Edge Elimination

对于一棵树上的边相邻定义为两个边有公共点 现在给定一棵树，每次可以删掉一条仍有偶数条边与之相邻的边，判断是否存在一个删边序列使得所有边都被删除了 如果可以在第一行输出 `YES` 之后输出删边顺序，否则输出一行一个 `NO` 多组测试数据，所有测试数据的 $\sum n\le 2\times 10^5$

You are given a tree (connected, undirected, acyclic graph) with $ n $ vertices. Two edges are adjacent if they share exactly one endpoint. In one move you can remove an arbitrary edge, if that edge is adjacent to an even number of remaining edges. Remove all of the edges, or determine that it is impossible. If there are multiple solutions, print any.

The input consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \le t \le 10^5 $ ) — 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 2 \cdot 10^5 $ ) — the number of vertices in the tree. Then $ n-1 $ lines follow. The $ i $ -th of them contains two integers $ u_i $ , $ v_i $ ( $ 1 \le u_i,v_i \le n $ ) the endpoints of the $ i $ -th edge. It is guaranteed that the given graph is a tree. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case print "NO" if it is impossible to remove all the edges. Otherwise print "YES", and in the next $ n-1 $ lines print a possible order of the removed edges. For each edge, print its endpoints in any order.

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

YES
2 1
NO
YES
2 3
3 4
2 1
YES
3 5
2 3
2 1
4 3
NO

Test case $ 1 $ : it is possible to remove the edge, because it is not adjacent to any other edge. Test case $ 2 $ : both edges are adjacent to exactly one edge, so it is impossible to remove any of them. So the answer is "NO". Test case $ 3 $ : the edge $ 2-3 $ is adjacent to two other edges. So it is possible to remove it. After that removal it is possible to remove the remaining edges too.