A14366 | 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 $2$ .

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 $2 \cdot 10^5$ .

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.