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.

假设你有 $k$ 条一维线段 $s_1, s_2, \dots, s_k$（每条线段由两个整数——其端点——表示）。那么可以在这些线段上构造如下图：该图包含 $k$ 个顶点，当且仅当线段 $s_i$ 与 $s_j$ 相交（即存在至少一个点同时属于这两条线段）时，第 $i$ 个顶点与第 $j$ 个顶点之间存在一条边（其中 $i \neq j$）。

例如，若 $s_1 = [1, 6], s_2 = [8, 20], s_3 = [4, 10], s_4 = [2, 13], s_5 = [17, 18]$，则所得到的图如下所示：

大小为 $m$ 的树被称为“好的”，当且仅当可以选出 $m$ 条一维线段，使得基于这些线段所构造的图恰好等于该树。

给你一棵树，你需要找出它的“好”的子树中最大可能的大小。注意：子树是指树的一个连通子图。

请注意，你需要回答 $q$ 个相互独立的查询。

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 $3 \cdot 10^5$.

第一行包含一个整数 $q$（$1 \le q \le 15 \cdot 10^4$）—— 查询的个数。

每个查询的第一行包含一个整数 $n$（$2 \le n \le 3 \cdot 10^5$）—— 树中顶点的数量。

接下来的 $n - 1$ 行中，每行包含两个整数 $x$ 和 $y$（$1 \le x, y \le n$），表示顶点 $x$ 与顶点 $y$ 之间存在一条边。保证所给图是一棵树。

保证所有查询中 $n$ 的总和不超过 $3 \cdot 10^5$。

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

对于每个查询，输出一个整数——给定树中好子树的最大大小。

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

在第一次查询中，存在一个大小为 $8$ 的好子树。属于该子树的顶点为 ${9, 4, 10, 2, 5, 1, 6, 3}$。