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())

mod = 10**9+7

dic = {}
L = [1]*(N+1)
L[0] = 0
L[1] = 0
for i in range(2, N+1):
    j = 2
    while i*j < N+1:
        L[i*j] = 0
        j += 1
        
for i in range(N+1):
    if L[i] == 1:
        dic[i] = 0

if N > 1:
    for i in range(2, N+1):
        j = 2
        while i > 1:
            if L[j] == 1 and i%j == 0:
                dic[j] += 1
                i //= j
            else:
                j += 1
            
    ans = 1
    for i in dic:
        if dic[i] > 0:
            ans *= (dic[i]+1)
            ans %= mod
else:
    ans = 1
        
print(ans)