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: Wrong Answer)

using System.Linq;
using System;
using static System.Console;
class E { static void Main() => new K(); }
class K
{
	const int MOD = 1000000007;
	public K()
	{
		var I = ReadLine().Split().Select(int.Parse).ToArray();
		int N = I[0], X = I[1], Y = I[2], Z = I[3];
		var M = 1 << (X + Y + Z);
		var m = M - 1;
		var n = (1 << (Z - 1)) | (1 << (Y + Z - 1)) | (1 << (X + Y + Z - 1));
		var d = new long[N + 1, M];
		d[0, 0] = 1;
		for (var i = 0; i < N; i++) for (var s = 0; s < M; s++) if (d[i, s] != 0) for (var a = 1; a <= 10; a++)
		{
			var t = ((s << a) | (1 << (a - 1))) & m;
			if ((t & n) != n) d[i + 1, t] = (d[i + 1, t] + d[i, s]) % MOD;
		}
		var p = 1L;
		for (var i = 0; i < N; i++) p = p * 10 % MOD;
		for (var s = 0; s < M; s++) p += MOD - d[N, s];
		WriteLine(p);
	}
}