Number of sextuplets (or six values) that satisfy an equation

Given an array of integers A, find the number of sextuplets that satisfy the equation (a * b + c) / d - e = f.

where a, b, c, d, e, f belong to the given array A.

Note: Since the answer can be very large, return the number of ways modulo (109 + 7).



Input Format

The only argument given is the integer array A.

Output Format

Return the find the number of sextuplets that satisfy the equation.

Constraints

1 <= length of the array <= 100
-10^6 <= A[i] <= 10^6
All elmemts of array A are distinct.

For Example

Input 1:
    A = [1]
Output 1:
    1
    a = b = c = d = e = f = 1 satisfy the equation.

Input 2:
    A = [1, -1]
Output 2:
    24
NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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