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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main

import (
	"fmt"
	"sort"
)

type Monster struct {
	position int
	hp       int
}

type Monsters []Monster

func (x Monsters) Len() int {
	return len(x)
}
func (x Monsters) Swap(i, j int) {
	x[i], x[j] = x[j], x[i]
}
func (x Monsters) Less(i, j int) bool {
	return x[i].position < x[j].position
}

func main() {
	var n, d, a int
	fmt.Scan(&n)
	fmt.Scan(&d)
	fmt.Scan(&a)

	var monsterArray []Monster = make([]Monster, n)
	for i := 0; i < n; i++ {
		var p, h int
		fmt.Scan(&p)
		fmt.Scan(&h)
		monsterArray[i] = Monster{p, h}
	}
	sort.Sort(Monsters(monsterArray))

	// 一番左(a1とする)を倒せるまでx1+Dの場所で爆弾を使う
	// 生き残ったモンスターで一番左のモンスター(a2とする)を倒せるまでx2+Dの場所で爆弾を使う
	// 以下繰り返し
	// 計算量　１回爆弾　O(D)　爆弾の位置の数 O(N/D)
	var target int = 0
	var bomb int = 0
	for target < n {
		if monsterArray[target].hp <= 0 {
			target++
			continue
		}
		// 爆弾使用
		bomb++
		for i := target; i < n; i++ {
			if monsterArray[i].position <= monsterArray[target].position+d*2 {
				monsterArray[i].hp -= a
			} else {
				break
			}
		}
	}

	fmt.Println(bomb)
}