Description:
You are given a tree$$$^{\dagger}$$$. In one zelda-operation you can do follows:
- Choose two vertices of the tree $$$u$$$ and $$$v$$$;
- Compress all the vertices on the path from $$$u$$$ to $$$v$$$ into one vertex. In other words, all the vertices on path from $$$u$$$ to $$$v$$$ will be erased from the tree, a new vertex $$$w$$$ will be created. Then every vertex $$$s$$$ that had an edge to some vertex on the path from $$$u$$$ to $$$v$$$ will have an edge to the vertex $$$w$$$.
Illustration of a zelda-operation performed for vertices $$$1$$$ and $$$5$$$.
Determine the minimum number of zelda-operations required for the tree to have only one vertex.
$$$^{\dagger}$$$A tree is a connected acyclic undirected graph.
Input Format:
Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The description of the test cases follows.
The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 10^5$$$) — the number of vertices.
$$$i$$$-th of the next $$$n − 1$$$ lines contains two integers $$$u_i$$$ and $$$v_i$$$ ($$$1 \le u_i, v_i \le n, u_i \ne v_i$$$) — the numbers of vertices connected by the $$$i$$$-th edge.
It is guaranteed that the given edges form a tree.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.
Output Format:
For each test case, output a single integer — the minimum number of zelda-operations required for the tree to have only one vertex.
Note:
In the first test case, it's enough to perform one zelda-operation for vertices $$$2$$$ and $$$4$$$.
In the second test case, we can perform the following zelda-operations:
1. $$$u = 2, v = 1$$$. Let the resulting added vertex be labeled as $$$w = 10$$$;
2. $$$u = 4, v = 9$$$. Let the resulting added vertex be labeled as $$$w = 11$$$;
3. $$$u = 8, v = 10$$$. After this operation, the tree consists of a single vertex.