Problem:
Score : 300 points

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

Solution in Python (3.8.2) (judge verdict: Accepted)

import math
N = int(input())
ans = 1
q = [1 for i in range(N + 1)]
for i in range(2,N + 1):
    k = i
    for i2 in range(2,i + 1):
        while k % i2 == 0:
            k /= i2
            q[i2] += 1
            
for i in range(N + 1):
    ans *= q[i]
    ans %= 10 ** 9 + 7

print(ans)