The tests for this problem consist of nine groups. Points for each group are awarded only if all tests in the group and all tests in some of the previous groups are passed. Note that passing the tests from the statement may not be required for some groups. \textbf{Offline checking} means that the results of testing your solution on this group will only be available after the competition ends.

Let $\sum n$ be the sum of $n$ over all test cases of this test.

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\begin{center}
\begingroup
\renewcommand{\arraystretch}{1.5}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
& & \multicolumn{1}{c|}{Constraints} & & \\
\cline{3-3}
\raisebox{2.25ex}[0cm][0cm]{Group}
& \raisebox{2.25ex}[0cm][0cm]{Points}
& $\sum n$
& \raisebox{2.25ex}[0cm][0cm]{\parbox{1.5cm}{\centering Required}}
& \raisebox{2.25ex}[0cm][0cm]{Comment}
\\
\hline
0       & 0     & --                & --       & Samples             \\
\hline
1       & 11     & $\sum n \le 3$    & 0        &                               \\
\hline
2       & 18    & $\sum n \le 30$   & 0, 1 &                               \\
\hline
3       & 6    & $\sum n \le 50$   & 0, 1, 2 &                               \\
\hline
4       & 13     & $\sum n \le 200$  & --       & All points on the convex hull are black \\
\hline
5       & 14    & $\sum n \le 200$  & 0 -- 4 &                               \\
\hline
6       & 8     & $\sum n \le 500$  & 4        & All points on the convex hull are black \\
\hline
7       & 7    & $\sum n \le 500$  & 0 -- 6 &                               \\
\hline
8       & 12    & $\sum n \le 2000$ & 4, 6     & \parbox{8cm}{\centering \vspace{2mm} {All points on the convex hull are black. \\ \textbf{Offline checking}}\vspace{2mm}}  \\
\hline
9       & 11   & $\sum n \le 2000$ & 0 -- 8 & \textbf{Offline checking}    \\
\hline
\end{tabular}
\endgroup
\end{center}