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 (2.4.0) (judge verdict: Accepted)

# -*- coding: UTF-8 -*-
def prime_t(t):
    i=2
    while i**2<=t:
        if t%i==0:
            return 0
        i+=1
    return 1
p=[]

for i in range(2,1008):
    if prime_t(i):
        p.append(i)
d={i:0 for i in p}
mod=10**9+7
n=int(input())
tmp=1
ans=1
R=[i for i in range(168)]
for i in range(1,n+1):
    tmp*=i
    for j in R:
        while tmp%p[j]==0:
            d[p[j]]+=1
            tmp//=p[j]
        if tmp<p[j]:
            break
for i in d:
    ans*=(d[i]+1)
    ans%=mod
print(ans)