Triples of Cows

문제

There are initially $N-1N-1$ pairs of friends among FJ's $NN$ ($2\le N\le 2\cdot {10}^{5}2\backslash le\; N\backslash le\; 2\backslash cdot\; 10^5$) cows labeled $1\dots N1\backslash dots\; N$, forming a tree. The cows are leaving the farm for vacation one by one. On day $ii$, the $ii$th cow leaves the farm, and then all pairs of the $ii$th cow's friends still present on the farm become friends.

For each $ii$ from $11$ to $NN$, just before the $ii$th cow leaves, how many ordered triples of distinct cows $(a,b,c)(a,b,c)$ are there such that none of $a,b,ca,b,c$ are on vacation, $aa$ is friends with $bb$, and $bb$ is friends with $cc$?

입력

The first line contains $NN$.

The next $N-1N-1$ lines contain two integers $u_{i}u\_i$ and $v_{i}v\_i$ denoting that cows $u_{i}u\_i$ and $v_{i}v\_i$ are initially friends ($1\le u_i,v_i\le N1\backslash le\; u\_i,v\_i\backslash le\; N$).

출력

The answers for $ii$ from $11$ to $NN$ on separate lines.