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: Time Limit Exceeded)

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

class Program
{
    static void Main()
    {
        string[] arr = Console.ReadLine().Split(' ');
        long N = long.Parse(arr[0]);
        long D = long.Parse(arr[1]);
        long A = long.Parse(arr[2]);
        List<Enemy> enemies = new List<Enemy>();

        for(int i = 0;i < N; i++)
        {
            string[] a = Console.ReadLine().Split(' ');
            enemies.Add(new Enemy(a[0], a[1]));
        }

        enemies = enemies.OrderBy(a => a.posistion).ToList();
        long cnt = 0;

        while(0 < enemies.Count)
        {
            long bombPosition = enemies[enemies.Count - 1].posistion - D * 2;
            long bombCnt = enemies[enemies.Count - 1 ].HP / A;
            cnt += bombCnt;

            List<long> kill = new List<long>();

            for(int i = enemies.Count - 1; 0 <= i; i--)
            {
                if(enemies[i].posistion < bombPosition)
                {
                    break;
                }

                enemies[i].HP -= A * bombCnt;
                if(enemies[i].HP <= 0)
                {
                    kill.Add(i);
                }
            }

            for(int i = 0; i < kill.Count; i++)
            {
                enemies.RemoveAt((int)kill[i]);
            }
        }

        Console.WriteLine(cnt);
    }

    class Enemy
    {
        public Enemy(string p, string h)
        {
            posistion = long.Parse(p);
            HP = long.Parse(h);
        }
        public long posistion { get; set; }
        public long HP { get; set; }
    }

}