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: Runtime Error)

<?php
$N = trim(fgets(STDIN));
$factorial = 1;
$i = 1;
$ans = 1;
while($i <= $N){
	$factorial = bcmul($factorial, $i);
	$i++;
}
$i = 2;
while($i <= $N){
	if(bcmod($factorial, $i) == 0){
		$factorial = bcdiv($factorial, $i);
		if(isset($div_array[$i])) $div_array[$i] += 1;
		else $div_array[$i] = 1;
	}else{
		$i = bcadd($i, 1);
	}
}
while($pop = array_pop($div_array)) $ans = bcmul($ans, $pop + 1);
echo bcmod($ans, 1000000007);
?>