For this test what should be answer?
3
0 0
1 1
2 2

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1 2 3  or 1 2 2 ?

(Answer written by GPT-5.5, verified with AC solution)

The size of a convex hull is not the number of points in the set. According to the statement, if the convex hull is a segment, its size is 2.

For the whole set, the delegate is (2, 2), because it has the greatest ordinate. The convex hull of all three collinear points is just the segment from (0, 0) to (2, 2), so its size is 2.

Then Vadim takes the points to the left of the delegate: (0, 0) and (1, 1). Their delegate is (1, 1), and their convex hull is also a segment, so its size is 2.

Finally, (0, 0) is alone, so its convex hull size is 1.

So in input order the answer is 1 2 2.