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 PHP (5.6.30) (judge verdict: Time Limit Exceeded)

<?php
    $input1 = fgets(STDIN);
    $sum = 1;
    $count = 0;
 
    for($i=0;$i<$input1;$input1--) {
        $sum = $sum * $input1;
    }
 
    for($j=1;$j<=$sum;$j++) {
        if($sum % $j == 0) {
            $count++;
        }
    }
    echo $count % 100000007;
?>