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: Wrong Answer)

import functools

mod = 1e9 + 7
n = int(input())
fact = [1] * (n+1)

for i in range(2, n+1):
    for j in range(2, 32):
        if i == 0:
            break
        while True:
            if i % j == 0:
                i /= j
                fact[j] += 1
            else:
                break
    if i != 0:
        fact[int(i)] += 1

print(fact)
print(int(functools.reduce(lambda x, y: (x * y) % mod, fact[2:])))