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 Scala (2.11.7) (judge verdict: Accepted)

object Main extends App {
  val in = new java.util.Scanner(System.in)
  val N, D, A = in.nextInt
  case class Monster(x: Long, hp: Long)
  val Monsters = Array.fill(N)(Monster(in.nextLong, in.nextLong)).sortBy(_.x)

  case class Attack(x: Long, damage: Long)
  val q = new scala.collection.mutable.Queue[Attack]

  def calcDamage(pos: Long, cur: Long): Long = {
    q.headOption match {
      case None => cur
      case Some(attack) => 
        if (attack.x < pos) {
          q.dequeue
          calcDamage(pos, cur - attack.damage)
        } else cur
    }
  }

  def attack(i: Int, sum: Long, preDamage: Long): Long = {
    if (i == N) sum
    else {
      val m = Monsters(i)
      val newDamage = calcDamage(m.x, preDamage)
      if (m.hp <= newDamage) attack(i + 1, sum, newDamage)
      else {
        val attacks = (m.hp - newDamage + A - 1) / A
        q += Attack(m.x + 2 * D, A * attacks)
        attack(i + 1, sum + attacks, newDamage + A * attacks)
      }
    }
  }

  println(attack(0, 0L, 0L))
}