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 = Integer.parseInt(sc.next());
        int d = Integer.parseInt(sc.next());
        int a = Integer.parseInt(sc.next());
        
        long[] xh = new long[n];
        for(int i=0; i<n; i++){
            long x = Integer.parseInt(sc.next());
            long h = Integer.parseInt(sc.next());
            xh[i] = (x<<32) + h;
        }
        Arrays.sort(xh);
        
        PriorityQueue<Long> q = new PriorityQueue<>();
        q.add(-1L >>> 1);
        long ans = 0;
        long exp = 0;
        for(int i=0; i<n; i++){
            int x = (int)(xh[i]>>32);
            int h = (int)xh[i];
            
            long peek = q.peek();
            while((peek>>32)<x){
                exp -= (int)peek;
                q.poll();
                peek = q.peek();
            }
            
            long add = (h+a-1)/a - exp;
            add = Math.max(0, add);
            ans += add;
            
            exp += add;
            if((x+d*2L)<=(long)1e9){
                q.add(((x+d*2L)<<32)+add);
            }
        }
        System.out.println(ans);
    }
}