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.*;

class Main {

	public static void main(String[] args) throws Exception {
		final Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		long D = sc.nextLong();
		long A = sc.nextLong();
		long[][] XH = new long[N][2];
		for (int i = 0; i < N; i++) {
			XH[i][0] = sc.nextLong();
			XH[i][1] = sc.nextLong();
		}

		Arrays.sort(XH, (a, b) -> Long.compare(a[0], b[0]));

		long[] B = new long[N];
		long currentBomb = 0;
		long answer = 0;
		for (int i = 0; i < N; i++) {
			if (i > 0) currentBomb -= B[i - 1];

			if (XH[i][1] <= 0) continue;

			long nBomb = (XH[i][1] / A) + ((XH[i][1] % A > 0) ? 1 : 0);
			if (currentBomb >= nBomb) continue;
			answer += (nBomb - currentBomb);

			int l = i;
			int r = N;
			while (r - l > 1) {
				int m = (l + r) / 2;
				if (XH[m][0] <= 2 * D + XH[i][0]) {
					l = m;
				} else {
					r = m;
				}
			}
			B[l] += (nBomb - currentBomb);
			currentBomb = nBomb;
		}

		System.out.println(answer);
	}
}