You are so lucky because the story of this problem which was about cheating has been censored by the manager of the contest, and you don't have to read that long story! Given n points in a 2D plane, You have to use these points to make a magical shape like a bow tie. Our bow tie like shape consists of two triangles that share a vertex. We call it center point. Now you may want to know a little more about this bow tie like shape. As you can see in the picture this shape is made up of 5 points and 6 segments that make two triangles. Four of these six segments must share the center point as a point and these segments must be in two lines that intersect each other in center point. One another important condition to make a bow tie like shape is that no other points are allowed to be inside or on the segments of the shape. In this problem you must count the number of different bow ties like shapes that can be drawn using the points.
The first line of input is the number of points in plane, n (5 ≤ n ≤ 500). In the next lines there are n lines with two integer numbers that are coordinates of points, xi and yi ( - 104 ≤ xi, yi ≤ 104). The points are different, but clearly some points maybe collinear.
Output the number of different bow tie like shapes that we can make using this set of points.
## Input
The first line of input is the number of points in plane, n (5 ≤ n ≤ 500). In the next lines there are n lines with two integer numbers that are coordinates of points, xi and yi ( - 104 ≤ xi, yi ≤ 104). The points are different, but clearly some points maybe collinear.
## Output
Output the number of different bow tie like shapes that we can make using this set of points.
[samples]
**Definitions**
Let $ n \in \mathbb{Z} $, $ 5 \leq n \leq 500 $, be the number of distinct points in $ \mathbb{R}^2 $.
Let $ P = \{ p_1, p_2, \dots, p_n \} $ be the set of points, where $ p_i = (x_i, y_i) \in \mathbb{R}^2 $.
A *bow tie shape* is defined by an ordered 5-tuple of distinct points $ (c, a, b, d, e) \in P^5 $ such that:
- $ c $ is the *center point*.
- Points $ a, b $ lie on one line through $ c $, with $ c $ strictly between $ a $ and $ b $.
- Points $ d, e $ lie on another line through $ c $, with $ c $ strictly between $ d $ and $ e $.
- The two lines $ \overleftrightarrow{ab} $ and $ \overleftrightarrow{de} $ are distinct and intersect only at $ c $.
- No point in $ P \setminus \{c, a, b, d, e\} $ lies on any of the segments $ \overline{ca}, \overline{cb}, \overline{cd}, \overline{ce}, \overline{ad}, \overline{ae}, \overline{bd}, \overline{be} $ — i.e., no other point lies on any of the six segments forming the two triangles $ \triangle cad $, $ \triangle cbe $ (or equivalently, the bow tie $ cadb e $).
**Constraints**
1. All points in $ P $ are distinct.
2. Coordinates satisfy $ -10^4 \leq x_i, y_i \leq 10^4 $.
3. No three points are collinear unless explicitly used in defining a line through the center.
**Objective**
Count the number of distinct bow tie shapes, i.e., the number of 5-tuples $ (c, a, b, d, e) \in P^5 $ satisfying the above conditions, where two shapes are identical if they use the same set of five points with the same center and same pair of crossing lines (unordered pairs $ \{a,b\} $, $ \{d,e\} $, and unordered lines).
Equivalently, count the number of unordered pairs of distinct lines $ \ell_1, \ell_2 $ through a common center point $ c \in P $, each containing at least two other points of $ P $ symmetric about $ c $, such that no other point of $ P $ lies on the segments of the resulting bow tie.