write a go solution for Description:
The only difference between this problem and D2 is the bound on the size of the tree.

You are given an unrooted tree with n vertices. There is some hidden vertex x in that tree that you are trying to find.

To do this, you may ask k queries v_1,v_2,ldots,v_k where the v_i are vertices in the tree. After you are finished asking all of the queries, you are given k numbers d_1,d_2,ldots,d_k, where d_i is the number of edges on the shortest path between v_i and x. Note that you know which distance corresponds to which query.

What is the minimum k such that there exists some queries v_1,v_2,ldots,v_k that let you always uniquely identify x (no matter what x is).

Note that you don't actually need to output these queries.

Input Format:
Each test contains multiple test cases. The first line contains the number of test cases t (1<=t<=100). Description of the test cases follows.

The first line of each test case contains a single integer n (1<=n<=2000)  — the number of vertices in the tree.

Each of the next n-1 lines contains two integers x and y (1<=x,y<=n), meaning there is an edges between vertices x and y in the tree.

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 2000.

Output Format:
For each test case print a single nonnegative integer, the minimum number of queries you need, on its own line.

Note:
In the first test case, there is only one vertex, so you don't need any queries.

In the second test case, you can ask a single query about the node 1. Then, if x=1, you will get 0, otherwise you will get 1.. Output only the code with no comments, explanation, or additional text.