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C. Tree Pruning
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
t+pazolite, ginkiha, Hommarju - Paved Garden
⠀

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?

Input

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 $$$5 \cdot 10^5$$$.

Output

For each test case, output a single integer: the minimum number of operations needed to achieve your goal.

Example
Input
3
7
1 2
1 3
2 4
2 5
4 6
4 7
7
1 2
1 3
1 4
2 5
3 6
5 7
15
12 9
1 6
6 14
9 11
8 7
3 5
13 5
6 10
13 15
13 6
14 12
7 2
8 1
1 4
Output
2
2
5
Note

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 $$$2$$$.