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;

public class AtCoder_153_F
{
    public struct Pair
    {
        public int x;
        public int h;

        public Pair(int x_, int h_)
        {
            x = x_;
            h = h_;
        }
    }

    public static void Main()
    {
        //var exStdIn = new System.IO.StreamReader("input.txt");
        //System.Console.SetIn(exStdIn);

        int[] lines = Console.ReadLine().Split(' ').Select(x_ => int.Parse(x_)).ToArray();
        int n = lines[0];
        int d = lines[1];
        int a = lines[2];

        Pair[] pair = new Pair[n];
        for (int i = 0; i < n; i++)
        {
            int[] line = Console.ReadLine().Split(' ').Select(x_ => int.Parse(x_)).ToArray();
            int xxx = line[0];
            int hhh = line[1] % a == 0 ? line[1] / a : line[1] / a + 1;
            pair[i] = new Pair(xxx, hhh);
        }
        pair = pair.OrderBy(p => p.x).ToArray();
        int[] x = pair.Select(aa => aa.x).ToArray();
        int[] h = pair.Select(aa => aa.h).ToArray();

        long count = 0;
        for (int i = 0; i < n; i++)
        {
            if (h[i] <= 0) continue;
            int hh = h[i];
            count += hh;
            int j = i;
            while (j < n && x[j] <= x[i] + d + d)
            {
                h[j] -= hh;
                j++;
            }
        }

        Console.WriteLine(count);
    }
}