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.io.*;
import java.util.*;

public class Main {

	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		int n = sc.nextInt();
		long d = sc.nextLong();
		long a = sc.nextLong();
		Pair[] ps = new Pair[n];
		for(int i = 0; i < n; i++) {
			long x = sc.nextLong();
			long h = sc.nextLong();
			ps[i] = new Pair(x, h);
		}
		Arrays.sort(ps);
		long res = 0;
		long count = 0;
		LinkedList<Pair> pos = new LinkedList<Pair>();
		for(int i = 0; i < n; i++) {
			long x = ps[i].a;
			while(!pos.isEmpty() && pos.peekFirst().a < x) {
				count -= pos.peekFirst().b;
				pos.removeFirst();
			}
			long rem = Math.max(ps[i].b - count * a, 0);
			long dif = (long)Math.ceil(rem*1.0/a);
			res += dif;
			count += dif;
			pos.add(new Pair(x + 2*d, dif));
		}
		System.out.println(res);
	}
	static class Pair implements Comparable<Pair>{
		long a, b;
		public Pair(long a, long b) {
			this.a = a; this.b = b;
		}
		@Override
		public int compareTo(Pair p) {
			return a < p.a ? -1: a == p.a? 0: 1;
		}
	}
	
	static class FastScanner {
		public BufferedReader reader;
		public StringTokenizer tokenizer;
		public FastScanner() {
			reader = new BufferedReader(new InputStreamReader(System.in), 32768);
			tokenizer = null;
		}
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public String nextLine() {
			try {
				return reader.readLine();
			} catch(IOException e) {
				throw new RuntimeException(e);
			}
		}
	}

}