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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
//error_reporting(0);
//$H = trim(fgets(STDIN));
list($N,$D,$A) = explode(" ",trim(fgets(STDIN)));
//$P = explode(" ",trim(fgets(STDIN)));
//$H = array_map('intval',explode(" ",trim(fgets(STDIN))));
//function chmax(&$a,$b) {if ($a<$b){$a=$b;return true;}return false;}
//function chmix(&$a,$b) {if ($a>$b){$a=$b;return true;}return false;}

//https://atcoder.jp/contests/abc153/submissions/9775434
$N=(int)$N;
$D=(int)$D;
$A=(int)$A;
for($i=0;$i<$N;$i++) {
  list($x,$h) = explode(" ",trim(fgets(STDIN)));
  $m[]=array('pos'=>(int)$x,'hp'=>(int)$h);
  $s[]=array('pos'=>(int)$x);
}
array_multisort($m,SORT_ASC,$s);

$ans=0;
$j=1;
for($i=1;$i<=$N;++$i) {
  $imos[$i] += $imos[$i-1];
  $h = $m[$i]['hp'] - $imos[$i];
  if ($h > 0) {
    $t = intdiv(($h-1),$A)+1;
    $ans += $t;
    $t *= $A;
    $j = bs($j,$m[$i]['pos'] + $D);
    $imos[$i] += $t;
    $imos[$j+1]-= $t;
  }
}
printf("%d\n", $ans);


function bs($l,$x) {
  global $N,$m;
  $r = $N+1;

  while($l < $r) {
    $p = $l+$r;
    if ($m[$p]['pos'] <= $x) {
      $l=$p+1;
    }
    else {
      $r = $p;
    }
  }
  return $l-1;
}