VMILI - Military Story


Military headquaters plan to develop a better protection for a spaceport. They suppose that the spaceport would be best protected if it is surrounded with as many fences as possible and each fence is patroled by armed guards. The corresponding order was issued and military engineers started to develop a project.

Wishing to be promoted, sergeant Stupid sent soldiers to dig in fence poles before the project was actually ready. Without much thinking, the soldiers put a lot of poles at random. Help the sergeant to decide how to make barbwire fences using the poles so that the number of fences is maximal.

Input

The first line contains an integer 3 ≤ N ≤ 4000, which is the number of the poles. Each of the following N lines contains two integers 0 ≤ x, y ≤ 10000, which are the coordinates of a corresponding pole. No two poles have the same position.

Output

The output should contain a single integer number, which is the maximal possible number of nested fences that can be constructed. Each fence is a closed polygonal line without self-crossing whose vertices are poles. Different fences should not have common points.

Example

Input:
4
100 100
200 100
100 200
300 300


Output:
1

hide comments
naveenbanda: 2016-07-24 09:03:55

plz provide me any additional test case. I'm getting wrong answer



Archangel: 2015-03-05 03:19:42

AC in first attempt, I thought I might get TLE, thanks for this problem though, I finally was able to implement this task :)

Mohd Irtefa: 2014-10-31 01:48:52

Does this not work with Python 2.7, I always get a time limit exceeded!

Naman Goyal: 2014-07-26 14:38:29

Can't understand if the Time Limit is 1s then how did my code get accepted in 1.71s. Is it because judge runs with more than one test case?

Viktor Fonic: 2013-12-20 09:16:37

Note that when you have 2 poles left, you can't make a fence

Monkey D. Luffy : 2013-03-20 10:43:24

@Phenomenal more test cases please

Last edit: 2013-03-20 10:43:44
maharaja: 2012-01-21 19:28:26

can someone provide additional testcases

Robin Lee: 2011-06-07 02:15:29

Note to others: "no common points" in this case means no common vertices. Situations where an internal vertex touches an external edge are permissible.


Added by:Phenomenal
Date:2009-02-16
Time limit:0.162s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:acm.timus.ru