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 JavaScript (node.js v5.12) (judge verdict: Accepted)

var input = require("fs").readFileSync("/dev/stdin", "utf8").trim().split("\n");
var obj = {
  "list" : input,
  "index" : 0,
  "max" : input.length,
  "next" : function(){
    if(!this.hasNext()){throw "NoSuchElementException:次に要素は無いよ";}
    var returnObj = this.list[this.index];
    this.index++;
    return returnObj;
  },
  "hasNext" : function(){return (this.index < this.max);}
}
Main();
function next(){return obj.next();}
function hasNext(){return obj.hasNext();}
function myout(t){console.log(t);}//standard output
function myerr(t){console.error(t);}//standard error
//[no]要素の扱い。数値型
//不明値、異常時:引数そのまま返す　1:数値へ変換
//2:半角SPで分割 4:半角SPで分割し、数値配列へ
//6:1文字で分割  7:1文字で分割し、数値配列へ
//8:半角SPで結合 9:改行で結合 0:文字なしで結合
function myconv(i,no){try{switch(no){case 1:return parseInt(i);case 2:return i.split(" ");case 4:return i.split(" ").map((a)=>Number(a));case 6:return i.split("");case 7:return i.split("").map((a)=>Number(a));case 8:return i.join(" ");case 9:return i.join("\n");case 0:return i.join("");default:return i;}}catch(e){return i;}}
function Main(){
  var one = myconv(next(),4);
  var N = one[0];
  var C = one[1];
  var K = one[2];
  var list = new Array(N);
  for(var i = 0; i < N; i ++){
    list[i] = myconv(next(),1);
  }
  list.sort(function(a,b){
  	return a - b;
  });
  myerr(list);
  var first = null;
  var jokyaku = 0;
  var output = 0;
  for(var i = 0; i < N; i++){
      if(first == null){
         first = list[i];
        myerr("最初更新?");
        output++;
      }
      if(first + K >= list[i]){
        myerr("時間セーフ");
         jokyaku++;
         if(jokyaku == C){
           myerr("定員MAX" + i);
           jokyaku = 0;
           first = null;
         }
      }else{
        myerr("時間オーバー");
        output++;
        jokyaku = 1;
        first = list[i];
      }
  }
  myout(output);
}