Triples

You are given a tree, that is, a connected undirected graph with no cycles. For every two vertices $x, y$, let $d(x, y)$ denote the length (the number of edges) of the unique simple path between $x$ and $y$. Count all the (unordered) triples $\{x,y,z\}$ such that $d(x,y) = d(y,z) = d(z,x) > 0$.

The first line contains the number of test cases $z$ ($1 \leq z \leq 20$). The descriptions of the test cases follow.

The first line of each test case contains the number of vertices $n$ ($3 \leq n \leq 100\,000$). Each of the next $n - 1$ lines contains two integers $a, b$ ($1 \leq a, b \leq n$), meaning there is an edge between vertices $a$ and $b$.

For each test case, output one integer: the number of triples in question.