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: Time Limit Exceeded)

<?php

fscanf(STDIN, "%d", $n);

$answer = 0;
for ($c = 1; $c < $n; ++$c) {
    $prod = $n - $c;

    for ($a = 1; $a * $a < $prod; ++$a) {
        if ($prod % $a === 0) {
            $answer += 2;
        }
    }

    if ($a * $a === $prod) {
        ++$answer;
    }
}

echo $answer;