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)

def erat(n):
    n+=1
    l=[1 for _ in range(n)]
    l[0],l[1]=0,0
    for i in range(4,n,2):
        l[i]=0
    for i in range(9,n,6):
        l[i]=0
    for i in range(6,n,6):
        if l[i-1]:
            for j in range((i-1)*(i-1),n,i-1):
                l[j]=0
        if l[i+1]:
            for j in range((i+1)*(i+1),n,i+1):
                l[j]=0
    return l
prime=[]
for i in range(1001):
    if erat(1000)[i]:
        prime.append(i)
n=int(input())
u=[0]*1001
for i in range(1,n+1):
    for j in prime:
        while i%j==0:
            i//=j
            u[j]+=1
ans=1
for i in u:
    ans*=i+1
print(ans%(10**9+7))