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 (3.4.3) (judge verdict: Runtime Error)

import math

# input
N = int(input())

N_f = math.factorial(N)

ans = 0

for i in range(1, math.ceil(math.sqrt(N_f))):
    if N_f % i == 0:
        ans += 1
        if N_f != i ** 2:
            ans += 1

ans = ans % (10 ** 9 + 7)

print(ans)