Can anyone explain how to solve C?

I tried an $$$O(n^3)$$$ solution: enumerating all possible initial direction $$$(dx,dy)$$$,(which is $$$O(n^2$$$)) and then checking how many holes are lying in the same direction: $$$(x_i-x_j,y_i-y_j)=\alpha \cdot(dx,dy)$$$.

The holes lying in the same direction can always be reached because we can use a zig zag path to connect them.

And we can add two more additional holes as the start and end.

I thought it should work, but I got an WA for that. Is there anything wrong in my solution?

Somehow they managed to make a round 2 which is even more boring than last year.

I wonder what possible explanation there is for the correlation between the platform change and the quality drop in the contests.