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Home » Practice(easy) » Nice Quadrangles

Nice Quadrangles

Problem code: NICEQUAD

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All submissions for this problem are available.

There are n points with integer coordinates. We can form different quadrangles out of them by taking four different points and connecting them with lines. Let’s call a quadrangle ABCD nice if and only if:

  • Ax > 0 and Ay > 0;
  • Bx > 0 and By < 0;
  • Cx < 0 and Cy < 0;
  • Dx < 0 and Dy > 0;
  • ABCD has an integer area.

Your task is to count all different nice quadrangles that can be formed on the given points.

Input

The first line of input file contains number t – the number of test cases. Then the description of each test case follows. The first line of each test case contains number n – the number of points. Then n lines follow each consisting of two integers x, y – the coordinates of a point. No two points in the same test case coincide.

Constraints

1 <= t <= 10
1 <= n <= 30000
-30000 <= x, y <= 30000

Output

For each test case print the number of nice quadrangles that can be formed using given points.

Example

Input:
1
6
1 1
2 2
-1 -1
-2 2
2 -1
-3 -4

Output:
2


Author: spooky
Tester: keshav_57
Editorial http://discuss.codechef.com/problems/NICEQUAD
Date Added: 9-04-2010
Time Limit: 1 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, FORT, FS, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, NODEJS, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TEXT, WSPC


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Comments

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getting TLE....any hints

jimmy valentine @ 16 Dec 2010 11:20 AM

getting TLE....any hints regarding optimization technique here?

i changed my from cin,cout to

jayesh02 @ 29 Jan 2011 03:34 AM

i changed my from cin,cout to scanf,printf and my solution got accepted. Earlier it was givin TLE...

That's why the FAQ says you

triplem @ 29 Jan 2011 03:57 AM

That's why the FAQ says you should never use cin and cout ;)

In above example can't we

pradeep001946 @ 20 Sep 2012 07:32 AM
In above example can't we make 4 quadrangles,{ [(1,1),(2,-1),(-1,-1),(-2,2)], [(1,1),(2,-1),(-3,-4),(-2,2)], [(2,2),(2,-1),(-1,-1),(-2,2)], [(2,2),(2,-1),(-3,-4),(-2,2)]} ?? or did I miss something??

Another condition says its

krishnx @ 20 Sep 2012 03:55 PM
Another condition says its area is an integer. Hence only 2 I guess.

I have tested two of the

xins @ 22 Sep 2012 09:56 AM
I have tested two of the existing solutions by @dolka1 and @karlheinz_jung, and the problem is that if I enter a combination of { (1,1),(-3,1),(1,-3),(-1,-1) }, the program treats it as TRUE. However, it is not even a Quadrangles. It is a triangle. How should we deal with this problem?

@xins : u always get a

katana @ 25 Dec 2012 12:40 AM
@xins : u always get a quadrangle....because the four points always lie in different quadrants..

i couldn't get the solution

asheesh_jnu @ 21 Mar 2013 02:21 AM
i couldn't get the solution to break the quadrat further into 4. can any one explain it.

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