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)

N = int(input())
prime = [0]*(N+1)
ans = 1
for i in range(2,N+1):
    d = 1
    while i > 1:
        d+=1
        while i % d == 0:
            i = i//d
            prime[d]+= 1
for j in range(N):
    ans = ans *(prime[j]+1)%(10**9+7)
print(ans)