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 System.Text;
using System.Threading.Tasks;
using static ABC122.Util;

namespace ABC122
{
    class Program
    {
        static void Main(string[] args)
        {
            // 結果：A,B,Cは解けたが、D解けず。Dなんだよこれ（怒）
            // 感想戦後：D簡単やん

            // DoubleHelix(); // 5min
            // AtCoder(); // 11min
            // GeTAC(); // 1h5m
            // WeLikeAGC(); //解けず

            WeLikeAGC();
        }

        readonly static int MOD = 1000000007;
        static void ModAdd(ref long a, long b)
        {
            a += b;
            if (a >= MOD)
                a -= MOD;
        }

        static long Solve(int N)
        {
            long[,,,] dp = new long[N+1,5,5,5];
            dp[0, 0, 0, 0] = 1;

            for(int n = 0; n < N; n++)
                for (int i = 0; i < 5; i++)
                    for (int j = 0; j < 5; j++)
                        for (int k = 0; k < 5; k++)
                            for (int l = 1; l < 5; l++)
                            {
                                if (i == 1 && j == 2 && l == 3) continue;
                                if (i == 1 && k == 2 && l == 3) continue;
                                if (j == 1 && k == 2 && l == 3) continue;
                                if (j == 2 && k == 1 && l == 3) continue;
                                if (j == 1 && k == 3 && l == 2) continue;
                                ModAdd(ref dp[n + 1,j,k,l], dp[n,i,j,k]);
                            }

            long res = 0;
            for (int i = 1; i < 5; i++)
                for (int j = 1; j < 5; j++)
                    for (int k = 1; k < 5; k++)
                        ModAdd(ref res, dp[N, i, j, k]);

            return res;
        }


        static void WeLikeAGC()
        {
            int N = ReadInt();

            long ans = Solve(N);

            Console.WriteLine(ans);
        }

        static void GeTAC()
        {
            var tmp = ReadIntArray();
            var N = tmp[0];
            var Q = tmp[1];

            var S = Console.ReadLine();
            var lr = new int[Q][];

            for(int i = 0; i < Q; i++)
            {
                lr[i] = ReadIntArray();
            }

            // 累積和を作る
            int[] cusum = new int[N];
            for (int i = 1; i < N; i++)
            {
                if (S[i] == 'C' && S[i - 1] == 'A')
                {
                    cusum[i] = cusum[i - 1] + 1;
                }
                else
                {
                    cusum[i] = cusum[i - 1];
                }
            }

            // 答えを出していく
            for (int i = 0; i < Q; i++)
            {
                // 1ベースなので0ベースに変換
                var l = lr[i][0] - 1;
                var r = lr[i][1] - 1;

                int ans = cusum[r] - cusum[l];

                Console.WriteLine(ans);
            }
        }

        static void AtCoder()
        {
            string agct = "AGCT";
            string input = Console.ReadLine();
            int len = input.Length;

            int ans = 0;
            int cur = 0;
            for (int i = 0; i < len; i++)
            {
                if (agct.Contains(input[i]))
                {
                    cur++;
                }
                else
                {
                    ans = Math.Max(ans, cur);
                    cur = 0;
                }
            }

            ans = Math.Max(ans, cur);

            Console.WriteLine(ans);
        }

        static void DoubleHelix()
        {
            string input = Console.ReadLine();

            string ans = string.Empty;
            if (input == "A")
            {
                ans = "T";
            }
            else if (input == "T")
            {
                ans = "A";
            }
            else if (input == "C")
            {
                ans = "G";
            }
            else if (input == "G")
            {
                ans = "C";
            }

            Console.WriteLine(ans);
        }
    }

    public static class Util
    {
        public static void Times(this int times, Action<int> action)
        {
            for(int i = 0; i < times; i++)
            {
                action(i);
            }
        }

        public static T[] ReverseSort<T>(T[] array)
        {
            Array.Sort<T>(array);
            Array.Reverse(array);
            return array;
        }

        public static int[] ReadBinaryString()
        {
            return Console.ReadLine().Select(c => int.Parse(c.ToString())).ToArray();
        }

        public static bool[] ReadBoolArray()
        {
            return Console.ReadLine().Select(c => c == '1').ToArray();
        }

        public static long ReadLong()
        {
            return long.Parse(Console.ReadLine());
        }
        public static long[] ReadLongArray()
        {
            return Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        }

        public static int ReadInt()
        {
            return int.Parse(Console.ReadLine());
        }

        public static int[] ReadIntArray()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }
    }

    /// <summary>
    /// EqualsとGetHashCodeを提供します。IEqualityComparer<T>を実装するクラスです。
    /// HashSetのコンストラクタに渡すために使います。
    /// </summary>
    /// <typeparam name="T"></typeparam>
    public class EqualityComparer<T> : IEqualityComparer<T>
    {
        private Func<T, T, bool> _equals;
        private Func<T, int> _getHashCode;

        public EqualityComparer(Func<T, T, bool> equals, Func<T, int> getHashCode)
        {
            _equals = equals;
            _getHashCode = getHashCode;
        }

        public bool Equals(T x, T y)
        {
            return _equals(x, y);
        }

        public int GetHashCode(T obj)
        {
            return _getHashCode(obj);
        }
    }

    public class PriorityQueue<T> where T : IComparable
    {
        private Comparison<T> _comparison = null;
        private int _type = 0;

        private T[] _heap;
        private int _sz = 0;

        private int _count = 0;

        /// <summary>
        /// Priority queue
        /// </summary>
        /// <param name="maxSize">max size</param>
        /// <param name="type">0: asc, 1:desc</param>
        public PriorityQueue(int maxSize, int type = 0)
        {
            _heap = new T[maxSize];
            _type = type;
        }

        public PriorityQueue(int maxSize, Comparison<T> comparison)
        {
            _heap = new T[maxSize];
            _comparison = comparison;
        }


        private int Compare(T x, T y)
        {
            if (_comparison != null) return _comparison(x, y);
            return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
        }

        public void Push(T x)
        {
            _count++;

            //node number
            var i = _sz++;

            while (i > 0)
            {
                //parent node number
                var p = (i - 1) / 2;

                if (Compare(_heap[p], x) <= 0) break;

                _heap[i] = _heap[p];
                i = p;
            }

            _heap[i] = x;
        }

        public T Pop()
        {
            _count--;

            T ret = _heap[0];
            T x = _heap[--_sz];

            int i = 0;
            while (i * 2 + 1 < _sz)
            {
                //children
                int a = i * 2 + 1;
                int b = i * 2 + 2;

                if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

                if (Compare(_heap[a], x) >= 0) break;

                _heap[i] = _heap[a];
                i = a;
            }

            _heap[i] = x;

            return ret;
        }

        public int Count()
        {
            return _count;
        }

        public T Peek()
        {
            return _heap[0];
        }

        public bool Contains(T x)
        {
            for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
            return false;
        }

        public void Clear()
        {
            while (this.Count() > 0) this.Pop();
        }

        public IEnumerator<T> GetEnumerator()
        {
            var ret = new List<T>();

            while (this.Count() > 0)
            {
                ret.Add(this.Pop());
            }

            foreach (var r in ret)
            {
                this.Push(r);
                yield return r;
            }
        }

        public T[] ToArray()
        {
            T[] array = new T[_sz];
            int i = 0;

            foreach (var r in this)
            {
                array[i++] = r;
            }

            return array;
        }
    }
}