# 描述

A rooted tree is a well-known data structure in computer science and engineering. An example is shown below:

In the figure, each node is labeled with an integer from {1, 2,…,16}. Node 8 is the root of the tree. Node x is an ancestor of node y if node x is in the path between the root and node y. For example, node 4 is an ancestor of node 16. Node 10 is also an ancestor of node 16. As a matter of fact, nodes 8, 4, 10, and 16 are the ancestors of node 16. Remember that a node is an ancestor of itself. Nodes 8, 4, 6, and 7 are the ancestors of node 7. A node x is called a common ancestor of two different nodes y and z if node x is an ancestor of node y and an ancestor of node z. Thus, nodes 8 and 4 are the common ancestors of nodes 16 and 7. A node x is called the nearest common ancestor of nodes y and z if x is a common ancestor of y and z and nearest to y and z among their common ancestors. Hence, the nearest common ancestor of nodes 16 and 7 is node 4. Node 4 is nearer to nodes 16 and 7 than node 8 is.

For other examples, the nearest common ancestor of nodes 2 and 3 is node 10, the nearest common ancestor of nodes 6 and 13 is node 8, and the nearest common ancestor of nodes 4 and 12 is node 4. In the last example, if y is an ancestor of z, then the nearest common ancestor of y and z is y.

Write a program that finds the nearest common ancestor of two distinct nodes in a tree.

## Input

The input consists of T test cases. The number of test cases T is given in the first line of the input file. Each test case starts with a line containing an integer N , the number of nodes in a tree, $2<=N<=10,000$. The nodes are labeled with integers $1, 2,…, N$. Each of the next $N -1$ lines contains a pair of integers that represent an edge —the first integer is the parent node of the second integer. Note that a tree with N nodes has exactly $N - 1$ edges. The last line of each test case contains two distinct integers whose nearest common ancestor is to be computed.

## Output

Print exactly one line for each test case. The line should contain the integer that is the nearest common ancestor.

• intput

• output

# 代码

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