You must have heard the name of Kernighan and Ritchie, the authors of The C Programming Language. While coding in C, we use different control statements and loops, such as, if-then-else, for, do-while, etc. Consider the following fragment of pseudo code: //execution starts here do { U; V; } while(condition); W; In the above code, there is a bias in each conditional branch. Such codes can be represented by control flow graphs like below: Let the probability of jumping from one node of the graph to any of its adjacent nodes be equal. So, in the above code fragment, the expected number of times U executes is 2. In this problem, you will be given with such a control flow graph and find the expected number of times a node is visited starting from a specific node. Input Input consists of several test cases. There will be maximum 100 test cases. Each case starts with an integer: n (n ≤ 100). Here n is the number of nodes in the graph. Each node in the graph is labeled with 1 to n and execution always starts from 1. Each of the next few lines has two integers: start and end which means execution may jump from node start to node end. A value of zero for start ends this list. After this, there will be an integer q (q ≤ 100) denoting the number of queries to come. Next q lines contain a node number for which you have to evaluate the expected number of times the node is visited. The last test case has value of zero for n which should not be processed. Output Output for each test case should start with ‘Case #i:’ with next q lines containing the results of the queries in the input with three decimal places. There can be situations where a node will be visited forever (for example, an infinite for loop). In such cases, you should print ‘infinity’ (without the quotes). See the sample output section for details of formatting.

2/2 Sample Input 3 12 23 21 00 3 1 2 3 3 12 23 31 00 3 3 2 1 0 Sample Output Case #1: 2.000 2.000 1.000 Case #2: infinity infinity infinity