Root the Tree SOLUTION ROOTTREE

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Root the Tree SOLUTION ROOTTREE

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?

 

Input

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.

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

[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]

Subtasks

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

2

3

1 2

3 2

3

1 2

2 3

Example Output

1

0

Explanation

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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