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<bits/stdc++.h>
using namespace std;
const int N=(1<<18);
const int mod=1e9+7;
int dp[50][N];
int n,a,b,c;
int main()
{
	//freopen("H:\\c++1\\in.txt","r",stdin);
	//freopen("H:\\c++1\\out.txt","w",stdout);
	scanf("%d",&n);
	scanf("%d",&a);scanf("%d",&b);scanf("%d",&c);
	int bz=(1<<(a-1))|(1<<(a+b-1))|(1<<(a+b+c-1));
	int mx=(1<<(a+b+c));
	dp[0][0]=1;
	int p=1;
	for(int i=1;i<=n;i++){
		p=(1ll*10*p)%mod;
		for(int j=0;j<mx;j++){
			if(dp[i-1][j]==0)continue;
			for(int k=1;k<=10;k++){
				int now=(j<<k)|(1<<(k-1));
				now&=(mx-1);
				if((now&bz)!=bz){
					dp[i][now]=(dp[i][now]+dp[i-1][j])%mod;
				}
			}
		}	
	}
	int ans=p;
	for(int i=0;i<mx;i++){
		ans=(ans-dp[n][i]+mod)%mod;
	}
	printf("%d\n",ans);
	return 0;
}