Given two different points A and B, your task is to find a regular polygon of n sides, passing through these two points, so that the polygon area is minimized.
There will be at most 100 test cases. Each case contains 5 integers xA, yA, xB, yB, n (0<=xA,yA,xB,yB<=100, 3<=n<=10000), the coordinates of A and B, and the number of sides of the regular polygon. The two points A and B are always different. The last test case is followed by a line with five zeros, which should not be processed.
For each test case, print the smallest area of the regular polygon to six decimal places.
0 0 1 1 4 1 2 3 4 5 2 3 4 5 6 0 0 0 0 0
1.000000 5.257311 5.196152