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 {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int D = sc.nextInt();
		int A = sc.nextInt();
		int[][] X = new int[N][2];
		for(int i = 0; i < N; i++) {
			X[i][0] = sc.nextInt();
			X[i][1] = sc.nextInt();
		}
		Arrays.sort(X, (x, y) -> x[0] - y[0]);
		long ans = 0;
		long[] S = new long[N+1];
		int d = 1;
		for(int i = 0; i < N; i++) {
			long temp = X[i][0] + D * 2;
			while(d < N && X[d][0] <= temp)
				d++;
			long k = Math.max(0, (X[i][1] - S[i] + A - 1) / A);
			S[i+1] += S[i] + k * A;
			S[d] -= k * A;
			ans += k;
		}
		System.out.println(ans);
	}

}