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.*;

public class Main {
	static class Monster {
		int X,H;

		public Monster(int x, int h) {
			X = x;
			H = h;
		}
		
	}
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int N = sc.nextInt();
		int D = sc.nextInt();
		int A = sc.nextInt();
		Monster[] monster = new Monster[N];
		for(int i=0; i<N; i++) {
			monster[i] = new Monster(sc.nextInt(), sc.nextInt());
		}
		Arrays.sort(monster, new Comparator<Monster>() {
			public int compare(Monster m1, Monster m2) {
				return Integer.compare(m1.X, m2.X); 
			}
		});

		int[] XX = new int[N];
		for(int i=0; i<N; i++)
			XX[i] = monster[i].X;
		
		int[] right = new int[N];
		for(int i=0; i<N; i++) {
			int to = monster[i].X + D*2;
			int idx = Arrays.binarySearch(XX, to);
			if(idx<0)
				idx = -idx-2;
			right[i] = idx+1;
		}

		long[] diff = new long[N+1];
		long ans = 0;
		long damage = 0;
		for(int i=0; i<N; i++) {
			damage += diff[i];
			if(monster[i].H-damage > 0) {
				long bomb = (monster[i].H-damage +A-1)/A;
				ans += bomb;
				damage += bomb*A;
				diff[right[i]] -= bomb*A;
			}
		}
		
		System.out.println(ans);
		sc.close();
	}
	
}