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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;


public class Hello
{
    class Mons
    {
        public int Pos { get; set; }
        public int HP {  get ; set; }
    }

    public Hello()
    {
        var inputs = Console.ReadLine().Split();
        int n = int.Parse(inputs[0]);
        int d = int.Parse(inputs[0]) * 2 + 1;
        int a = int.Parse(inputs[0]);
        var mons = Enumerable.Range(0, n)
            .Select(x => Console.ReadLine().Split())
            .Select(x => new Mons() { Pos = int.Parse(x[0]), HP = int.Parse(x[1])})
            .OrderBy(x => x.Pos)
            .ToArray();

        int dmg = 0;
        var que = new Queue<Mons>();
        long ans = 0;
        foreach(var m in mons)
        {
            if(que.Any() && m.Pos > que.Peek().Pos)
            {
                dmg -= que.Dequeue().HP;
            }
            if(m.HP > dmg)
            {
                int t = m.HP - dmg;
                ans += t;
                que.Enqueue(new Mons() { HP = t, Pos = m.Pos + d});
                dmg = m.HP;
            }
        }
        Console.WriteLine(ans);
    }
    static void Main()
    {
        new Hello();
    }
}