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A directed tree is a directed graph such that if all edges were undirected, this graph would be a tree. A rooted directed tree is a directed tree in which there is one vertex (the root, let's denote it by $r$) such that it is possible to reach all vertices of the graph from $r$ by moving along the directed edges.

You are given a directed tree with $N$ vertices (numbered $1$ through $N$). You may perform the following operation on it any number of times (including zero):
Choose some edge which currently exists in the graph.
Remove this edge.
Add a new edge in such a way that the graph becomes a directed tree again.

What is the smallest number of operations which need to be performed in order to make the directed tree rooted?

------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains a single integer $N$.
Each of the next $N-1$ lines contains two space-separated integers $u$ and $v$ denoting that there is a directed edge from $u$ to $v$ in the tree.

------ Output ------
For each test case, print a single line containing one integer ― the smallest number of operations we need to perform to create a rooted directed tree.

------ Constraints ------
$1 ≤ N ≤ 10^{4}$
$1 ≤ u, v ≤ N$
the graph described on the input is a directed tree
the sum of $N$ over all test cases does not exceed $10^{5}$

------ Subtasks ------
Subtask #1 (20 points): for each edge, $u = 1$ or $v = 1$ (the graph is a directed star)

Subtask #2 (80 points): original constraints

----- Sample Input 1 ------
2

3

1 2

3 2

3

1 2

2 3
----- Sample Output 1 ------
1

0
----- explanation 1 ------
Example case 1: We can delete the edge from vertex $3$ to vertex $2$ and insert an edge from $3$ to $1$. Then, the graph becomes a rooted directed tree with vertex $3$ as the root. However, there are many other possible solutions.

Example case 2: The graph is already a rooted directed tree; the root is vertex $1$.

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