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 class Pair{
        int coor;
        long h;
        public Pair(int x,int y) {
            this.coor=x;
            this.h=y;
        }
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int d = sc.nextInt();
        int a = sc.nextInt();
        Pair[] pairs=new Pair[n];
        for (int i = 0; i < n; i++) {
            int x=sc.nextInt();
            int y=sc.nextInt();
            pairs[i]=new Pair(x,y);
        }
        long res=0;
        Arrays.sort(pairs,(b,c)->  (b.coor-c.coor));
        int[] diff=new int[n+1];
       for(int i=0;i<n;i++)
        {
            int j=bs(pairs,i,d);
            long need=Math.max((pairs[i].h+a-1-diff[i]*a)/a,0);
            res+=need;
            diff[i]+=need;
            diff[j]-=need;
            diff[i+1]+=diff[i];
        }
        System.out.println(res);
    }
    public static int bs(Pair[] pairs, int start, int d)
    {
        int end=pairs.length;
        int left=0;
        while(left<end){
            int mid=left+(end-left)/2;
            if(pairs[mid].coor-pairs[start].coor<=2*d)
            {
                left=mid+1;
            }
            else
            {
                end=mid;
            }
        }
        return left;
    }
}