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 static class Program {
    public static void Main() {
        long[] nda=Console.ReadLine().Split().Select(long.Parse).ToArray();
        long n=nda[0];
        long d=nda[1];
        long a=nda[2];

        var data=new List<Tuple<long,long>>();
        for(int i=0;i<n;i++){
            long[]xh=Console.ReadLine().Split().Select(long.Parse).ToArray();
            data.Add(new Tuple<long,long>(xh[0],(xh[1]+a-1)/a));
        }
        data.Sort();

        long ans=0;
        long now=0;
        long[] lazy=new long[n+1];
        int j=0;
        for(int i=0;i<n;i++){
            long x=data[i].Item1;
            long h=data[i].Item2;
            now-=lazy[i];
            h=Math.Max(0,h-now);
            ans+=h;
            now+=h;
            while(j<n&&data[j].Item1<=x+2*d+1)j++;
            lazy[j]+=h;
        }
        Console.WriteLine(ans);
    }
}

/*
まず、爆弾は固定ダメージですから、HP をすべて A で割っておくことで、A = 1 としてよいです。
敵を座標でソートして、敵を左から順に、なるべく右に爆弾を置いて倒します。
このとき巻き添えになる敵がたくさんいたら間に合いませんから、それは隣接差で遅延評価しましょう。
配列を用意して、それの累積和が与えたダメージになるようにしておきましょう。
ただし、累積和をとってはいけません。せっかく順番に動いていますから、現在の累積和を管理しておきましょう。
*/