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>
#define fr(i,x,y) for(int i=x;i<=y;++i)
#define rf(i,x,y) for(int i=x;i>=y;--i)
#define LL long long 
using namespace std;
const int N=41,MK=(1<<17),mod=1e9+7;
LL dp[N][MK];

LL add(LL x,LL y){
	return (x+y)%mod;
}

LL mul(LL x,LL y){
	return x*y%mod;
}

void Add(LL &x,LL y){
	x=(x+y)%mod;
}

void Mul(LL &x,LL y){
	x=(x*y)%mod;
}

int main(){
	int n,x,y,z;scanf("%d%d%d%d",&n,&x,&y,&z);
	int wr=(1<<(x-1))|(1<<(x+y-1))|(1<<(x+y+z-1));
	dp[0][0]=1;
	int mk=(1<<(x+y+z))-1;
	LL ans=1;
	fr(i,1,n) Mul(ans,10);
	fr(i,1,n) fr(j,0,mk){
		if(!dp[i-1][j]) continue;
		fr(k,1,10){
			int now=(j<<k)|(1<<(k-1));
			now&=mk;
			//printf("%d\n",now);
			if((now&wr)==wr) continue;
			else Add(dp[i][now],dp[i-1][j]);
		}
	}
	//fr(i,0,mk) printf("%lld\n",dp[n][i]);
	fr(i,0,mk) Add(ans,add(mod,-dp[n][i]));
	printf("%lld\n",ans);
	return 0;
}