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: Accepted)

n = int(input())

INF = 10**9 + 7

s = [0] * (n+1)

for i in range(1, n+1):
    ni = i
    p = 2
    while ni > 1:
        while ni % p == 0:
            ni //= p
            s[p] += 1
        p += 1

ans = 1
for i in s:
    ans *= i+1

print(ans % INF)