A tree is a connected graph with no cycles.

A rooted tree is a tree in which one special vertex is called the root. If there is an edge between $X$ and $Y$ in a rooted tree, we say that $Y$ is a child of $X$ if $X$ is closer to the root than $Y$ (in other words, the shortest path from the root to $X$ is shorter than the shortest path from the root to $Y$).

A full binary tree is a rooted tree where every node has either exactly 2 children or 0 children.

You are given a tree $G$ with $N$ nodes (numbered from $1$ to $N$). You are allowed to delete some of the nodes. When a node is deleted, the edges connected to the deleted node are also deleted. Your task is to delete as few nodes as possible so that the remaining nodes form a full binary tree for some choice of the root from the remaining nodes.

Input Specification

The first line of the input gives the number of test cases, $T$. $T$ test cases follow. The first line of each test case contains a single integer $N$, the number of nodes in the tree. The following $N-1$ lines each one will contain two space-separated integers: $X_i$ $Y_i$, indicating that $G$ contains an undirected edge between $X_i$ and $Y_i$.

Output Specification

For each test case, output one line containing Case #x: y, where $x$ is the test case number (starting from 1) and $y$ is the minimum number of nodes to delete from $G$ to make a full binary tree.

Limits

Memory limit: 1 GB.

$1\le T\le 100$.

$1\le X_i,Y_i\le N$.

Each test case will form a valid connected tree.

Small Dataset

Time limit: 60 seconds.

$2\le N\le 15$.

Large Dataset

Time limit: 120 seconds.

$2\le N\le 1000$.

Sample Input

3
3
2 1
1 3
7
4 5
4 2
1 2
3 1
6 4
3 7
4
1 2
2 3
3 4

Sample Output

Case #1: 0
Case #2: 2
Case #3: 1

In the first case, $G$ is already a full binary tree (if we consider node 1 as the root), so we don't need to do anything.

In the second case, we may delete nodes 3 and 7; then 2 can be the root of a full binary tree.

In the third case, we may delete node 1; then 3 will become the root of a full binary tree (we could also have deleted node 4; then we could have made 2 the root).

Note

This problem has different time limits for different batches. If you exceed the Time Limit for any batch, the judge will incorrectly display >120.000s regardless of the actual time taken. Refer to the Limits section for batch-specific time limits.