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 (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

type t struct {
	X int
	H int
}
type byX []t

func (a byX) Len() int           { return len(a) }
func (a byX) Swap(i, j int)      { a[i], a[j] = a[j], a[i] }
func (a byX) Less(i, j int) bool { return a[i].X < a[j].X }

func main() {
	N := readInt()
	D := readInt()
	A := readInt()
	XH := make([]t, N)
	for i := 0; i < N; i++ {
		XH[i].X = readInt()
		XH[i].H = (readInt() + (A - 1)) / A
	}

	sort.Sort(byX(XH))
	result := 0
	for i := 0; i < N; i++ {
		if XH[i].H < 0 {
			continue
		}
		result += XH[i].H
		for j := i + 1; j < N; j++ {
			if XH[j].X > XH[i].X+2*D {
				break
			}
			XH[j].H -= XH[i].H
		}
	}
	fmt.Println(result)
}

const (
	ioBufferSize = 1 * 1024 * 1024 // 1 MB
)

var stdinScanner = func() *bufio.Scanner {
	result := bufio.NewScanner(os.Stdin)
	result.Buffer(make([]byte, ioBufferSize), ioBufferSize)
	result.Split(bufio.ScanWords)
	return result
}()

func readString() string {
	stdinScanner.Scan()
	return stdinScanner.Text()
}

func readInt() int {
	result, err := strconv.Atoi(readString())
	if err != nil {
		panic(err)
	}
	return result
}