A16273. Begginer's Zelda

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.

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 $10^5$ .

For each test case, output a single integer — the minimum number of zelda-operations required for the tree to have only one vertex.

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.