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>
#define maxn 45
#define maxm 131072
#define mod 1000000007
int n,x,y,z,dp[maxn][maxm+5],ans;
int powmod(int a,int n)
{
	int res=1;
	while(n)
	{
		if(n&1) res=1ll*res*a%mod;
		a=1ll*a*a%mod;
		n>>=1;
	}
	return res;
}
int main()
{
	scanf("%d%d%d%d",&n,&x,&y,&z);
	dp[0][0]=1;
	for(int i=0;i<n;i++)
		for(int j=0;j<maxm;j++)
			if(dp[i][j])
				for(int k=1;k<=10;k++)
				{
					int j1=((j<<k)+(1<<(k-1)))%maxm;
					if((j1&(1<<(x+y+z-1)))&&(j1&(1<<(y+z-1)))&&(j1&(1<<(z-1))))
						ans=1ll*(ans+1ll*dp[i][j]*powmod(10,n-i-1))%mod;
					else dp[i+1][j1]=(dp[i+1][j1]+dp[i][j])%mod;
				}
	printf("%d\n",ans);
}