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문제

You and your friends have invented an interesting game called “Trivial Points”. It’s played between 2 players and involves placing points in a 3D space in a special way respecting a certain set of rules. Being very excited about this game, you, together with your friends, have decided to create a computer version in which one of the players is a human and the other is computer.

For the purposes of the development of this game you are responsible to write a program that receives a set of points in a 3D space and computes how many different lines are there so that each contains at least 3 of the given points.

입력

Input contains on the first line a single integer number n, which is the number of given points. Then n lines follow, each containing the 3 integer coordinates of a point, more specifically the i-th of these n lines contains the integer coordinates xi, yi, zi, separated by single spaces, of the i-th point.

출력

Output will contain on the first line a single integer number that is the number of lines asked in problem’s statement.

제한

  • 4 ≤ n ≤ 1000.
  • Coordinates xi, yi, zi are integers.
  • -10 000 ≤ xi, yi, zi ≤ 10 000, i = 1, 2, 3, ..., n.

예제 입력 1

7
1 0 -1
3 4 5
2 2 2
3 3 3
-5 -5 -5
1 1 1
-3 4 0

예제 출력 1

2

힌트

The first line contains points (-5; -5; -5), (1; 1; 1), (2; 2; 2), and (3; 3; 3), and the second line contains points (1; 0; -1), (2; 2; 2), (3; 4; 5).