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.

Samples

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

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.