2591 - The Tree Movers North America - North Central - 2002/2003
			Submit		Ranking

Given two binary search trees, A and B, with nodes identified by (that is, having keys equal to) positive, non-zero integers, and the use of commands ``delete K " and ``add K " (defined below), what is the smallest number of commands that can be used to transform tree A into tree B?

Recall that in a binary search tree, the keys of all nodes in the left subtree of a node with key K must be less than K . Similarly, the keys of all nodes in the right subtree of a node with key K must be greater than K . There are no duplicate nodes.

The ``delete K " command will delete the tree (or subtree) with its root at the node with the key K . Deleting the root of the entire tree leaves an empty tree. The ``add K " command will add a new node identified by the integer K . This node will naturally be a leaf node.

Since we seek to transform tree A into tree B, it follows that commands will be applied only to tree A; tree B is ``read only".

It is easy to see that it should never require more than N + 1 commands to achieve the transformation of A into B, since deletion of the root node of tree A followed by the addition of one node for each of the N nodes in B (in the proper order) will achieve the desired goal. Equally easy to determine is the minimum number of commands required: if A and B are identical, then zero commands are required.

Input 

There will be multiple input cases. For each case, the input contains the description of tree A followed by the description of tree B. Each tree description consists of an integer N that specifies the number of nodes in the tree, following by the keys of the N nodes in an order such that N ``add" commands would create the tree. The last case is followed by the integer `-1'. No node will have a key larger than 10⁹ , and N will be no larger than 100.

Output 

For each case, display a single line containing the input case number (1, 2,...) and the number of commands required to transform tree A into tree B, formatted as shown in the examples below.

Sample Input 

4 5 2 7 4 6 5 3 7 1 4 9
0 0
1 100 0
0 1 100
3 100 49 37 2 200 152
-1

Sample Output 

Case 1: 5 commands.
Case 2: 0 commands.
Case 3: 1 command.
Case 4: 1 command.
Case 5: 3 commands.