CF1238F.The Maximum Subtree

Assume that you have $k$ one-dimensional segments $s_1, s_2, \dots s_k$ (each segment is denoted by two integers — its endpoints). Then you can build the following graph on these segments. The graph consists of $k$ vertexes, and there is an edge between the $i$ -th and the $j$ -th vertexes ( $i \neq j$ ) if and only if the segments $s_i$ and $s_j$ intersect (there exists at least one point that belongs to both of them).

For example, if $s_1 = [1, 6], s_2 = [8, 20], s_3 = [4, 10], s_4 = [2, 13], s_5 = [17, 18]$ , then the resulting graph is the following:

A tree of size $m$ is good if it is possible to choose $m$ one-dimensional segments so that the graph built on these segments coincides with this tree.

You are given a tree, you have to find its good subtree with maximum possible size. Recall that a subtree is a connected subgraph of a tree.

Note that you have to answer $q$ independent queries.

The first line contains one integer $q$ ( $1 \le q \le 15 \cdot 10^4$ ) — the number of the queries.

The first line of each query contains one integer $n$ ( $2 \le n \le 3 \cdot 10^5$ ) — the number of vertices in the tree.

Each of the next $n - 1$ lines contains two integers $x$ and $y$ ( $1 \le x, y \le n$ ) denoting an edge between vertices $x$ and $y$ . It is guaranteed that the given graph is a tree.

It is guaranteed that the sum of all $n$ does not exceed $3 \cdot 10^5$ .

For each query print one integer — the maximum size of a good subtree of the given tree.

In the first query there is a good subtree of size $8$ . The vertices belonging to this subtree are ${9, 4, 10, 2, 5, 1, 6, 3}$ .