-1][6];
						dp[counter][2]+=dp[counter-1][3];
						dp[counter][4]+=dp[counter-1][6];
						dp[counter][5]+=dp[counter-1][0];
						dp[counter][7]+=dp[counter-1][3];
						dp[counter][8]+=dp[counter-1][0];
						for(int j=0; j<9; j++) {
							dp[counter][j]%=MOD;
						}
						for(int j=0; j<9; j++) {
							dp[counter+1][j]=dp[counter][j];
						}
						counter+=2;
					}
					else if(stat.charAt(counter-1)=='2') {
						dp[counter][1]+=dp[counter-1][7]+dp[counter-1][4]+dp[counter-1][5];
						dp[counter][2]+=dp[counter-1][4]+dp[counter-1][7]+dp[counter-1][8];
						dp[counter][4]+=dp[counter-1][8]+dp[counter-1][1]+dp[counter-1][2];
						dp[counter][5]+=dp[counter-1][1]+dp[counter-1][8]+dp[counter-1][7];
						dp[counter][7]+=dp[counter-1][5]+dp[counter-1][2]+dp[counter-1][1];
						dp[counter][8]+=dp[counter-1][2]+dp[counter-1][5]+dp[counter-1][4];
						for(int j=0; j<9; j++) {
							dp[counter][j]%=MOD;
						}
						for(int j=0; j<9; j++) {
							dp[counter+1][j]=dp[counter][j];
						}
						counter+=2;
					}
				}
			}
			long ans=0;
			for(int i=0; i<9; i++) {
				ans+=dp[N-1][i];
			}
			for(int i=0; i<9; i++) {
				ans-=dp[mannaka][i];
			}
			while(ans<0) {
				ans+=MOD;
			}
			pl(ans);
			System.exit(0);
		}
		else {
			int counter=0;
			if(stat.charAt(0)=='1') {
				dp[0][0]=1;
				dp[0][3]=1;
				dp[0][6]=1;
				counter++;
			}
			else if(stat.charAt(0)=='2'){
				dp[0][1]=1; dp[1][1]=dp[0][1];
				dp[0][2]=1; dp[1][2]=dp[0][2];
				dp[0][4]=1; dp[1][4]=dp[0][4];
				dp[0][5]=1; dp[1][5]=dp[0][5];
				dp[0][7]=1; dp[1][7]=dp[0][7];
				dp[0][8]=1; dp[1][8]=dp[0][8];
				counter+=2;
			}
			while(counter<N) {
				if(stat.charAt(counter)=='1') {
					if(stat.charAt(counter-1)=='1') {
						dp[counter][0]+=dp[counter-1][3]+dp[counter-1][6];
						dp[counter][3]+=dp[counter-1][0]+dp[counter-1][6];
						dp[counter][6]+=dp[counter-1][0]+dp[counter-1][3];
						for(int j=0; j<9; j++) {
							dp[counter][j]%=MOD;
						}
						counter++;
					}
					else if(stat.charAt(counter-1)=='2') {
						dp[counter][0]+=dp[counter-1][3]+dp[counter-1][5]+dp[counter-1][6]+dp[counter-1][8];
						dp[counter][3]+=dp[counter-1][0]+dp[counter-1][2]+dp[counter-1][6]+dp[counter-1][7];
						dp[counter][6]+=dp[counter-1][0]+dp[counter-1][1]+dp[counter-1][3]+dp[counter-1][4];
						for(int j=0; j<9; j++) {
							dp[counter][j]%=MOD;
						}
						counter++;
					}
				}
				else if(stat.charAt(counter)=='2') {
					if(stat.charAt(counter-1)=='1') {
						dp[counter][1]+=dp[counter-1][6];
						dp[counter][2]+=dp[counter-1][3];
						dp[counter][4]+=dp[counter-1][6];
						dp[counter][5]+=dp[counter-1][0];
						dp[counter][7]+=dp[counter-1][3];
						dp[counter][8]+=dp[counter-1][0];
						for(int j=0; j<9; j++) {
							dp[counter][j]%=MOD;
						}
						for(int j=0; j<9; j++) {
							dp[counter+1][j]=dp[counter][j];
						}
						counter+=2;
					}
					else if(stat.charAt(counter-1)=='2') {
						dp[counter][1]+=dp[counter-1][7]+dp[counter-1][4]+dp[counter-1][5];
						dp[counter][2]+=dp[counter-1][4]+dp[counter-1][7]+dp[counter-1][8];
						dp[counter][4]+=dp[counter-1][8]+dp[counter-1][1]+dp[counter-1][2];
						dp[counter][5]+=dp[counter-1][1]+dp[counter-1][8]+dp[counter-1][7];
						dp[counter][7]+=dp[counter-1][5]+dp[counter-1][2]+dp[counter-1][1];
						dp[counter][8]+=dp[counter-1][2]+dp[counter-1][5]+dp[counter-1][4];
						for(int j=0; j<9; j++) {
							dp[counter][j]%=MOD;
						}
						for(int j=0; j<9; j++) {
							dp[counter+1][j]=dp[counter][j];
						}
						counter+=2;
					}
				}
			}
		}
		long ans=0;
		for(int i=0; i<9; i++) {
			ans+=dp[N-1][i];
		}
		pl(ans%MOD);
	}
	static class SC {
		private BufferedReader reader = null;
		private StringTokenizer tokenizer = null;
		public SC(InputStream in) {
			reader = new BufferedReader(new InputStreamReader(in));
		}
		public String next() {
			if (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new UncheckedIOException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new UncheckedIOException(e);
			}
		}
	}
	public static void pl(Object o) {
		System.out.println(o);
	}
	public static void pl() {
		System.out.println();
	}
	public static void p(Object o) {
		System.out.print(o);
	}
}