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 C (GCC 5.4.1) (judge verdict: Accepted)

M=1e9+7;f[999];n;k;long a=1;main(i,N){for(scanf("%d",&N);n=N;f[n]++,--N)for(k=2;k*k<=n;)n%k?k++:(n/=k,f[k]++);for(;++i<998;)a=a*-~f[i]%M;printf("%d",a);}