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.Arrays;
import java.util.Comparator;
import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);

    int N = scanner.nextInt();
    int D = scanner.nextInt();
    int A = scanner.nextInt();
    Monster[] monsters = new Monster[N];
    for (int i = 0; i < N; i++) {
      int x = scanner.nextInt();
      int h = scanner.nextInt();
      monsters[i] = new Monster(x, (h - 1) / A + 1);
    }
    Arrays.sort(monsters, Comparator.comparingLong(m -> m.x));

    long cum = 0;
    int[] delta = new int[N];
    int j = 0;
    for (int i = 0; i < N; i++) {
      while (j < i && monsters[j].x + 2 * D < monsters[i].x) {
        cum -= delta[j];
        j++;
      }
      if (monsters[i].h > cum) delta[i] = monsters[i].h - (int) cum;
      cum += delta[i];
    }
    long res = 0;
    for (int i = 0; i < N; i++) res += delta[i];
    System.out.println(res);
  }

  private static class Monster {
    private final long x;
    private final int h;

    private Monster(int x, int h) {
      this.x = x;
      this.h = h;
    }
  }
}