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.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.Scanner;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Main {
    // TODO solve
    public static void main(final String[] args) {
        final Scanner scanner = new Scanner(System.in);
        final int n = scanner.nextInt();
        final int d = scanner.nextInt();
        final int a = scanner.nextInt();

        final List<Monster> list = IntStream.range(0, n)
                .mapToObj(i -> new Monster(scanner.nextInt(), scanner.nextInt()))
                .sorted(Comparator.comparingLong(monster -> monster.x))
                .collect(Collectors.toList());

        final List<Integer> indices = list.stream()
                .map(m -> m.x)
                .collect(Collectors.toList());

        long sum = 0;
        long counter = 0;
        final long[] array = new long[n];
        for (int i = 0; i < list.size(); i++) {
            final Monster monster = list.get(i);
            if (sum < monster.hp) {
                final long diff = monster.hp - sum;
                final long tmp = (diff + a - 1) / a;
                counter += tmp;
                sum += tmp * a;

                final int last = monster.x + 2 * d;
                final int found = Collections.binarySearch(indices, last);
                if (found >= 0) {
                    int idx = found;
                    if(idx >=n){
                        idx = n-1;
                    }
                    array[idx] += tmp * a;
                } else {
                    int idx = ~found - 1;
                    if (idx >= n) {
                        idx = n - 1;
                    } else if (idx < 0) {
                        idx = 0;
                    }
                    array[idx] += tmp * a;
                }
            }
            sum -= array[i];
        }
        System.out.println(counter);
    }

    static class Monster {
        final int x;
        final long hp;

        Monster(final int x, final int hp) {
            this.x = x;
            this.hp = hp;
        }
    }
}