Yummy Triangular Pizza

Time Limit: 32000 ms Memory Limit: 524288 KiB

Problem Description

       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).
179

Input

 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)

Output

 For each test case, output a single integer denoting the number of possible different shapes of the pizza.

Sample Input

3
2
4
10

Sample Output

Case  #1:  1
Case  #2:  4
Case  #3:  866

Hint

 

Source

2011 The 36th ACM-ICPC Asia Shanghai Regional Contest - hosted by Fudan University