A toy company recently found that toys like revolver, ma- chine guns, fighting planes are making children violent and destroying the peace of the world. The parents also be- gan to avoid these toys and inclined to educational toys. So they decided to manufacture educational toys. One of these is a electric touch pad on which children can put four points and the program will automatically join the points to form a closed shape. Children will try to guess the shape and when they press a button then it will automatically an- nounce the shape. But they are struggling to determine the shape and seek your help. Your task is simple. You are given four points, no three of them are collinear, you have to output the simple polyg- onal shape formed by these points in the following order: Square Rectangle Rhombus Parallelogram Trapezium Ordinary Quadrilateral For example if it is possible to form a square with the four points you must output ‘Square’, if it is not possible to form a square but possible to form a rectangle you must output ‘Rectangle’ and so on. Input Input starts with an integer T, the number of test cases (T ≤ 50000). Each test case contains 4 lines. Each of the lines contains two space separated integers xi yi (−10000 ≤ xi,yi ≤ 10000) which are the coordinate values of a point. Output For each set of input output one line in the format ‘Case k: s’. Here k is the case number starting from 1 and s is the shape as described above. See sample input output for more details. Note: If you have forgotten elementary geometry, here is the definitions to remind you: • Square: All sides are of equal size all angles are 90◦ • Rectangle: Opposite sides are of equal size and all angles are 90◦ • Rhombus: All sides are of equal size but no angle is 90◦ • Parallelogram: Opposite sides are of equal size but no angle is 90◦ • Trapezium: Any two opposite sides are parallel but the other two is not. • Simple Polygon: Polygon having no self intersecting edge.
2/2 Sample Input 6 00 20 22 02 00 30 32 02 00 84 50 34 00 20 32 12 00 50 43 13 00 50 43 14 Sample Output Case 1: Square Case 2: Rectangle Case 3: Rhombus Case 4: Parallelogram Case 5: Trapezium Case 6: Ordinary Quadrilateral