Problem: 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.

Examples

Input

3 3 2
1 2
5 4
9 2


Output

2


Input

9 4 1
1 5
2 4
3 3
4 2
5 1
6 2
7 3
8 4
9 5


Output

5


Input

3 0 1
300000000 1000000000
100000000 1000000000
200000000 1000000000


Output

3000000000

Solution (in JAVA):

Solution:

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Objects;
import java.util.PriorityQueue;
import java.util.Scanner;

class Monster implements Comparable<Monster> {
    long x;
    long h;
    Monster(long x, long h) {
        this.x = x;
        this.h = h;
    }
    void setH(long h) {
        this.h = h;
    }
    @Override
    public int compareTo(Monster o) {
        return Long.compare(this.x, o.x);
    }
}
class Bomb implements Comparable<Bomb>{
    public long end;
    public long times;
    Bomb(long end, long times) {
        this.end = end;
        this.times = times;
    }
    void setTimes(long times) {
        this.times = times;
    }

    @Override
    public int compareTo(Bomb o) {
        if (this.end < o.end) {
            return - 1;
        } else if (this.end == o.end) {
            return Long.compare(this.times, o.times);
        } else {
            return 1;
        }
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;
        Bomb bomb = (Bomb) o;
        return end == bomb.end &&
                times == bomb.times;
    }

    @Override
    public int hashCode() {
        return Objects.hash(end, times);
    }
}
public class Main {
    public static void main(String [] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        long d = scanner.nextLong();
        long a = scanner.nextLong();
        Monster[] monsters = new Monster[n];
        for (int i = 0; i < n; ++i) {
            long x = scanner.nextLong();
            long h = scanner.nextLong();
            monsters[i] = new Monster(x, h);
        }
        Arrays.sort(monsters);
        long ans = 0;
        List<Bomb> bombs = new ArrayList<>();
        List<Long> decreasedHealths = new ArrayList<>();
        long totalDecreasedHealths = 0;
        for (int i = 0; i < n; ++i) {
            long x = monsters[i].x;
            long h = monsters[i].h;
            if (h <= 0) {
                continue;
            }
            int index = Collections.binarySearch(
                    bombs,
                    new Bomb(x - 1, Long.MAX_VALUE)
            );
            int firstCoveredIndex = index >= 0 && index < bombs.size() ?
                    index :
                    -(index + 1);
            int lastNotCoveredIndex = firstCoveredIndex - 1;
//            System.out.print("current x: " + x + " firstCoveredIndex: " + firstCoveredIndex + " ");

            long decreasedHealth = totalDecreasedHealths;
            if (lastNotCoveredIndex >= 0 && lastNotCoveredIndex < decreasedHealths.size()) {
                decreasedHealth -= decreasedHealths.get(lastNotCoveredIndex);
            }
            long remainH = h - decreasedHealth;
            if (remainH <= 0) {
                continue;
            }
            long bombTimes = remainH / a;
            if (remainH % a != 0) {
                bombTimes++;
            }
            ans += bombTimes;
            Bomb bomb = new Bomb(x + 2 * d, bombTimes);
//            System.out.println(" remainHealth: " + remainH +
//                     " bomb: (" + bomb.end + " " + bomb.times + ")");
            bombs.add(bomb);
            totalDecreasedHealths += bombTimes * a;
            decreasedHealths.add(totalDecreasedHealths);
        }
        System.out.print(ans);
    }
}