Problem:
Score : 300 points

Problem Statement

Given is a positive integer N.
How many tuples (A,B,C) of positive integers satisfy A \times B + C = N?

Constraints

2 \leq N \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

3

Sample Output 1

3

There are 3 tuples of integers that satisfy A \times B + C = 3: (A, B, C) = (1, 1, 2), (1, 2, 1), (2, 1, 1).

Sample Input 2

100

Sample Output 2

473

Sample Input 3

1000000

Sample Output 3

13969985

Solution in PHP (7.4.4) (judge verdict: Accepted)

<?php


[$N] = fscanf(STDIN, "%d");

$list = array_fill(1,1000000,0);
for($i=1;$i<=1000;$i++){
    for($j=$i;$j<=1000000;$j++){
        if($i * $j > 1000000){
            break;
        }
        if($i === $j){
            $list[$i * $j]++;
        }else{
            $list[$i * $j]+=2;
        }

    }
}
$ans = 0;
for($i=1;$i<$N;$i++){
    $ans += $list[$i];
}

echo $ans;