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: Runtime Error)

n=int(input())
p=[1 for i in range(10000)]
p[0]=0
p[1]=0
for i in range(2,n+1):
  if p[i]==1:
  	for j in range(i*i,n+1,i):
      p[j]=0
ans=1
for i in range(2,n+1):
  if p[i]:
    c=0
    k=i
    while n//k>0:
      c=c+(n//k)%m
      k=k*k
    ans=(ans*((c+1)%m))%m
print(ans)