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.io.*;
 
public class Main {
    static ArrayList<Monster> ml;
    public static void main(String[] args) throws Exception {
        FastScanner sc = new FastScanner(System.in);
        int n = sc.nextInt();
        long d = sc.nextLong();
        long a = sc.nextLong();
        ml = new ArrayList<>();
        for(int i = 0; i < n; i++){
            ml.add(new Monster(sc.nextLong(),sc.nextLong()));
        }
        Collections.sort(ml);
        boolean isMaximum = false;
        int[] rl = new int[n];
        for(int i = 0; i < n; i++){
            if(isMaximum){
                rl[i] = n-1;
                continue;
            }
            rl[i] = beamSearch(ml.get(i).x+2*d);
            if(rl[i] == n-1){
                isMaximum = true;
            }
        }
        long ans = 0;
        long[] cum = new long[n+1];
        for(int i = 0; i < n; i++){
            long hp = ml.get(i).h-cum[i];
            if(hp > 0){
                long cnt = hp/a;
                if(hp%a > 0){
                    cnt++;
                }
                int r = rl[i];
                cum[i] += cnt*a;
                cum[r+1] -= cnt*a;
                ans += cnt;
            }
            cum[i+1] += cum[i];
        }
        System.out.println(ans);
    }
    
    private static int beamSearch(long v){
        int left = 0;
        int right = ml.size();
        while(right - left > 1){
            int mid = (right + left)/2;
            if(v >= ml.get(mid).x){
                left = mid;
            }else{
                right = mid;
            }
        }
        return left;
    }
}

class Monster implements Comparable<Monster>{
    long x,h;
    public Monster(long x, long h){
        this.x = x;
        this.h = h;
    }
    public int compareTo(Monster m){
        if(this.x < m.x){
            return -1;
        }else if(this.x > m.x){
            return 1;
        }else{
            return 0;
        }
    }
}

class FastScanner {
    private BufferedReader reader = null;
    private StringTokenizer tokenizer = null;
    public FastScanner(InputStream in) {
        reader = new BufferedReader(new InputStreamReader(in));
        tokenizer = null;
    }

    public String next() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public String nextLine() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken("\n");
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public double nextDouble() {
         return Double.parseDouble(next());
    }

    public int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        return a;
    }

    public long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nextLong();
        return a;
    } 
}