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.Generic;
using System.Linq;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;

namespace AtCoderProject
{
    class AGCT
    {
        public BigInteger sum;
        public BigInteger ag;
        public BigInteger ac;
        public BigInteger ga;

        public BigInteger three;
    }
    public class Program
    {
        public object Calc()
        {
            const int mod = 1000000007;

            var N = consoleReader.Int32();
            var result = new AGCT[N + 1];
            result[0] = new AGCT { sum = 1 };
            result[1] = new AGCT { sum = 4 };
            result[2] = new AGCT { sum = 16, ag = 1, ac = 1, ga = 1 };
            result[3] = new AGCT { sum = 61, ag = 4, ac = 3, ga = 4, three = 3 };

            for (int i = 4; i <= N; i++)
            {
                var next = new AGCT();

                next.sum = 4 * result[i - 1].sum - result[i - 1].ag - result[i - 1].ac - result[i - 1].ga - result[i - 1].three;

                next.ag = result[i - 2].sum ;
                next.ac = 3 * result[i - 3].sum - result[i - 3].ag - result[i - 3].ga - result[i - 3].three;
                next.ga = result[i - 2].sum - result[i - 2].ac;
                next.three = 3 * result[i - 3].sum;

                result[i] = next;
            }


            return result[N].sum % mod;
        }

        private readonly ConsoleReader consoleReader;
        public Program() : this(new ConsoleReader()) { }
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program().Calc());
    }

    public class ConsoleReader
    {
        public virtual string String() => Console.ReadLine();
        public int Int32() => int.Parse(String());
        public long Int64() => long.Parse(String());
        public ulong UInt64() => ulong.Parse(String());
        public double Double() => double.Parse(String());
        public string[] Split() => String().Split().ToArray();
        public int[] SplitInt32() => String().Split().Select(s => int.Parse(s)).ToArray();
        public long[] SplitInt64() => String().Split().Select(s => long.Parse(s)).ToArray();
        public ulong[] SplitUInt64() => String().Split().Select(s => ulong.Parse(s)).ToArray();
        public double[] SplitDouble() => String().Split().Select(s => double.Parse(s)).ToArray();

        public IEnumerable<string> Repeat(int count)
        {
            for (int i = 0; i < count; i++)
                yield return String();
        }
        public IEnumerable<int> RepeatInt32(int count)
        {
            for (int i = 0; i < count; i++)
                yield return Int32();
        }
        public IEnumerable<long> RepeatInt64(int count)
        {
            for (int i = 0; i < count; i++)
                yield return Int64();
        }
        public IEnumerable<string[]> RepeatSplit(int count)
        {
            for (int i = 0; i < count; i++)
                yield return Split();
        }
        public IEnumerable<int[]> RepeatSplitInt32(int count)
        {
            for (int i = 0; i < count; i++)
                yield return SplitInt32();
        }
    }
    static class DicExt
    {
        public static V GetOrDefault<K, V>(this Dictionary<K, V> dic, K key, V defaultValue = default(V))
        {
            V val;
            return dic.TryGetValue(key, out val) ? val : defaultValue;
        }
    }
}