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())
S = math.factorial(N)
T = [i for i in range(2, N+1)]
s = 1
while len(T)>0:
  c = 1
  while S%T[0]==0:
    S //= T[0]
    c += 1
  s *= c
  s %= 10**9+7
  T = [t for t in T if t%T[0]]
print(s)