Temple of Dune

The Archaeologists of the Current Mille- nium (ACM) now and then discover an- cient artifacts located at the vertices of regular polygons. In general it is neces- sary to move one sand dune to uncover each artifact. After discovering three ar- tifacts, the archaeologists wish to com- pute the minimum number of dunes that must be moved to uncover all of them. Input The first line of input contains a positive integer n, the number of test cases. Each test case consists of three pairs of real numbers giving the x and y coordinates of three vertices from a regular polygon. Output For each line of input, output a single integer stating the fewest vertices that such a polygon might have. You may assume that each input case gives three distinct vertices of a regular polygon with at most 200 vertices. Sample Input 4 10.00000 0.00000 0.00000 -10.00000 -10.00000 0.00000 22.23086 0.42320 -4.87328 11.92822 1.76914 27.57680 156.71567 -13.63236 139.03195 -22.04236 137.96925 -11.70517 129.400249 -44.695226 122.278798 -53.696996 44.828427 -83.507917 Sample Output 4 6 23 100