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
list($n,$d,$a)=explode(" ",trim(fgets(STDIN)));
$i=0;
while($i<$n){
  list($x,$h)=explode(" ",trim(fgets(STDIN)));
  $key[]=$x;
  $m[$x]=$h;
  ++$i;
}
sort($key);
$ans=0;
$i=0;
$k=0;
while($i<$n){
  $b=(int)ceil($m[$key[$i]]/$a);
  $ans+=(int)$b;
  $j=$i;
  while($j<=$i+$d*2){
    if(isset($m[$j])){
      $m[$j]-=$b;
      if($m[$j]<=0){
        unset($m[$j]);
        unset($key[$i+1]);
        --$n;
        ++$k;
      }
    }
    ++$j;
  }
  $i+=$k+1;
  $k=0;
}
echo $ans;