409020: GYM103415 L Dynamic Convex Hull

There are $$$N$$$ points.

You will be given $$$M$$$ queries. Each query will give you several points. You must answer the area of the convex hull of these points merged with the initial $$$N$$$ points.

This problem contains multiple test cases.

The first line contains an integer $$$T$$$ ($$$1 \le T \le 10^5$$$) — the number of test cases.

For each test case:

The first line contains an integer $$$N$$$ ($$$3 \le N \le 2 \times 10^5$$$) — the number of the initial points.

Then $$$N$$$ lines follow. The $$$i$$$-th of them contains two integers $$$x_i,y_i$$$ ($$$|x_i|,|y_i| \le 10^9$$$) — the coordinate of the $$$i$$$-th initial point.

The next line contains an integer $$$M$$$ ($$$1 \le M \le 2 \times 10^5$$$) — the number of queries.

Then $$$M$$$ queries follow. For each query: the first line contains an integer $$$k$$$ ($$$1 \le k \le 10$$$) — the number of points in this query; then $$$k$$$ lines follow, the $$$i$$$-th of which contains two integers $$$x_i,y_i$$$ ($$$|x_i|,|y_i| \le 10^9$$$) — the coordinate of the $$$i$$$-th point in this query.

It is guaranteed that in all test cases, the sum of $$$N$$$ is no more than $$$10^6$$$, and the sum of $$$k$$$ is no more than $$$10^6$$$.

For each query in each test case, output $$$2 \times S$$$ in one line. $$$S$$$ indicates the area in this query.

It can be proved that $$$2 \times S$$$ is always an integer.

1
8
-1 2
-2 1
-2 -1
-1 -2
1 -2
2 -1
2 1
1 2
1
3
0 3
0 4
1 5

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