The tests for this problem consist of 11 groups. The rules by which points are awarded for groups are described below. Note that passing the tests from the statement is not required for some groups. The final score for each group is equal to the maximum score obtained for that group of tests across all submissions.

The score for a solution for a group of tests is equal to the minimum score obtained across all tests in the group.

\begin{itemize}
\item If your solution makes an incorrect call to \texttt{compare} or returns an answer that does not satisfy the mandatory conditions, it will receive $0$ points for the test.
\item In each test, your solution is allowed to make no more than $2 \cdot 10^6$ calls to the function \texttt{compare}. If the limit is exceeded, your solution will receive $0$ points for the test.
\item In some groups, it is required to maximize the number of pieces in the answer. In such groups, if the number of pieces is not maximally possible, your solution will receive $0$ points for the test.
\end{itemize}

If none of the described conditions for the test are violated, the answer for the test is considered correct. Let the full score for the group of tests be $p$. Some groups are evaluated using a formula, while others are evaluated without using a formula:

\begin{itemize}
\item If the group is evaluated without using a formula, the score for the test is equal to $p$.
\item Otherwise, if the group is evaluated using a formula, let $q$ be the number of calls to \texttt{compare} made by your solution. Then the score for the test is equal to
$\left\lfloor p \cdot \frac{20n}{\max{(q, 20n)}} \right\rfloor$.
\end{itemize}

\begin{center}
\begingroup
\renewcommand{\arraystretch}{1.5}
\begin{tabular}{|c|c|c|c|c|c|p{5cm}|}
\hline
\multirow{2}{*}[-0.9ex]{\parbox{1.2cm}{\centering Group}}
& \multirow{2}{*}[-0.9ex]{\parbox{1.4cm}{\centering Full\\score}}
& \multicolumn{2}{c|}{Score}
& \parbox{2.2cm}{\centering \vspace{2mm}Additional\\constraints\vspace{2mm}}
& \multirow{2}{*}[-0.9ex]{\parbox{1.3cm}{\centering Required\\groups}}
& \multirow{2}{*}[-0.9ex]{\parbox{5cm}{\centering Comments}}
\\
\cline{3-5}
& & Max. & Formula & $n$ & & \\
\hline
\hline
0 & 0 & no & no & -- & -- & \parbox{5cm}{\centering Tests from the statement.} \\
\hline
\hline
1 & 13 & no & no & $n = 4$ & -- & \\
\hline
2 & 4 & yes & no & $n = 4$ & 1 & \\
\hline
\hline
3 & 13 & no & no & -- & -- & \parbox{5cm}{\centering \vspace{2mm}$(10^9, -10^9)$, $(-10^9, 10^9)$, $(10^9, 10^9)$ are in the set, the rest are random points inside this triangle}\vspace{2mm} \\
\hline
4 & 8 & yes & no & -- & 3 & \parbox{5cm}{\centering \vspace{2mm}$(10^9, -10^9)$, $(-10^9, 10^9)$, $(10^9, 10^9)$ are in the set, the rest are random points inside this triangle}\vspace{2mm} \\
\hline
\hline
5 & 11 & yes & yes & -- & -- & \parbox{5cm}{\centering \vspace{2mm} points are the vertices of a convex polygon \vspace{2mm}} \\
\hline
\hline
6 & 9 & no & no & $n \leq 100$ & -- & \parbox{5cm}{\centering random points} \\
\hline
7 & 8 & yes & no & $n \leq 100$ & 6 & \parbox{5cm}{\centering random points} \\
\hline
\hline
8 & 9 & no & yes & -- & -- & \parbox{5cm}{\centering random points} \\
\hline
9 & 8 & yes & yes & -- & -- & \parbox{5cm}{\centering random points} \\
\hline
\hline
10 & 9 & no & yes & -- & -- & \\
\hline
11 & 8 & yes & yes & -- & -- & \\
\hline
\end{tabular}
\endgroup
\end{center}

In groups 6--9, all points were chosen randomly and independently from the square $[-10^9, 10^9] \times [-10^9, 10^9]$. 

In groups 3--4, points other than $(10^9, -10^9)$, $(-10^9, 10^9)$, $(10^9, 10^9)$ were chosen randomly and independently from the triangle with vertices $(10^9, -10^9)$, $(-10^9, 10^9)$, $(10^9, 10^9)$.

In these groups, among such random tests, only those where all points are distinct, no three lie on the same line, and no four form a trapezoid are retained.