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 PyPy3 (7.3.0) (judge verdict: Accepted)

import math
from collections import Counter
n=math.factorial(int(input()))
dp=[]
for i in range(2,1001):
  while n%i==0:
    n//=i
    dp.append(i)
c=list(Counter(dp).items())
ans=1
for j in range(len(c)):
  ans*=c[j][1]+1
print(ans%1000000007)