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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <float.h>
#include <limits.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>

// 内部定数
#define D_HUMAN_MAX		100000									// 最大人数

// 内部変数
static FILE *szpFpI;											// 入力
static int siHCnt;												// 人数
static int siBMax;												// バス定員
static int siWait;												// 待ち時間
static int si1Time[D_HUMAN_MAX];								// 到着時刻

// 内部変数 - テスト用
#ifdef D_TEST
	static int siRes;
	static FILE *szpFpA;
	static int siTNo;
#endif

// １行出力
int
fOutLine(
	char *pcpLine				// <I> １行
)
{
	char lc1Buf[1024];

#ifdef D_TEST
	fgets(lc1Buf, sizeof(lc1Buf), szpFpA);
	if (strcmp(lc1Buf, pcpLine)) {
		siRes = -1;
	}
#else
	printf("%s", pcpLine);
#endif

	return 0;
}

// ソート関数 - int昇順
int
fSortFncIU(
	const void *pzpVal1			// <I> 値１
	, const void *pzpVal2		// <I> 値２
)
{
	int *lipVal1 = (int *)pzpVal1;
	int *lipVal2 = (int *)pzpVal2;

	// int昇順
	if (*lipVal1 > *lipVal2) {
		return 1;
	}
	else if (*lipVal1 < *lipVal2) {
		return -1;
	}

	return 0;
}

// 実行メイン
int
fMain(
)
{
	int i;
	char lc1Buf[1024];

	// 人数・バス定員・待ち時間 - 取得
	fgets(lc1Buf, sizeof(lc1Buf), szpFpI);
	sscanf(lc1Buf, "%d%d%d", &siHCnt, &siBMax, &siWait);

	// 到着時刻 - 取得
	for (i = 0; i < siHCnt; i++) {
		fgets(lc1Buf, sizeof(lc1Buf), szpFpI);
		sscanf(lc1Buf, "%d", &si1Time[i]);
	}
	qsort(si1Time, siHCnt, sizeof(int), fSortFncIU);

	// 台数 - 取得
	int liBCnt = 0;
	int liStart = INT_MIN;
	int liHCnt;
	for (i = 0; i < siHCnt; i++) {
		if (si1Time[i] <= liStart && liHCnt < siBMax) {
			liHCnt++;
		}
		else {
			liBCnt++;
			liStart = si1Time[i] + siWait;
			liHCnt = 1;
		}
	}

	return liBCnt;
}

// １回実行
int
fOne(
)
{
	int liRet;
	char lc1Buf[1024];

	// 入力 - セット
#ifdef D_TEST
	sprintf(lc1Buf, ".\\Test\\T%d.txt", siTNo);
	szpFpI = fopen(lc1Buf, "r");
	sprintf(lc1Buf, ".\\Test\\A%d.txt", siTNo);
	szpFpA = fopen(lc1Buf, "r");
	siRes = 0;
#else
	szpFpI = stdin;
#endif

	// 実行メイン
	liRet = fMain();

	// １行出力
	sprintf(lc1Buf, "%d\n", liRet);
	fOutLine(lc1Buf);

	// 残データ有無
#ifdef D_TEST
	lc1Buf[0] = '\0';
	fgets(lc1Buf, sizeof(lc1Buf), szpFpA);
	if (strcmp(lc1Buf, "")) {
		siRes = -1;
	}
#endif

	// テストファイルクローズ
#ifdef D_TEST
	fclose(szpFpI);
	fclose(szpFpA);
#endif

	// テスト結果
#ifdef D_TEST
	if (siRes == 0) {
		printf("OK %d\n", siTNo);
	}
	else {
		printf("NG %d\n", siTNo);
	}
#endif

	return 0;
}

// プログラム開始
int
main()
{

#ifdef D_TEST
	int i;
	for (i = D_TEST_SNO; i <= D_TEST_ENO; i++) {
		siTNo = i;
		fOne();
	}
#else
	fOne();
#endif

	return 0;
}