Triangle Pizza

A pizzeria has launched a "triangle pizza" whose every slice is shaped like an equilateral triangle.

A triangle pizza is built from equilateral triangular slices that are all the same size and are joined into a single connected piece. Two slices are considered directly connected when they share an edge.

Write a program that counts the number of distinct shapes a triangle pizza made of exactly $N$ slices can take.

Two shapes are considered the same if one can be rotated and translated so that it exactly overlaps the other. (Flipping the shape over is not allowed.)

The first line contains the number of test cases $T$.

Each test case consists of a single line containing $N$, the number of slices in the triangle pizza. ($1 \le N \le 16$)

For each test case, print one line in the format Case #x: y, where $x$ is the test case number (starting from 1) and $y$ is the number of distinct triangle-pizza shapes that can be formed from $N$ slices.