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())
l=[0]*n

for i in range(1,n+1):
    b=2
    while b <= i:
        while i%b==0:
            i = i//b
            l[b-1]+=1
        b+=1
x=1
for i in l:
    if i != 0:
        x=x*(i+1)%(10**9+7)
print(x)