You are given a tree with (n) nodes, rooted at node (1). In this problem, a leaf is a non-root node with degree (1). In one operation, you can remove a leaf and the edge adjacent to it (possibly, new leaves appear). What is the minimum number of operations that you have to perform to get a tree, also rooted at node (1), where all the leaves are at the same distance from the root? 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) ((3 \leq n \leq 5 \cdot 10^5)) — the number of nodes. Each of the next (n-1) lines contains two integers (u), (v) ((1 \leq u, v \leq n), (u \neq v)), describing an edge that connects (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 (5 \cdot 10^5). For each test case, output a single integer: the minimum number of operations needed to achieve your goal. In the first two examples, the tree is as follows: In the first example, by removing edges ((1, 3)) and ((2, 5)), the resulting tree has all leaves (nodes (6) and (7)) at the same distance from the root (node (1)), which is (3). The answer is (2), as it is the minimum number of edges that need to be removed to achieve the goal. In the second example, removing edges ((1, 4)) and ((5, 7)) results in a tree where all leaves (nodes (4) and (5)) are at the same distance from the root (node (1)), which is (2).