Problem:
Score : 600 points

Problem Statement

Silver Fox is fighting with N monsters.

The monsters are standing in a row, and we can assume them to be standing on a number line. The i-th monster, standing at the coordinate X_i, has the health of H_i.

Silver Fox can use bombs to attack the monsters.
Using a bomb at the coordinate x decreases the healths of all monsters between the coordinates x-D and x+D (inclusive) by A.
There is no way other than bombs to decrease the monster's health.

Silver Fox wins when all the monsters' healths become 0 or below.

Find the minimum number of bombs needed to win.

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq D \leq 10^9

1 \leq A \leq 10^9

0 \leq X_i \leq 10^9

1 \leq H_i \leq 10^9

X_i are distinct.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N D A
X_1 H_1
:
X_N H_N

Output

Print the minimum number of bombs needed to win.

Sample Input 1

3 3 2
1 2
5 4
9 2

Sample Output 1

2

First, let us use a bomb at the coordinate 4 to decrease the first and second monsters' health by 2.

Then, use a bomb at the coordinate 6 to decrease the second and third monsters' health by 2.

Now, all the monsters' healths are 0.
We cannot make all the monsters' health drop to 0 or below with just one bomb.

Sample Input 2

9 4 1
1 5
2 4
3 3
4 2
5 1
6 2
7 3
8 4
9 5

Sample Output 2

5

We should use five bombs at the coordinate 5.

Sample Input 3

3 0 1
300000000 1000000000
100000000 1000000000
200000000 1000000000

Sample Output 3

3000000000

Watch out for overflow.

Solution in PHP (7.4.4) (judge verdict: Time Limit Exceeded)

<?php

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

$monsters = [];
$x_list = [];
for ($i = 0; $i < $n; ++$i) {
    fscanf(STDIN, "%d%d", $x, $h);
    $monsters[] = [
        'x' => $x,
        'h' => $h,
        'involved_max_x' => $x + 2 * $d,
        'attack_num_to_defeat' => (int)ceil($h / $a)
    ];
    $x_list[] = $x;
}

array_multisort($monsters, $x_list, SORT_ASC, SORT_NUMERIC);

$total_attack_num = 0;
for ($i = 0; $i < $n; ++$i) {
    $target_monster = $monsters[$i];

    if ($target_monster['attack_num_to_defeat'] > 0) {
        $attack_num = $target_monster['attack_num_to_defeat'];
        $involved_min_x = $target_monster['x'];
        $involved_max_x = $target_monster['involved_max_x'];

        $total_attack_num += $attack_num;
        $monsters = array_map(function ($monster) use ($attack_num, $involved_min_x, $involved_max_x) {
            if ($monster['x']  >= $involved_min_x && $monster['x'] <= $involved_max_x) {
                $monster['attack_num_to_defeat'] -= $attack_num;
            }

            return $monster;
        }, $monsters);
    }
}

echo $total_attack_num;