Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Alarm Clock

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputEvery evening Vitalya sets *n* alarm clocks to wake up tomorrow. Every alarm clock rings during exactly one minute and is characterized by one integer *a*_{i} — 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* ≤ 2·10^{5}, 1 ≤ *m* ≤ 10^{6}) — number of alarm clocks, and conditions of Vitalya's waking up.

Second line contains sequence of distinct integers *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{6}) in which *a*_{i} 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 10^{6} 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.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/22/2019 08:23:15 (d1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|