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 (
	"container/list"
	"fmt"
	"sort"
)

type Mon struct {
	x int
	h int
}

type Mons []Mon

func (m Mons) Len() int {
	return len(m)
}

func (m Mons) Less(i, j int) bool {
	return m[i].x < m[j].x
}

func (m Mons) Swap(i, j int) {
	m[i], m[j] = m[j], m[i]
}

func main() {
	var N, D, A int
	fmt.Scan(&N, &D, &A)
	D *= 2
	M := make([]Mon, N)
	for i := range M {
		var x, h int
		fmt.Scan(&x, &h)
		M[i].x = x
		M[i].h = h
	}
	sort.Sort(Mons(M))
	q := list.New()
	total := 0
	ans := 0
	for i := range M {
		x := M[i].x
		h := M[i].h
		e := q.Front()
		for e != nil && e.Value.(*Mon).x < x {
			total -= e.Value.(*Mon).h
			q.Remove(e)
			e = q.Front()
		}
		h -= total
		if h > 0 {
			c := (h + A - 1) / A
			ans += c
			damage := A * c
			total += damage
			q.PushBack(&Mon{x + D, damage})
		}
	}
	fmt.Println(ans)
}