## VOCV - Con-Junctions

The city of Y-O is a network of two-way streets and junctions with the following properties:

1. There is no more than one street between each pair of junctions.
2. Every junction is connected to every other junction either directly via a street or through other junctions by a unique path.
3. When a light is placed at a junction, all the streets meeting at this junction are also lit.

A valid lighting is a set of junctions such that if lights were placed at these, all the streets would be lit. An optimal lighting is a valid lighting such that it contains the least number of junctions.

1. Find the number of lights in an optimal lighting.
2. Find the total number of such optimal lightings in the city.

### Input

• The first line of the input contains a positive integer t <= 20, denoting the number of test cases.
• The description of the test cases follows one after the other.
• Network Description:
• The first line of description of a network consists of a positive integer n <= 100010 denoting the number of junctions in the network.
• Each junction is numbered with a unique integer between 1 and n.
• The following n-1 lines contain a pair of integers u v (1 <= u,v <= n) separated by a single space denoting that there is a street between junction u and junction v.

### Output

The output must consist of t lines, the kth line corresponding to the kth network; (1 <= k <= t). The kth line must contain two integers separated by a single space. The first integer on the kth line must be the number of junctions in an optimal lighting of network k. The second integer must be N%10007, which is the remainder left by the number of optimal lightings when divided by 10007.

Input:
2
4
1 2
2 3
3 4
3
1 2
1 3

Output:
2 3
1 1