[SOLUTION !!!] Nastia Plays with a Tree Solution Codeforces 2021

   

Nastia Plays with a Tree Solution Codeforces 2021

SOLUTION

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Nastia has an unweighted tree with n$n$ 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$2$.

Input

The first line contains a single integer t$t$ (1≤t≤10000$1\le t\le 10000$) — the number of test cases.

The first line of each test case contains a single integer n$n$ (2≤n≤105$2\le n\le {10}^5$) — the number of vertices in the tree.

Next n−1$n-1$ lines of each test cases describe the edges of the tree in form ai$a_i$, bi$b_i$ (1≤ai,bi≤n$1\le a_i,b_i\le n$, ai≠bi$a_i\ne b_i$).

It's guaranteed the given graph is a tree and the sum of n$n$ in one test doesn't exceed 2⋅105$2\cdot {10}^5$.

Output

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

In the next k$k$ lines print 4$4$ integers x1$x_1$, y1$y_1$, x2$x_2$, y2$y_2$ (1≤x1,y1,x2,y2≤n$1\le x_1,y_1,x_2,y_2\le n$, x1≠y1$x_1\ne y_1$, x2≠y2$x_2\ne y_2$) — this way you remove the edge (x1,y1)$(x_1,y_1)$ and add an undirected edge (x2,y2)$(x_2,y_2)$.

Note that the edge (x1,y1)$(x_1,y_1)$ must be present in the graph at the moment of removing.

Example

input

Copy

2
7
1 2
1 3
2 4
2 5
3 6
3 7
4
1 2
1 3
3 4

output

Copy

2
2 5 6 7
3 6 4 5
0

Note

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.

SOLUTION

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