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 Perl (v5.18.2) (judge verdict: Accepted)

1x$_~~/^(11+)\1+$/||push@p,$_ for 2..1e3;
for$i(1..<>){
	for$p(@p){
		++$_[$p],$i/=$p while$i%$p==0
	}
}
$x=1;
$x*=$_+1,$x%=1e9+7for@_;
print$x,$/