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.*;

class Main {
	Scanner sc;
	int N, D, A;
	int[][] M;
	int[] B;
	
	private void calc() {
		sc = new Scanner(System.in);
		N = sc.nextInt();
		D = sc.nextInt();
		A = sc.nextInt();
		M = new int[N+1][2];
		for (int i = 1; i <= N; i++) {
			M[i][0] = sc.nextInt();
			M[i][1] = (sc.nextInt()+A-1)/A;
		}
		M[0][0] = -1;
		M[0][1] = 0;
		Arrays.sort(M, Comparator.comparingInt(m -> m[0]));
		B = new int[N+1];
		int l = 0;
		long as = 0;
		long ans = 0;
		for (int i = 1; i <= N; i++) {
			as += B[i-1];
			while (M[l][0] + 2*D < M[i][0]) as -= B[l++];
			B[i] = (int)Math.max(0L, M[i][1] - as);
			ans += B[i];
		}
		
		System.out.println(ans);
	}
	
	public static void main(String[] args) {
		new Main().calc();
	}
}