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.Linq;
using System.Collections.Generic;
using System.Text;

namespace Program
{
    public class ABC122D
    {
        static public void Main(string[] args)
        {
            var N = NextInt;
            var dp = new long[N + 1][][][];
            for (int i = 0; i <= N; ++i)
            {
                dp[i] = new long[4][][];
                for (int j = 0; j < 4; ++j)
                {
                    dp[i][j] = new long[4][];
                    for (int k = 0; k < 4; ++k)
                    {
                        dp[i][j][k] = new long[4];
                    }
                }
            }
            dp[0][3][3][3] = 1;
            for (int i = 0; i < N; ++i)
            {
                for (int i3 = 0; i3 < 4; ++i3)
                {
                    for (int i2 = 0; i2 < 4; ++i2)
                    {
                        for (int i1 = 0; i1 < 4; ++i1)
                        {
                            for (int a = 0; a < 4; ++a)
                            {
                                if (i2 == 0 && i1 == 2 && a == 1) continue;
                                if (i2 == 2 && i1 == 0 && a == 1) continue;
                                if (i2 == 0 && i1 == 1 && a == 2) continue;
                                if (i3 == 0 && i2 == 2 && a == 1) continue;
                                if (i3 == 0 && i1 == 2 && a == 1) continue;

                                dp[i + 1][i2][i1][a] = Mod.Add(dp[i + 1][i2][i1][a], dp[i][i3][i2][i1]);
                            }
                        }
                    }
                }
            }

            var ans = 0L;
            for (int i3 = 0; i3 < 4; ++i3)
            {
                for (int i2 = 0; i2 < 4; ++i2)
                {
                    for (int i1 = 0; i1 < 4; ++i1)
                    {
                        ans = Mod.Add(ans, dp[N][i3][i2][i1]);
                    }
                }
            }

