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

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;
using static System.Console;
using static System.Math;
class Z { static void Main() => new K(); }
class K
{
	int F => int.Parse(Str);
	long FL => long.Parse(Str);
	int[] G => Strs.Select(int.Parse).ToArray();
	uint[] GU => Strs.Select(uint.Parse).ToArray();
	decimal[] GD => Strs.Select(decimal.Parse).ToArray();
	long[] GL => Strs.Select(long.Parse).ToArray();
	string Str => ReadLine();
	string[] Strs => Str.Split(new char[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries);
	static T[] ConstantArray<T>(int n, T val) { var a = new T[n]; for (var i = 0; i < n; i++) a[i] = val; return a; }
	static T[] MakeArray<T>(int n, Func<int, T> f) { var a = new T[n]; for (var i = 0; i < n; i++) a[i] = f(i); return a; }
	static ulong One(int k) => 1ul << k;
	static ulong All(int k) => One(k) - 1;
	static bool Has(ulong s, int k) => (s & One(k)) != 0;
	const int MOD = 1000000007;
	public K()
	{
		SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
		Solve();
		Out.Flush();
	}
	void hoge(int[,][] x, int c, int f, int t)
	{
		x[f, c] = new[] { t };
	}
	readonly int[] Empty = new int[0];
	int[] Make(params int[] a) => a;
	void Solve()
	{
		// (AGC を含む) or (どこかを入れ替えると AGC を含む)
		// .* (AGC | ACG | GAC | A.GC | AG.C) .*
		var dict = new Dictionary<char, int> { ['A'] = 0, ['G'] = 1, ['C'] = 2, ['T'] = 3 };
		var nfa = new int[8, 4][];
		for (var i = 0; i < 8; i++) for (var j = 0; j < 4; j++) nfa[i, j] = Empty;
		nfa[0, 0] = Make(0, 2);
		nfa[0, 1] = Make(0, 1);
		nfa[0, 2] = nfa[0, 3] = Make(0);
		nfa[1, 0] = Make(5);
		nfa[2, 1] = Make(3, 4, 5);
		nfa[2, 2] = Make(3, 6);
		nfa[2, 0] = nfa[2, 3] = Make(3);
		nfa[3, 1] = Make(5);
		for (var i = 0; i < 4; i++) nfa[4, i] = Make(5);
		nfa[5, 2] = Make(7);
		nfa[6, 1] = Make(7);
		var M = 1 << 7;
		var dfa = new int[M + 1, 4];
		for (var s = 0; s < M; s++)
			for (var c = 0; c < 4; c++)
			{
				var t = new HashSet<int>();
				for (var i = 0; i < 8; i++) if ((s & (1 << i)) != 0) t.UnionWith(nfa[i, c]);
				if (t.Contains(7)) dfa[s, c] = M;
				else
				{
					var x = 0;
					foreach (var i in t) x |= 1 << i;
					dfa[s, c] = x;
				}
			}
		for (var c = 0; c < 4; c++) dfa[M, c] = M;
		var N = F;
		var dp = new long[N + 1, M + 1];
		dp[0, 1] = 1;
		for (var i = 0; i < N; i++)
			for (var s = 0; s <= M; s++)
				for (var c = 0; c < 4; c++)
				{
					var t = dfa[s, c];
					dp[i + 1, t] = (dp[i + 1, t] + dp[i, s]) % MOD;
				}
		WriteLine((Pow(4, N, MOD) - dp[N, M] + MOD) % MOD);
	}
	public static long Pow(long a, long b, long mod)
	{
		var p = 1L;
		var x = a;
		while (b > 0)
		{
			if ((b & 1) == 1) p = (p * x) % mod;
			b >>= 1;
			x = (x * x) % mod;
		}
		return p;
	}
}