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())


def solve(n, p):
    ans = 0
    cnt = 1
    tmp = 1
    while tmp >= 1:
        tmp = n // p**cnt
        ans += tmp
        cnt += 1
    return ans


primes = set(range(2, n+1))

for i in range(2, int(n**0.5+1)):
    primes.difference_update(range(i*2, n+1, i))

primes = list(primes)


li = [solve(n, x) + 1 for x in primes]
mod = 10**9 + 7

ans = 1
for x in li:
    ans *= x
    ans %= mod

print(ans)