CF1521D.Nastia Plays with a Tree

Nastia has an unweighted tree with $n$ vertices and wants to play with it!

The girl will perform the following operation with her tree, as long as she needs:

1. Remove any existing edge.
2. Add an edge between any pair of vertices.

What is the minimum number of operations Nastia needs to get a bamboo from a tree? A bamboo is a tree in which no node has a degree greater than $2$.

娜斯佳有一棵包含 $n$ 个顶点的无权树，她想和这棵树玩！

女孩将对她的树反复执行以下操作，直到她满意为止：

1. 删除任意一条已存在的边；
2. 在任意一对顶点之间添加一条边。

娜斯佳至少需要多少次操作，才能将这棵树变成一根“竹子”？所谓“竹子”，是指一棵树，其中任意节点的度数均不超过 $2$。

The first line contains a single integer $t$ ($1 \le t \le 10\,000$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($2 \le n \le 10^5$) — the number of vertices in the tree.

Next $n - 1$ lines of each test cases describe the edges of the tree in form $a_i$, $b_i$ ($1 \le a_i, b_i \le n$, $a_i \neq b_i$).

It's guaranteed the given graph is a tree and the sum of $n$ in one test doesn't exceed $2 \cdot 10^5$.

第一行包含一个整数 $t$（$1 \le t \le 10\,000$）—— 测试用例的数量。

每个测试用例的第一行包含一个整数 $n$（$2 \le n \le 10^5$）—— 树中顶点的数量。

每个测试用例的接下来 $n - 1$ 行以 $a_i$、$b_i$ 的形式描述树的边（$1 \le a_i, b_i \le n$，且 $a_i \neq b_i$）。

保证所给图是一棵树，且单个测试用例中所有 $n$ 的总和不超过 $2 \cdot 10^5$。

For each test case in the first line print a single integer $k$ — the minimum number of operations required to obtain a bamboo from the initial tree.

In the next $k$ lines print $4$ integers $x_1$, $y_1$, $x_2$, $y_2$ ($1 \le x_1, y_1, x_2, y_{2} \le n$, $x_1 \neq y_1$, $x_2 \neq y_2$) — this way you remove the edge $(x_1, y_1)$ and add an undirected edge $(x_2, y_2)$.

Note that the edge $(x_1, y_1)$ must be present in the graph at the moment of removing.

对于每个测试用例，在第一行输出一个整数 $k$ —— 从初始树得到竹子结构所需的最少操作次数。

接下来的 $k$ 行中，每行输出四个整数 $x_1$、$y_1$、$x_2$、$y_2$（满足 $1 \le x_1, y_1, x_2, y_{2} \le n$，且 $x_1 \neq y_1$，$x_2 \neq y_2$），表示删除无向边 $(x_1, y_1)$ 并添加一条无向边 $(x_2, y_2)$。

注意：在执行删除操作时，边 $(x_1, y_1)$ 必须存在于当前图中。

Note the graph can be unconnected after a certain operation.

Consider the first test case of the example:

The red edges are removed, and the green ones are added.

注意：经过某次操作后，图可能变为非连通图。

考虑示例中的第一个测试用例：

红色边被删除，绿色边被添加。