Edge Elimination

Description:

Input:

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 $$$2 \cdot 10^5$$$.

Output:

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.

Sample Input:

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

Sample Output:

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

Note:

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.