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 maxn 51
#define mod (int)(1e9+7)
using namespace std;

#define mask (1<<17)-1

int f[maxn][mask];
inline int Append(int st,int x){
	st = ((st << x) | (1 << (x-1))) & mask;
	return st;
}

int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	
	int n,x,y,z;
	cin>>n>>x>>y>>z;
	
	int stc = 0;
	stc = Append(stc,x);
	stc = Append(stc,y);
	stc = Append(stc,z);
	
	f[0][0] = 1;
	for (int i=1;i<=n;i++)
		for (int j=0;j<=mask;j++)
			for (int k=1;k<=10;k++){
				int ns = Append(j,k);
				if ((stc & ns) != stc){
					f[i][ns] = (f[i-1][j] + f[i][ns]) % mod;
				}
			}
			
	int ans = 1;
	for (int i=1;i<=n;i++) ans = 10LL * ans % mod;
	
	for (int i=1;i<=mask;i++) ans = (ans - f[n][i]) % mod;
	
	cout<<(ans+mod)%mod<<endl;
	return 0;
}