Little Nina is learning to read. Her favorite letter is N, and she looks for it everywhere.
There is a set of points on the plane. Let's consider four different points from the set and name them , , , and (in that order). Nina says that these four points form the letter N if all the following conditions are met:
- is located strictly to the right of ray (in this order).
- is located strictly to the left of ray (in this order).
- Angle
- Angle
How many Ns can she find? We consider letters to be sets of four points, and two letters differ if the value of one or more of the points (i.e., , or ) differs between the two corresponding sets of points. For example, if two sets of points have differing values, then they are different letters. In addition, letters that can be transformed into each other only by reversing point order are considered to be the same letter.
Input Format
The first line contains a single integer, , denoting the number of points.
Each line of the subsequent lines contain two space-separated integers, and , describing the respective coordinates of point . No two points coincide.
Constraints
Output Format
Print a single integer denoting the number of different Ns.
Sample Input
4
0 0
0 2
2 0
2 2
Sample Output
2
Explanation
To make this easier to read, we'll label our points as , , , and .
There are two different letter Ns:
Sets and (as well as their reversed variants) don't meet conditions and (we get a reversed N, like the Russian letter И).
Sets and are reversed variants of and , so we don't add them to our answer.