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: Accepted)

<?php
// Here your code !
    $n = fgets(STDIN);
    $prime = array();
    $prime[0] = 2;
    for($i=3;$i<=1000;$i+=2){
        $flag = 1;
        foreach ($prime as $value) {
            if($i % $value == 0){;
                $flag = 0;
            }
        }
        if($flag == 1){
            array_push($prime,$i);
        }
    }
    
    $check = array();
    $temp = 0;
    for($i = 1; $i<=$n; $i++){
        foreach ($prime as $value) {
            $temp = $i;
            while($temp % $value == 0){
                $check[$value]++;
                $temp = $temp / $value;
            }
        }
    }
    
//    var_dump($check);
    
    $answer = 1;
    foreach ($check as $value) {
        $answer = $answer * ($value + 1);
        $answer = $answer % 1000000007;
        if($answer<0){
        $answer += 1000000007;
    }
    }
    
//    while($answer > 1000000007){
//        $answer -= 1000000007;
//    }

    echo $answer;
?>