题目描述 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. 输入格式 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 and less than $10000$. 输出格式 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 $1$). 输入样例 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 输出样例 Case 1 is a tree. Case 2 is a tree. Case 3 is not a tree.