Is It A Tree?

Time Limit: 2 Seconds
Memory Limit: 65536 KB

A tree is a well-known data structure that is either empty (null, void, nothing)
or is a set of one or more nodes connected by directed edges between nodes satisfying
the following properties.

There is exactly one node, called the root, to which no directed edges point.

Every node except the root has exactly one edge pointing to it.

There is a unique sequence of directed edges from the root to each node.

For example, consider the illustrations below, in which nodes are represented
by circles and edges are represented by lines with arrowheads. The first two
of these are trees, but the last is not.

In this problem you will be given several descriptions of collections of nodes
connected by directed edges. For each of these you are to determine if the collection
satisfies the definition of a tree or not.

**Input**

The input will consist of a sequence of descriptions (test cases) followed by
a pair of negative integers. Each test case will consist of a sequence of edge
descriptions followed by a pair of zeroes Each edge description will consist
of a pair of integers; the first integer identifies the node from which the
edge begins, and the second integer identifies the node to which the edge is
directed. Node numbers will always be greater than zero.

**Output **

For each test case display the line ``Case k is a tree." or the line ``Case
k is not a tree.", where k corresponds to the test case number (they are
sequentially numbered starting with 1).

** Sample Input **

6 8 5 3 5 2 6 4

5 6 0 0

8 1 7 3 6 2 8 9 7 5

7 4 7 8 7 6 0 0

3 8 6 8 6 4

5 3 5 6 5 2 0 0

-1 -1

**Sample Output **

Case 1 is a tree.

Case 2 is a tree.

Case 3 is not a tree.

Source:

**North Central North America 1997**
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