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 (GCC 5.4.1) (judge verdict: Accepted)

long ans=1,mod=1e9+7,dp[41][1<<17];
no,i,j,k,nxt,M;
main(n,x,y,z)
{
	scanf("%d%d%d%d",&n,&x,&y,&z);
	no=((1|1<<x)<<y|1)<<z-1;
	dp[0][0]=1;
	M=1<<17;
	for(;i++<n;)
	{
		for(j=0;j<10;j++)
		{
			for(k=0;k<M;k++)
			{
				nxt=(k+k+1<<j)&M-1;
				if(~nxt&no)
				{
					dp[i][nxt]+=dp[i-1][k];
					dp[i][nxt]%=mod;
				}
			}
		}
		ans=ans*10%mod;
	}
	for(;M--;)ans=(ans-dp[n][M]+mod)%mod;
	printf("%d\n",ans);
}