Codeforces Round #451 (Div. 2) D. Alarm Clock (貪心+雙指針)

D. Alarm Clock

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Every evening Vitalya sets n alarm clocks to wake up tomorrow. Every alarm clock rings during exactly one minute and is characterized by one integer ai — number of minute after midnight in which it rings. Every alarm clock begins ringing at the beginning of the minute and rings during whole minute.

Vitalya will definitely wake up if during some m consecutive minutes at least k alarm clocks will begin ringing. Pay attention that Vitalya considers only alarm clocks which begin ringing during given period of time. He doesn't consider alarm clocks which started ringing before given period of time and continues ringing during given period of time.

Vitalya is so tired that he wants to sleep all day long and not to wake up. Find out minimal number of alarm clocks Vitalya should turn off to sleep all next day. Now all alarm clocks are turned on.

Input

First line contains three integers n, m and k (1 ≤ k ≤ n ≤ 2·105, 1 ≤ m ≤ 106) — number of alarm clocks, and conditions of Vitalya's waking up.

Second line contains sequence of distinct integers a1, a2, ..., an (1 ≤ ai ≤ 106) in which ai equals minute on which i-th alarm clock will ring. Numbers are given in arbitrary order. Vitalya lives in a Berland in which day lasts for 106 minutes.

Output

Output minimal number of alarm clocks that Vitalya should turn off to sleep all next day long.

Examples

input

3 3 2
3 5 1

output

1

input

5 10 3
12 8 18 25 1

output

0

input

7 7 2
7 3 4 1 6 5 2

output

6

input

2 2 2
1 3

output

0

Note

In first example Vitalya should turn off first alarm clock which rings at minute 3.

In second example Vitalya shouldn't turn off any alarm clock because there are no interval of 10 consequence minutes in which 3 alarm clocks will ring.

In third example Vitalya should turn off any 6 alarm clocks.

#include <bits/stdc++.h>
using namespace std;    
const int maxn = 200010;
int cnt[maxn], a[maxn];
int main(){
	int n, m, k;
	cin>>n>>m>>k;
	for(int i = 1; i <= n; ++i){
		scanf("%d", &a[i]);
	}
	sort(a + 1, a + 1 + n);
	int l = 1, r = 1, ans = 0, cur = 1;
	memset(cnt, 0, sizeof(cnt));
	while(r <= n){
		while(a[r] - a[l] + 1 > m){
			if(cnt[l] == 0) cur--;
			l++;
		}
		if(cur >= k){
			ans++;
			cnt[r] = 1;
			cur--;
		}
		r++;
		cur++;
	}
	cout<<ans<<endl;
}    
  
/*
題意：
2e5個數，表示時間，連續的m分鐘內不能有超過k個數，問最少要去掉多少個數。

思路：
貪心即可，排序後從小往大掃，當不得不去掉當前數時，就去掉，然後用左邊的指針維護一下時間範圍，
不超過m分鐘。
*/