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.*;
import java.util.stream.*;
import java.io.*;


class Monster implements Comparable<Monster> {
    final long x, h;

    Monster(long x, long h){
        this.x = x;
        this.h = h;
    }

    public int compareTo(Monster m){
        return Long.compare(this.x, m.x);
    }
}

public class Main {

    public static void main(String[] args) throws IOException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] in1 = br.readLine().split(" ");
        long N = Long.parseLong(in1[0]);
        long D = Long.parseLong(in1[1]);
        long A = Long.parseLong(in1[2]);
        List<Monster> monsters = new ArrayList<>();
        for(int i = 0; i < N; i++){
            in1 = br.readLine().split(" ");
            long X = Long.parseLong(in1[0]);
            long H = Long.parseLong(in1[1]);
            monsters.add(new Monster(X, H));
        }
        br.close();

        Collections.sort(monsters);
        Queue<long[]> position = new ArrayDeque<>();
        long tmp_attack_count = 0L;
        long total_attack_count = 0L;

        for(int n = 0; n < N; n++){

            long now_x = monsters.get(n).x;
            long now_h = monsters.get(n).h;

            while(!position.isEmpty() && position.peek()[0] + 2 * D < now_x){
                tmp_attack_count -= position.poll()[1];
            }

            long attack_count = (now_h - tmp_attack_count * A + A - 1L) / A;
            if(attack_count <= 0) continue;

            total_attack_count += attack_count;
            tmp_attack_count += attack_count;
            position.add(new long[] {now_x, attack_count});
        }

        System.out.println(total_attack_count);
    }
}