Onion

The onion, a biennial plant of the amaryllis family and one of the oldest vegetables cultivated by humankind, has been known for more than 5000 years. The onion's homeland is probably Central Asia (the areas of India, Afghanistan, Uzbekistan, and Iran), from where it spread to China, to the countries of the Middle East, and around the Mediterranean basin. It reached Europe through the Roman legions.

The edible part of the plant is the underground bulb, wrapped in a papery skin, together with the above-ground part, the green shoots: tubular, hollow, green leaves and the stalk hidden among them.

Computer scientists have their own onion too, one that can be computed from a given set of points on a plane. The onion consists of layers. A layer is formed by the points that are vertices of a convex polygon together with the points lying on the boundary of that polygon. A layer can be peeled off the onion when, at the moment of peeling, there are no points outside it. Compute the minimum number of moves in which the onion can be peeled apart into its layers.

The first line of input contains a small integer $z$, the number of datasets that follow one after another. One dataset is described as follows.

The first line contains a single integer $n$, the number of points ($0 \le n \le 5000$). Each of the next $n$ lines contains two integers $x$ and $y$ ($-10^9 \le x, y \le 10^9$), the $x$- and $y$-coordinates of a point. The points are pairwise distinct.

For each dataset, print a single line containing the number of onion layers computed for the given set of points.