Problem: 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.

Examples

Input

3 5 7 5


Output

1


Input

4 5 7 5


Output

34


Input

37 4 2 3


Output

863912418


Input

40 5 7 5


Output

562805100

Solution (in CPP):

Solution:
#include<cstdio>
const int mod=1000000007;
int N,X,Y,Z,f[41][1<<17|1],g[1<<17|1][11];
int main(){
	scanf("%d%d%d%d",&N,&X,&Y,&Z);
	Y+=X;Z+=Y;
	for(int s=1;s<=1<<Z;s++){
		for(int x=1;x<=10;x++){
			g[s][x]=1;
			for(int i=0;i<Z&&i+x<=Z;i++)if(s>>i&1){
				if(!(i<X&&i+x>X)&&!(i<Y&&i+x>Y))g[s][x]|=1<<i+x;
			}
			if(s==1<<Z||g[s][x]>=1<<Z)g[s][x]=1<<Z;
		}
	}
	f[0][1]=1;
	for(int i=0;i<N;i++)
		for(int j=1<<Z;j;j--)
			for(int x=1;x<=10;x++)(f[i+1][g[j][x]]+=f[i][j])%=mod;
	printf("%d\n",f[N][1<<Z]);
}