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: [Image] 

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.


-----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.


-----Example-----
Input
1
10
1 2
1 3
1 4
2 5
2 6
3 7
3 8
4 9
4 10

Output
8



-----Note-----

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

Source: codeforces | Difficulty: HARD
Tags: Tree algorithms

Graph algorithms

Graph traversal

Dynamic programming


Solutions:
import sys
input = sys.stdin.readline
t = int(input())
for _ in range(t):
	n = int(input())
	ab = [list(map(int, input().split())) for i in range(n - 1)]
	graph = [[] for i in range(n + 1)]
	deg = [0] * (n + 1)
	for (a, b) in ab:
		graph[a].append(b)
		graph[b].append(a)
		deg[a] += 1
		deg[b] += 1
	pnt = [max(deg[i] - 1, 1) for i in range(n + 1)]
	root = 1
	stack = [root]
	dist = [0] * (n + 1)
	dist[root] = pnt[root]
	while stack:
		x = stack.pop()
		for y in graph[x]:
			if dist[y] == 0:
				dist[y] = dist[x] + pnt[y]
				stack.append(y)
	far = dist.index(max(dist))
	root = far
	stack = [root]
	dist = [0] * (n + 1)
	dist[root] = pnt[root]
	while stack:
		x = stack.pop()
		for y in graph[x]:
			if dist[y] == 0:
				dist[y] = dist[x] + pnt[y]
				stack.append(y)
	print(max(dist))