Diamond

Jack works as a jeweler. One day an unusually large and beautiful rough diamond arrives at his shop. Two customers want to buy it, so Jack decides to cut the diamond into two pieces (the two pieces need not have equal mass) and sell one piece to each customer.

Diamonds are extremely hard and can only be cut by a saw with a diamond blade. Cutting is expensive and slow: it takes about an hour to cut through two millimeters. Jack can afford only a single cut along one plane, and both resulting pieces will be sold to the two customers.

Jack wants to make his customers as happy as possible. Since the combined mass of the two pieces always equals the mass of the whole diamond, Jack instead decides to maximize the total number of faces of the two pieces. He does not know how to cut it that way, so he asks you for help.

The first line contains a single integer $n$ ($4 \le n \le 80$), the number of vertices of the diamond. Each of the next $n$ lines contains three integers $x_i$, $y_i$, $z_i$ ($-360 \le x_i, y_i, z_i \le 360$) separated by single spaces, the coordinates of the $i$-th vertex. The diamond is the smallest convex polyhedron that contains all of the given points. No point lies in the interior of the diamond, and no four vertices lie in a common plane.

Print a single integer: the largest possible total number of faces of the two pieces obtained by cutting the diamond with a single plane exactly once.