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 (7.4.4) (judge verdict: Accepted)

<?php
  list($n) = explode(" ", trim(fgets(STDIN)));

  $mod = 1000000007;

  $array = array_fill(0, $n+1, 1);
  for ($i=1; $i<=$n; $i++) {
    $res = factorize($i);
//    var_dump($res);
    foreach($res as $k => $v){
      $array[$k]+=$v;
    }
  }

  $ans = 1;
  for ($i=1; $i<=$n; $i++) {
    $ans = $ans * $array[$i] % $mod;
  }

  echo $ans;

function factorize($n){
  $res = [];
  for($i=2; $i*$i<=$n; $i++){
    if($n % $i != 0) continue;
    $res[$i]=0;
    while($n % $i == 0){      
      $res[$i]++;
      $n /= $i;
    }
  }
  if($n != 1){
    $res[$n]=1;
  }
  return $res;
}