D. Nastia Plays with a Treetime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputNastia 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:  Remove any existing edge.  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.InputThe 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.OutputFor 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.ExampleInput
2
7
1 2
1 3
2 4
2 5
3 6
3 7
4
1 2
1 3
3 4
Output
2
2 5 6 7
3 6 4 5
0NoteNote 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.
2
7
1 2
1 3
2 4
2 5
3 6
3 7
4
1 2
1 3
3 4

2 2 5 6 7 3 6 4 5 0
['constructive algorithms', 'data structures', 'dfs and similar', 'dp', 'dsu', 'greedy', 'implementation', 'trees', '*2500']