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.Comparator;
import java.util.Scanner;

public class Main {

	public static void main (String[] args)  {

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int d = sc.nextInt();
		int a = sc.nextInt();
		Pair[] monster = new Pair[n];

		ArrayList<Integer> hitPos = new ArrayList<>();
		ArrayList<Long> hitSum = new ArrayList<>();
		
		hitSum.add(0L);

		for (int i=0;i<n;i++) {
			Pair p = new Pair();
			p.left =sc.nextInt();
			p.right =(sc.nextInt()-1)/a+1;
			monster[i]=p;
		}
		Arrays.sort(monster, Comparator.comparing((Pair p)->p.left));

		for (int i=0;i<n;i++) {
			int tmp = Collections.binarySearch(hitPos, monster[i].left-d);
			long damage = 0;
			if (tmp>=0) {
				damage = hitSum.get(hitSum.size()-1)-hitSum.get(tmp);
			} else {
				damage = hitSum.get(hitSum.size()-1)-hitSum.get(-tmp-1);
			}
			if (monster[i].right-damage>0) {
				hitPos.add(monster[i].left+d);
				hitSum.add(hitSum.get(hitSum.size()-1)+monster[i].right-damage);
			}
		}
		System.out.println(hitSum.get(hitSum.size()-1));
	}
	
}

class Pair {
	int left;
	long right;
}