Contest Duration: - (local time) (100 minutes) Back to Home
E - Iroha and Haiku /

Time Limit: 4 sec / Memory Limit: 512 MB

### 問題文

ただし、XYZを含むとは以下のように定義されます。

• 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

を満たす 0 ≦ x < y < z < w ≦ N が存在する。

なお、答えは非常に大きくなることがあるので、答えは 10^9+7 で割ったあまりを出力してください。

• 3 ≦ N ≦ 40
• 1 ≦ X ≦ 5
• 1 ≦ Y ≦ 7
• 1 ≦ Z ≦ 5

### 入力

N X Y Z


### 出力

XYZを含む数列の個数を 10^9+7 で割ったあまりを出力せよ。

### 入力例 1

3 5 7 5


### 出力例 1

1


\{5,7,5\} という数列のみが条件を満たします。

### 入力例 2

4 5 7 5


### 出力例 2

34


### 入力例 3

37 4 2 3


### 出力例 3

863912418


### 入力例 4

40 5 7 5


### 出力例 4

562805100


Score : 700 points

### Problem Statement

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.

• 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.

### Sample Input 1

3 5 7 5


### Sample Output 1

1


Here, the only sequence that contains a 5,7,5-Haiku is [5, 7, 5].

### Sample Input 2

4 5 7 5


### Sample Output 2

34


### Sample Input 3

37 4 2 3


### Sample Output 3

863912418


### Sample Input 4

40 5 7 5


### Sample Output 4

562805100