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 [Math Processing Error]) such that it is possible to reach all vertices of the graph from [Math Processing Error] by moving along the directed edges.

You are given a directed tree with [Math Processing Error] vertices (numbered [Math Processing Error] through [Math Processing Error]). 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?



The first line of the input contains a single integer [Math Processing Error] denoting the number of test cases. The description of [Math Processing Error] test cases follows.

The first line of each test case contains a single integer [Math Processing Error].

Each of the next [Math Processing Error] lines contains two space-separated integers [Math Processing Error] and [Math Processing Error] denoting that there is a directed edge from [Math Processing Error] to [Math Processing Error] in the tree.


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.



[Math Processing Error]

[Math Processing Error]

the graph described on the input is a directed tree

the sum of [Math Processing Error] over all test cases does not exceed [Math Processing Error]


Subtask #1 (20 points): for each edge, [Math Processing Error] or [Math Processing Error] (the graph is a directed star)

Subtask #2 (80 points): original constraints

Example Input



1 2

3 2


1 2

2 3

Example Output




Example case 1: We can delete the edge from vertex [Math Processing Error] to vertex [Math Processing Error] and insert an edge from [Math Processing Error] to [Math Processing Error]. Then, the graph becomes a rooted directed tree with vertex [Math Processing Error] 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 [Math Processing Error].

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