Little Tomy likes to cover his bread with some milk. He does this by putting it in the cup so that one of its sides (called bottom side) touches the bottom of the cup, just as the picture below:
The input will contain no more than 10 test cases. Each test case begins with a line containing three integers n,k and h (3<=n<=20, 0<=k<=8, 0<=h<=10). A piece of bread is guaranteed to be a convex polygon of n vertices. In the following n lines, each line contains two integers xi and yi(0<=xi,yi<=1000), representing the Cartesianism coordinate of the ith vertex. The vertices are anti-clockwise numbered. The test case containing n=0, k=0, h=0 will terminate the input, you should not give an answer to this case.
Output the area of the largest possible area of bread covered with milk with two decimal places. Output one line for each test case.
4 2 1 1 0 3 0 5 2 0 4 0 0 0
7.46