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: Wrong Answer)

from math import factorial
from collections import Counter

def prime_factorize(n):
    a = []
    while n%2 == 0:
        a.append(2)
        n //=2
    f = 3
    while f*f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

def prime_factoring(n):
    from collections import Counter
    a = prime_factorize(n)
    return Counter(a)

def make_divisors(n):
    divisors = []
    for i in range(1, int(n**.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n //i:
                divisors.append(n//i)
    divisors.sort()
    return divisors

n = int(input())
mod = 10**9+7
N =factorial(n)
import numpy as np
List = np.array(list(prime_factoring(N).values()))+1
List = List%mod
print(np.prod(List)%mod)