The Maximum Subtree
Description
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.
Input
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 $3 \cdot 10^5$.
Output
For each query print one integer — the maximum size of a good subtree of the given tree.
Samples
1
10
1 2
1 3
1 4
2 5
2 6
3 7
3 8
4 9
4 10
8
Note
In the first query there is a good subtree of size $8$. The vertices belonging to this subtree are ${9, 4, 10, 2, 5, 1, 6, 3}$.