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

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