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?

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分