D. Reachability and Treetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputLet $$$u$$$ and $$$v$$$ be two distinct vertices in a directed graph. Let's call the ordered pair $$$(u, v)$$$ good if there exists a path from vertex $$$u$$$ to vertex $$$v$$$ along the edges of the graph.You are given an undirected tree with $$$n$$$ vertices and $$$n - 1$$$ edges. Determine whether it is possible to assign a direction to each edge of this tree so that the number of good pairs in it is exactly $$$n$$$. If it is possible, print any way to direct the edges resulting in exactly $$$n$$$ good pairs. One possible directed version of the tree for the first test case. InputThe first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.The first line of each test case contains one integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the number of vertices in the tree.The next $$$n - 1$$$ lines describe the edges. The $$$i$$$-th line contains two integers $$$u_i$$$ and $$$v_i$$$ ($$$1 \le u_i, v_i \le n$$$; $$$u_i \neq v_i$$$) — the vertices connected by the $$$i$$$-th edge.It is guaranteed that the edges in each test case form an undirected tree and that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.OutputFor each test case, print "NO" (case-insensitive) if it is impossible to direct all edges of the tree and obtain exactly $$$n$$$ good pairs of vertices.Otherwise, print "YES" (case-insensitive) and then print $$$n - 1$$$ pairs of integers $$$u_i$$$ and $$$v_i$$$ separated by spaces — the edges directed from $$$u_i$$$ to $$$v_i$$$.The edges can be printed in any order. If there are multiple answers, output any.ExampleInput451 22 41 33 551 21 31 44 522 143 11 22 4OutputYES 1 2 3 1 3 5 4 2 YES 2 1 3 1 4 1 5 4 NO YES 1 3 2 1 2 4 NoteThe tree from the first test case and its possible directed version are shown in the legend above. In this version, there are exactly $$$5$$$ good pairs of vertices: $$$(3, 5)$$$, $$$(3, 1)$$$, $$$(3, 2)$$$, $$$(1, 2)$$$, and $$$(4, 2)$$$.One possible directed version of the tree from the second test case is shown below: In the presented answer, there are exactly $$$5$$$ good pairs of vertices: $$$(2, 1)$$$, $$$(3, 1)$$$, $$$(4, 1)$$$, $$$(5, 4)$$$, and $$$(5, 1)$$$.In the third test case, there are only two directed pairs of vertices, but for any direction of the edge, only one pair will be good.