            Console.WriteLine(ans);
        }

        static class Console_
        {
            private static Queue<string> param = new Queue<string>();
            public static string NextString()
            {
                if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item);
                return param.Dequeue();
            }
        }
        static int NextInt => int.Parse(Console_.NextString());
        static List<int> NextIntList(int N)
        {
            var ret = new List<int>(N);
            for (int i = 0; i < N; ++i) ret.Add(NextInt);
            return ret;
        }
        static long NextLong => long.Parse(Console_.NextString());
        static List<long> NextLongList(int N)
        {
            var ret = new List<long>(N);
            for (int i = 0; i < N; ++i) ret.Add(NextLong);
            return ret;
        }
        static string NextString => Console_.NextString();
        static void Sort<T>(List<T> l) where T : IComparable => l.Sort();
        static void RevSort<T>(List<T> l) where T : IComparable => l.Sort((x, y) => y.CompareTo(x));
        static IEnumerable<long> Prime(long x)
        {
            if (x < 2) yield break;
            yield return 2;
            var halfx = x / 2;
            var table = new bool[halfx + 1];
            var max = (long)(Math.Sqrt(x) / 2);
            for (long i = 1; i <= max; ++i)
            {
                if (table[i]) continue;
                var add = 2 * i + 1;
                yield return add;
                for (long j = 2 * i * (i + 1); j <= halfx; j += add) table[j] = true;
            }
            for (long i = max + 1; i <= halfx; ++i) if (!table[i]) yield return 2 * i + 1;
        }
        static IEnumerable<long> Divisor(long x)
        {
            if (x < 1) yield break;
            var max = (long)Math.Sqrt(x);
            for (long i = 1; i < max; ++i)
            {
                if (x % i != 0) continue;
                yield return i;
                if (i != x / i) yield return x / i;
            }
        }
        static long GCD(long a, long b)
        {
            long tmpa = a, tmpb = b;
            while (tmpb > 0) { var tmp = tmpb; tmpb = tmpa % tmpb; tmpa = tmp; }
            return tmpa;
        }
        class PQ<T> where T : IComparable
        {
            private List<T> h;
            private Comparison<T> c;
            public PQ(int cap, Comparison<T> c, bool asc = true) { h = new List<T>(cap); this.c = asc ? c : (x, y) => c(y, x); }
            public PQ(Comparison<T> c, bool asc = true) { h = new List<T>(); this.c = asc ? c : (x, y) => c(y, x); }
            public PQ(int cap, bool asc = true) : this(cap, (x, y) => x.CompareTo(y), asc) { }
            public PQ(bool asc = true) : this((x, y) => x.CompareTo(y), asc) { }
            public void Push(T v)
            {
                var i = h.Count;
                h.Add(v);
                while (i > 0)
                {
                    var ni = (i - 1) / 2;
                    if (c(v, h[ni]) >= 0) break;
                    h[i] = h[ni]; i = ni;
                }
                h[i] = v;
            }
            public T Peek => h[0];
            public int Count => h.Count;
            public T Pop
            {
                get
                {
                    var r = h[0];
                    var v = h[h.Count - 1];
                    h.RemoveAt(h.Count - 1);
                    if (h.Count == 0) return r;
                    var i = 0;
                    while (i * 2 + 1 < h.Count)
                    {
                        var i1 = i * 2 + 1;
                        var i2 = i * 2 + 2;
                        if (i2 < h.Count && c(h[i1], h[i2]) > 0) i1 = i2;
                        if (c(v, h[i1]) <= 0) break;
                        h[i] = h[i1]; i = i1;
                    }
                    h[i] = v;
                    return r;
                }
                private set { }
            }
        }
        class PQ<TKey, TValue> where TKey : IComparable
        {
            private PQ<Tuple<TKey, TValue>> q;
            public PQ(int cap, Comparison<TKey> c, bool asc = true) { q = new PQ<Tuple<TKey, TValue>>(cap, (x, y) => c(x.Item1, y.Item1), asc); }
            public PQ(Comparison<TKey> c, bool asc = true) { q = new PQ<Tuple<TKey, TValue>>((x, y) => c(x.Item1, y.Item1), asc); }
            public PQ(int cap, bool asc = true) : this(cap, (x, y) => x.CompareTo(y), asc) { }
            public PQ(bool asc = true) : this((x, y) => x.CompareTo(y), asc) { }
            public void Push(TKey k, TValue v) => q.Push(Tuple.Create(k, v));
            public Tuple<TKey, TValue> Peek => q.Peek;
            public int Count => q.Count;
            public Tuple<TKey, TValue> Pop => q.Pop;
        }
        static class Mod
        {
            static public long _mod = 1000000007;
            static public long Add(long x, long y) => (x + y) % _mod;
            static public long Sub(long x, long y) => (x - y) % _mod;
            static public long Multi(long x, long y) => (x * y) % _mod;
            static public long Div(long x, long y) => (x * Inverse(y)) % _mod;
            static public long Pow(long x, long y)
            {
                var a = 1L;
                while (y != 0)
                {
                    if ((y & 1) == 1) a = Mod.Multi(a, x);
                    x = Mod.Multi(x, x);
                    y >>= 1;
                }
                return a;
            }
            static public long Inverse(long x)
            {
                var b = _mod;
                var r = 1L;
                var u = 0L;
                while (b > 0L)
                {
                    var q = x / b;
                    var t = u; u = r - q * u; r = t;
                    t = b; b = x - q * b; x = t;
                }
                return r < 0 ? r + _mod : r;
            }
            static private List<long> _fact = new List<long>();
            static private List<long> _ifact = new List<long>();
            static private void Build(int n)
            {
                if (n >= _fact.Count)
                    for (int i = _fact.Count; i <= n; ++i)
                        if (i == 0L) { _fact.Add(1); _ifact.Add(1); }
                        else { _fact.Add(Mod.Multi(_fact[i - 1], i)); _ifact.Add(Mod.Multi(_ifact[i - 1], Mod.Pow(i, _mod - 2))); }
            }
            static public long Comb(int n, int k)
            {
                Build(n);
                if (n == 0 && k == 0) return 1;
                if (n < k || n < 0) return 0;
                return Mod.Multi(Mod.Multi(_ifact[n - k], _ifact[k]), _fact[n]);
            }
        }
    }
}