Problem:
Score : 700 points

Problem Statement

Haiku is a short form of Japanese poetry. A Haiku consists of three phrases with 5, 7 and 5 syllables, in this order.

Iroha is looking for X,Y,Z-Haiku (defined below) in integer sequences.

Consider all integer sequences of length N whose elements are between 1 and 10, inclusive. Out of those 10^N sequences, how many contain an X,Y,Z-Haiku?

Here, an integer sequence a_0, a_1, ..., a_{N-1} is said to contain an X,Y,Z-Haiku if and only if there exist four indices x, y, z, w (0 ≦ x < y < z < w ≦ N) such that all of the following are satisfied:

a_x + a_{x+1} + ... + a_{y-1} = X

a_y + a_{y+1} + ... + a_{z-1} = Y

a_z + a_{z+1} + ... + a_{w-1} = Z

Since the answer can be extremely large, print the number modulo 10^9+7.

Constraints

3 ≦ N ≦ 40

1 ≦ X ≦ 5

1 ≦ Y ≦ 7

1 ≦ Z ≦ 5

Input

The input is given from Standard Input in the following format:

N X Y Z

Output

Print the number of the sequences that contain an X,Y,Z-Haiku, modulo 10^9+7.

Sample Input 1

3 5 7 5

Sample Output 1

1

Here, the only sequence that contains a 5,7,5-Haiku is [5, 7, 5].

Sample Input 2

4 5 7 5

Sample Output 2

34

Sample Input 3

37 4 2 3

Sample Output 3

863912418

Sample Input 4

40 5 7 5

Sample Output 4

562805100

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

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;
namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dx = { 0, 1, 0, -1 };
        static readonly int[] dy = { 1, 0, -1, 0 };
        static int N, X, Y, Z;
        
        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();
            
            var input = cin.SplitRead();
            N = input[0];
            X = input[1];
            Y = input[2];
            Z = input[3];


            var pow10 = new long[N + 1];
            pow10[0] = 1;
            for (var i = 1; i <= N; i++)
            {
                pow10[i] = (pow10[i - 1] * 10) % MOD;
            }

            long bit = 1 << (X + Y + Z);
            

            var dp = new long[N + 1, bit];
            for(var i = 0; i <= N; i++)
            {
                for(var j = 0; j < bit; j++)
                {
                    dp[i, j] = 0;
                }
            }
            dp[0, 0] = 1;

            for(var i = 0; i < N; i++)
            {
                for(var b = 0; b < bit; b++)
                {
                    for(var j = 1; j <= 10; j++)
                    {
                        long next = Bshift(b, j, bit);
                        if (BitCheck(next)){ continue; }

                        dp[i + 1, next] = (dp[i + 1, next] + dp[i, b]) % MOD;
                    }
                }
            }

            long ans = pow10[N];
            for(var s = 0; s < bit; s++)
            {
                ans = (ans - dp[N, s] + MOD) % MOD;
            }

            Console.WriteLine(ans);

            //Console.Out.Flush();
        }

        static long Bshift(long bit, int shift, long max)
        {
            return ((bit << shift) + (1 << (shift - 1))) % max;
        }
         static bool BitCheck(long bit)
        {
            long XYZ = (1 << (X + Y + Z - 1)) + (1 << (X + Y - 1)) + (1 << (X - 1));
            return (bit ^ XYZ) == (bit - XYZ);
        }
        
    }
    

    public class Scanner
    {
        public int[] SplitRead()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReadL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }
    }

    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }
    }
}