Unrumpf

While preparing a brute-force solution for the problem 'Rumpf', we wrote a program that repeatedly does the following. It picks a random number $n_i$ uniformly at random between 10 and 100. It then generates $n_i$ random points with integer coordinates, choosing each coordinate independently and uniformly at random from all integers between 0 and $10^9$, inclusive. Finally, it finds the convex hull of those points.

You are given 10000 polygons generated by this program. For each polygon, guess the value $n_i$ that was used to generate it.

The first line contains the number $k$ of convex hulls to process. $k$ is always equal to 10000. Each of the next $k$ lines describes one convex hull. A line starts with the number of vertices $m_i$, followed by $m_i$ pairs of integers, which are the coordinates of the vertices. The vertices are given in counterclockwise order, and no three consecutive vertices lie on the same line.

It is guaranteed that the convex hulls were generated by the method described above.

Output $k$ lines, each with one integer: your guess for the initial number $n_i$ of random vertices used to generate the corresponding convex hull. Each guess must be between 10 and 100, inclusive.

Your answer is accepted if the average, over all 10000 hulls, of the absolute difference between the natural logarithm of your guess and the natural logarithm of the true $n_i$ is below 0.2.

In the sample case, your answer is accepted if all your guesses are between 10 and 100, inclusive.

There are 10 non-sample test cases for this problem.