Tree2cycle

Time Limit: 15000/8000 MS (Java/Others) Memory Limit: 102400/102400 K (Java/Others)

Total Submission(s): 2161 Accepted Submission(s): 508

Problem Description

A tree with N nodes and N-1 edges is given. To connect or disconnect one edge, we need 1 unit of cost respectively. The nodes are labeled from 1 to N. Your job is to transform the tree to a cycle(without superfluous edges) using minimal cost.

A cycle of n nodes is defined as follows: (1)a graph with n nodes and n edges (2)the degree of every node is 2 (3) each node can reach every other node with these N edges.

Input

The first line contains the number of test cases T( T<=10 ). Following lines are the scenarios of each test case.

In the first line of each test case, there is a single integer N( 3<=N<=1000000 ) - the number of nodes in the tree. The following N-1 lines describe the N-1 edges of the tree. Each line has a pair of integer U, V ( 1<=U,V<=N ), describing a bidirectional edge (U, V).

Output

For each test case, please output one integer representing minimal cost to transform the tree to a cycle.

Sample Input

1 4 1 2 2 3 2 4

Sample Output

Hint

In the sample above, you can disconnect (2,4) and then connect (1, 4) and (3, 4), and the total cost is 3.

Source

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