As a child, Steve yearned for the mines! His mine can be represented as a tree(^{\text{∗}}) of (n) nodes. Unfortunately, Steve's mine has been infiltrated by his greatest nemesis, Herobrine! At any time, Herobrine is hiding in exactly one node; initially, he may be in any of them. Steve can perform the following operations: (1\,\,x) — Check if Herobrine is currently in node (x). If he is, Steve catches him. Otherwise, Herobrine may or may not move to any adjacent node ( except the one you just checked). (2\,\,x) — Destroy all edges connected to node (x); Herobrine will no longer be able to use them. Afterwards, Herobrine may or may not move to any adjacent node. Find a sequence of at most (\left\lfloor \frac{5}{4} \cdot n \right\rfloor) operations that will guarantee Steve catches Herobrine, regardless of Herobrine's initial location and moves. We have a proof that, under the given constraints, this is always possible. (^{\text{∗}})A tree is a connected graph without cycles. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). 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 nodes. Each of the next (n − 1) lines contains two integers (u) and (v) ((1 \le u, v \le n)), describing an edge between nodes (u) and (v). It is guaranteed that the given edges form 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, first output a single integer (k) ((1 \le k \le \left\lfloor \frac{5}{4} \cdot n \right\rfloor)) — the number of operations you wish to perform. Then output (k) lines. Line (i) ((1 \le i \le k)) should contain two integers (t_i) and (x_i) ((1 \le t_i \le 2), (1 \le x_i \le n)), indicating that the (i)-th operatio