How to make sure that the probability of both two operations are exactly $$$0.5$$$?

paulzrm can you explain it please, thanks a lot :)

I find a weird submission in Educational Codeforces Round 183: 342242159

The author wrote it in 5 minutes.

mocsecrofedoc How to do that?

So how to prove that important conclusion in the edtorial of 2127D?

I mean this part:

Now, we only need to arrange the leaves adjacent to each vertex relative to each other. Because their positions relative to the other vertices depend only on the four ways to arrange the main path. The proof of that is boring, so we won’t bore you with it :)

What is it?

I have two question. Can anyone help me? Thanks very much!

1. In the problem description, the permutation's name is $$$p$$$, but in the editorial the array's name is $$$a$$$. So what's that?

2. If we consider $$$a$$$ as $$$p$$$. The first paragraph of the editorial shows that if we choose a subset of $$$a_i \gt a_{i+1}$$$, then the subsequence is valid. But the last paragraph of the editorial says we should count the situation that $$$a_i \lt a_{i+1}$$$. Why's that?

Sorry for my bad English. :)

bestial-42-centroids can you explain this?

I'm really need help!