Time Limit: 10 Seconds
Memory Limit: 32768 KB
In a highly modernized fishing village, inhabitants there make a living on
fishery. Their major tools, fishing nets, are produced and fixed by computer.
After catching fishes each time, together with plenty of fishes, they will bring
back the shabby fishing nets, which might be full of leaks. Then they have to
inspect those nets. If there exist large leaks, they have to repair them before
launching out again.
Obviously, the smaller the leaks in the fishing nets are, the more fishes they
will catch. So after coming back, those fishermen will input the information
of the fishing nets into the computer to check whether the nets have leaks.
The checking principle is very simple: The computer regards each fishing net
as a simple graph constructed by nodes and edges. In the graph, if any circle
whose length (the number of edges) is larger than 3 must has at least one chord,
the computer will output "Perfect" indicating that the fishnet has
no leaks. Otherwise, "Imperfect" will be displayed and the computer
will try to repair the net.
Note: A circle is a closed loop, which starts from one node, passes through
other distinct nodes and back to the starting node. A chord is an edge, which
connects two different nodes on the circle, but it does not belong to the set
of edges on the circle.
The input file contains several test cases representing different fishing nets.
The last test case in the input file is followed by a line containing 0 0.
The first line of each test case contains two integers, n and m, indicating
the number of nodes and edges on the net respectively, 1 <= n <= 1000. It is followed
by m lines accounting for the details of the edges. Each line consists of two
integers xi and yi, indicating there is an edge between node xi and node yi.
For each test case, display its checking results. The word "Imperfect"
suggests that the corresponding fishing net is leaking, while the word "Perfect"
stands for a fishing net in good condition.
Follow the output for each net with a blank line.
Output for the Sample Input
Source: Asia 2001, Shanghai (Mainland China)