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C - Filling 3x3 array /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

6 個の整数 h_1, h_2, h_3, w_1, w_2, w_3 が与えられます。

• i=1,2,3 について、上から i 行目に書きこんだ数の和が h_i になる。
• j=1,2,3 について、左から j 列目に書きこんだ数の和が w_j になる。

さて、条件を満たす書きこみ方は全部で何通り存在しますか？

### 制約

• 3 \leq h_1, h_2, h_3, w_1, w_2, w_3 \leq 30
• 入力される値はすべて整数

### 入力

h_1 h_2 h_3 w_1 w_2 w_3


### 入力例 1

3 4 6 3 3 7


### 出力例 1

1


### 入力例 2

3 4 5 6 7 8


### 出力例 2

0


### 入力例 3

5 13 10 6 13 9


### 出力例 3

120


### 入力例 4

20 25 30 22 29 24


### 出力例 4

30613


Score : 300 points

### Problem Statement

You are given six integers: h_1, h_2, h_3, w_1, w_2, and w_3.
Consider writing a positive integer on each square of a 3 \times 3 grid so that all of the following conditions are satisfied:

• For i=1,2,3, the sum of numbers written in the i-th row from the top is h_i.
• For j=1,2,3, the sum of numbers written in the j-th column from the left is w_i.

For example, if (h_1, h_2, h_3) = (5, 13, 10) and (w_1, w_2, w_3) = (6, 13, 9), then all of the following three ways satisfy the conditions. (There are other ways to satisfy the conditions.)

How many ways are there to write numbers to satisfy the conditions?

### Constraints

• 3 \leq h_1, h_2, h_3, w_1, w_2, w_3 \leq 30
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

h_1 h_2 h_3 w_1 w_2 w_3


### Output

Print the number of ways to write numbers to satisfy the conditions.

### Sample Input 1

3 4 6 3 3 7


### Sample Output 1

1


The following is the only way to satisfy the conditions. Thus, 1 should be printed.

### Sample Input 2

3 4 5 6 7 8


### Sample Output 2

0


There may not be a way to satisfy the conditions.

### Sample Input 3

5 13 10 6 13 9


### Sample Output 3

120


### Sample Input 4

20 25 30 22 29 24


### Sample Output 4

30613