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)

NUM = 10**9 + 7
def solve():
    N = int(input())
    dict = {}
    for n in range(2, N + 1):
        for i in range(2, n + 1):
            while n % i == 0:
                n //= i
                if not i in dict.keys():
                    dict[i] = 1
                else:
                    dict[i] += 1
    res = 1
    for i in dict.values():
        res *= (i + 1)
        res %= NUM
    return res

if __name__ == '__main__':
    print(solve())