Problem Statement

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

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.

Constraints

• 1≤N≤10^3

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

见题面 Input 部分

见题面 Output 部分