Factorial Fraction Equation

You are given a positive integer $N$. Write a program that counts the ordered pairs of positive integers $(X, Y)$ satisfying the equation below.

$\frac{1}{N!} = \frac{1}{X} + \frac{1}{Y}$

Order matters. When $X \ne Y$, the pairs $(X, Y)$ and $(Y, X)$ count as two different solutions.

The first line contains the integer $N$ ($1 \le N \le 10^4$).

Print the number of solutions on the first line. The count grows very large, so print the exact value without taking any modulus.