Kingdom Division#1509
The king of Geometry-Land is in deep trouble. He has three sons who quarrel constantly. The king tried many different policies to stop them, but in vain. So, the king became anxious.
"How about dividing the kingdom?" the king thought to himself. He called the advisors and described his plan. They opened the map.
The kingdom is shaped like a triangle with vertices '', '', and ''. The king drew a line from to ( is any point on segment ) and a line from to ( is any point on segment ). The intersection of and was denoted by . This created four parts: (triangle ), (triangle ), (triangle ), and (quadrilateral ). The king decided to give the areas , , and to his three sons. Area would become the king's new kingdom. You are the head advisor. The king provides you the values , , and . You must find the value of . If it is not possible to determine , report this.
The input consists of at most tests. Each test contains three non-negative real numbers , , and (separated by spaces). Input is terminated by a test where a = -1. This test should not be processed.
For each test, print its number starting from . On the next line, print the value of (the area of the king's kingdom after division) rounded to decimal places, or Poor King! (without quotes) if the value of cannot be determined. The output format is shown in the sample.
Example 1