100522: [AtCoder]ABC052 C - Factors of Factorial

Problem Statement

You are given an integer $N$. Find the number of the positive divisors of $N!$, modulo $10^9+7$.

Constraints

• $1≤N≤10^3$

Input

The input is given from Standard Input in the following format:

$N$

Output

Print the number of the positive divisors of $N!$, modulo $10^9+7$.

Sample Input 1

3

Sample Output 1

4

There are four divisors of $3!$ $=6$: $1$, $2$, $3$ and $6$. Thus, the output should be $4$.

Sample Input 2

6

Sample Output 2

30

Sample Input 3

1000

Sample Output 3

972926972