Problem:
Score : 300 points

Problem Statement

Every day, N passengers arrive at Takahashi Airport.
The i-th passenger arrives at time T_i.

Every passenger arrived at Takahashi airport travels to the city by bus. Each bus can accommodate up to C passengers.
Naturally, a passenger cannot take a bus that departs earlier than the airplane arrives at the airport.
Also, a passenger will get angry if he/she is still unable to take a bus K units of time after the arrival of the airplane.
For that reason, it is necessary to arrange buses so that the i-th passenger can take a bus departing at time between T_i and T_i + K (inclusive).

When setting the departure times for buses under this condition, find the minimum required number of buses.
Here, the departure time for each bus does not need to be an integer, and there may be multiple buses that depart at the same time.

Constraints

2 \leq N \leq 100000

1 \leq C \leq 10^9

1 \leq K \leq 10^9

1 \leq T_i \leq 10^9

C, K and T_i are integers.

Input

The input is given from Standard Input in the following format:

N C K
T_1
T_2
:
T_N

Output

Print the minimum required number of buses.

Sample Input 1

5 3 5
1
2
3
6
12

Sample Output 1

3

For example, the following three buses are enough:

A bus departing at time 4.5, that carries the passengers arriving at time 2 and 3.

A bus departing at time 6, that carries the passengers arriving at time 1 and 6.

A bus departing at time 12, that carries the passenger arriving at time 12.

Sample Input 2

6 3 3
7
6
2
8
10
6

Sample Output 2

3

Solution in Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.InputStreamReader;

import java.util.Arrays;
import java.util.Collections;
import java.util.ArrayList;
import java.util.List;
import java.util.HashSet;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.util.Comparator;
import java.util.Set;
import java.util.HashMap;
import java.util.Map;

public class Main {
    // 標準入力
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    // 標準入力数値配列用 int
    static int[] inputval() throws Exception {
        String[] strarray = br.readLine().trim().split(" ");
        int[] intarray = new int[strarray.length];
        for (int i = 0; i < intarray.length; i++) {
            intarray[i] = Integer.parseInt(strarray[i]);
        }
        return intarray;
    }

    /* 標準入力数値配列用 long */
    static long[] inputLongArr() throws Exception {
        String[] strarray = br.readLine().trim().split(" ");
        long[] longarray = new long[strarray.length];
        for (int i = 0; i < longarray.length; i++) {
            longarray[i] = Long.parseLong(strarray[i]);
        }
        return longarray;
    }

    // 標準入力数値リスト用 int
    static List<Integer> inputIntList() throws Exception {
        List<String> strList = Arrays.asList(br.readLine().trim().split(" "));
        List<Integer> intList = new ArrayList<Integer>();
        for (String elem : strList){
            intList.add(Integer.parseInt(elem));
        }
        return intList;
    }

    // 標準入力数値配列用 integer 降順ソート用
    static Integer[] inputvalInteger() throws Exception {
        String[] strarray = br.readLine().trim().split(" ");
        Integer[] intarray = new Integer[strarray.length];
        for (int i = 0; i < intarray.length; i++) {
            intarray[i] = Integer.parseInt(strarray[i]);
        }
        return intarray;
    }

    /*標準入力long*/
    static long inputLong() throws Exception {
        return Long.parseLong(br.readLine());
    }

    /*標準入力long*/
    static int inputInt() throws Exception {
        return Integer.parseInt(br.readLine());
    }


    public static void main(String[] args) throws Exception {
        // write your code here
        long [] nck = inputLongArr();
        long n = nck[0];
        long c = nck[1];
        long k = nck[2];
        long [] tl = new long [(int) n];
        for (int i=0; i<n; i++){
            tl[i] = inputLong();
        }
        Arrays.sort(tl);
        long ans = 0;

        int index =0;
        if(c<n){
            while(index<n){
                for (int i=1; i<c; i++){
                    if (index+i >= n || tl[index+i] - tl[index] >k){
                        index+=i;
                        ans ++;
                        break;
                    }else if(i == c-1){
                        index+=c;
                        ans ++;
                    }
                }

            }

        }else{
            while(index<n){
                for (int i=1; i<n;i++){
                    if (index+i >= n || tl[index+i] - tl[index] >k){
                        index+=i;
                        ans ++;
                        break;
                    }else if(i == n-1){
                        index+=n;
                        ans ++;
                    }
                }

            }

        }

        System.out.println(ans);

    }

}