Solve the programming task below in a Python markdown code block.
Find the number of positive integral solutions for the equations 
$\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{N!}$

Input Format 

An integer N   

Output Format 

The number of positive integral solutions for the above equation modulo 1000007  

Constraints 

$1\leq N\leq10^6$  

Sample Input00  

1  

Sample Output00  

1

Sample Input01

32327

Sample Output01

656502  

Sample Input02

40921

Sample Output02

686720