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.Linq;

namespace AtCoderBeginnerContest153
{
	class Program
	{
		static void Main(string[] args)
		{
			var numbers = ReadLongArray();
			var monsters = new Monster[numbers[0]];
			for (var i = 0; i < numbers[0]; i++)
			{
				var tmp = ReadLongArray();
				monsters[i] = new Monster
				{
					Position= tmp[0],
					HitPoint= tmp[1],
				};
			}

			monsters = monsters.OrderBy(x => x.Position).ToArray();

			var count = 0L;
			while (true)
			{
				var monster = monsters.FirstOrDefault(x => x.HitPoint > 0);
				if(monster == null)
				{
					break;
				}

				var atackCount = (long)Math.Ceiling((double)monster.HitPoint / numbers[2]);
				var maxPosition = monster.Position + numbers[1] * 2;
				foreach(var target in monsters.Where(x => x.Position <= maxPosition))
				{
					target.Damage(atackCount * numbers[2]);
				}
				count += atackCount;
			}

			Console.WriteLine(count);
		}

		private class Monster
		{
			public long Position { get; set; }

			public long HitPoint { get; set; }

			public void Damage(long damage)
			{
				this.HitPoint -= damage;
			}
		}

		public static int ReadInt()
			=> int.Parse(Console.ReadLine());

		public static int[] ReadIntArray()
			=> Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();

		public static long ReadLong()
			=> long.Parse(Console.ReadLine());

		public static long[] ReadLongArray()
			=> Console.ReadLine().Split().Select(x => long.Parse(x)).ToArray();

		public static string ReadString()
			=> Console.ReadLine();

		public static string[] ReadStringArray()
			=> Console.ReadLine().Split();
	}
}