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 = [2]
Res = 1

for i in range(3, N+1, 2):
    flag = True
    for j in prime:
        if i % j == 0:
            flag = False
            break
    if flag:
        prime.append(i)

div = [0]*len(prime)

for i in range(2, N+1):
    for j in range(len(prime)):
        while i % prime[j] == 0:
            div[j] += 1
            i = i//prime[j]

for i in div:
    Res *= i+1

print(Res)