Magical Barrier

There are $N$ power sources, numbered from $1$ to $N$, scattered around the ICPC Kingdom. Power source $i$ is uniquely located at coordinate $(X_i , Y_i)$ in a 2D Cartesian plane such that there are no three power sources located in a straight line.

For each pair of distinct power sources $i$ and $j$ that satisfies $1 ≤ i < j ≤ N$, a magical barrier forms as a line segment that spans from $(X_i , Y_i)$ to $(X_j , Y_j )$.

You noticed a strange phenomenon. When two distinct magical barriers are intersecting, then both magical barriers are somewhat strengthened. To simplify things, you define the strength of a magical barrier $b$ as the number of magical barriers other than $b$ that intersects with $b$. Two distinct magical barriers are intersecting if and only if there exists exactly one point $(x, y)$ that lies on both magical barriers while none of the $N$ power sources are located at $(x, y)$.

You want to find the strength of the strongest magical barrier in the ICPC Kingdom.

Input begins with an integer $N$ ($2 ≤ N ≤ 1000$) representing the number of power sources. Each of the next $N$ lines contains $2$ integers $X_i$ $Y_i$ ($-10^9 ≤ X_i , Y_i ≤ 10^9$) representing the location of power source $i$. It is guaranteed that the location of each power source is unique, and there are no three power sources located in a straight line.

Output an integer in a single line representing the strength of the strongest magical barrier.