Problem:
Score : 400 points

Problem Statement

You are given an integer N. Find the number of strings of length N that satisfy the following conditions, modulo 10^9+7:

The string does not contain characters other than A, C, G and T.

The string does not contain AGC as a substring.

The condition above cannot be violated by swapping two adjacent characters once.

Notes

A substring of a string T is a string obtained by removing zero or more characters from the beginning and the end of T.

For example, the substrings of ATCODER include TCO, AT, CODER, ATCODER and (the empty string), but not AC.

Constraints

3 \leq N \leq 100

Input

Input is given from Standard Input in the following format:

N

Output

Print the number of strings of length N that satisfy the following conditions, modulo 10^9+7.

Sample Input 1

3

Sample Output 1

61

There are 4^3 = 64 strings of length 3 that do not contain characters other than A, C, G and T. Among them, only AGC, ACG and GAC violate the condition, so the answer is 64 - 3 = 61.

Sample Input 2

4

Sample Output 2

230

Sample Input 3

100

Sample Output 3

388130742

Be sure to print the number of strings modulo 10^9+7.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main{

	static int [][][][]memo;
	static int MOD=(int)1e9+7,n;
	
	static boolean ok(int x1,int x2,int x3,int x4) {
		if(x1==0 && x2==1 && x3==2)
			return false;
		if(x2==0 && x3==1 && x4==2)
			return false;
		return true;
	}
	static int dp(int idx,int x1,int x2,int x3) {
		if(idx==n)
			return 1;
		if(memo[x1][x2][x3][idx]!=0)
			return memo[x1][x2][x3][idx];
		int ans=0;
		for(int nxt=0;nxt<=3;nxt++) {
			if(!ok(x1,x2,x3,nxt))
				continue;
			if(!ok(x1,x2,nxt,x3))
				continue;
			if(!ok(x1,x3,x2,nxt))
				continue;
			if(!ok(x2,x1,x3,nxt))
				continue;
			ans+=dp(idx+1, x2, x3, nxt);
			ans%=MOD;
		}
		return memo[x1][x2][x3][idx]=ans;
	}
	
	public static void main(String[] args) throws IOException {
		Scanner sc=new Scanner();
		PrintWriter out=new PrintWriter(System.out);
		n=sc.nextInt();
		memo=new int [5][5][5][n];
		out.println(dp(0, 4, 4,4));
		out.close();

	}
	static class Scanner
	{
		BufferedReader br;
		StringTokenizer st;
		Scanner(){
			br=new BufferedReader(new InputStreamReader(System.in));
		}
		Scanner(String fileName) throws FileNotFoundException{
			br=new BufferedReader(new FileReader(fileName));
		}
		String next() throws IOException {
			while(st==null || !st.hasMoreTokens())
				st=new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		String nextLine() throws IOException {
			return br.readLine();
		}
		int nextInt() throws IOException{
			return Integer.parseInt(next());
		}
		long nextLong()  throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}
		double nextDouble() throws NumberFormatException, IOException {
			return Double.parseDouble(next());
		}
	}
}