YUMMY - Yummy Triangular Pizza
Pizzahat has released a new pizza with triangular shaped pieces. This pizza is composed of some equal-sized equilateral triangle. Moreover, all the triangles are connected. Also, if two triangles are directly connected, they must share a common edge.
How many different shapes of this kind of N-pieces pizza are there? Two patterns are considered as same if they can completely overlap after rotation and shifting (note that flipping is not included).
There are multiple test cases. The first line of input contains a single integer denoting the number of test cases.
For each test case, there is only one line with only one integer N denoting the number of pieces that can be used. (1 <= N <= 16)
For each test case, output a single integer denoting the number of possible different shapes of the pizza.
Input: 3 2 4 10 Output: Case #1: 1 Case #2: 4 Case #3: 866
This problem is first (and only) solved by team Cabbage (Zhongnan University) at 225 minutes after the onsite contest starts. (They have 1 wrong try before they get Accepted.)