Problem Statement

Snuke has found two trees A and B, each with N vertices numbered 1 to N.
The i-th edge of A connects Vertex a_i and b_i, and the j-th edge of B connects Vertex c_j and d_j.
Also, all vertices of A are initially painted white.
Snuke would like to perform the following operation on A zero or more times so that A coincides with B:

• Choose a leaf vertex that is painted white. (Let this vertex be v.)
• Remove the edge incident to v, and add a new edge that connects v to another vertex.
• Paint v black.

Determine if A can be made to coincide with B, ignoring color. If the answer is yes, find the minimum number of operations required.
You are given T cases of this kind. Find the answer for each of them.

Input

Input is given from Standard Input in the following format:
T
case_1
:
case_{T}

Each case is given in the following format:
N
a_1 b_1
:
a_{N-1} b_{N-1}
c_1 d_1
:
c_{N-1} d_{N-1}

Output

For each case, if A can be made to coincide with B ignoring color, print the minimum number of operations required, and print -1 if it cannot.

Constraints

• $1 \leq T \leq 20$
• $3 \leq N \leq 50$
• $1 \leq a_i,b_i,c_i,d_i \leq N$
• All given graphs are trees.

Sample Input 1

2
3
1 2
2 3
1 3
3 2
6
1 2
2 3
3 4
4 5
5 6
1 2
2 4
4 3
3 5
5 6

Sample Output 1

1
-1

• The graph in each case is shown below.
• In case 1, A can be made to coincide with B by choosing Vertex 1, removing the edge connecting 1 and 2, and adding an edge connecting 1 and 3. Note that Vertex 2 is not a leaf vertex and thus cannot be chosen.

Sample Input 2

3
8
2 7
4 8
8 6
7 1
7 3
5 7
7 8
4 2
5 2
1 2
8 1
3 2
2 6
2 7
4
1 2
2 3
3 4
3 4
2 1
3 2
9
5 3
4 3
9 3
6 8
2 3
1 3
3 8
1 7
4 1
2 8
9 6
3 6
3 5
1 8
9 7
1 6

Sample Output 2

6
0
7

• A may coincide with B from the beginning.

见题面 Input 部分

见题面 Output 部分