Filling a Board with N-Ominoes

An N-omino is a flat shape made of $N$ unit squares joined edge to edge. A 1-omino is a single $1 \times 1$ square. An N-omino is an (N-1)-omino with one more $1 \times 1$ square attached along an edge. Two N-ominoes count as the same shape when one can be rotated or flipped onto the other.

The five possible 4-ominoes are shown below.

Some of the 108 7-ominoes are shown below.

Richard and Gabriel play the following game for fixed $X$, $R$ and $C$.

1. Richard chooses one of the possible X-ominoes.
2. Gabriel fills the $R \times C$ board with X-ominoes so that no cell is left empty and no piece sticks out. He must use at least one copy of the X-omino Richard chose, and every piece may be rotated or flipped.

Gabriel wins if he fills the board under these rules, and Richard wins if Gabriel cannot. Given $X$, $R$ and $C$, decide which player wins.

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

Each of the next $T$ lines contains $X$, $R$ and $C$, separated by spaces.

$1 \le T \le 100$, $1 \le X, R, C \le 20$

For each test case, print one line in the form Case #x: y. Here $x$ is the test case number starting from 1. If at least one X-omino guarantees a win for Richard, $y$ is RICHARD. If no such X-omino exists, $y$ is GABRIEL.

In test case 1 of the sample, the only 2-omino Richard can choose is the $1 \times 2$ rectangle. Two of those rectangles always fill a $2 \times 2$ board, so Gabriel wins.

In test case 2 the only choice is again the $1 \times 2$ rectangle. Wherever Gabriel puts it on a $1 \times 3$ board, one cell is left over, so Richard wins.

In test case 3 Richard chooses the 4-omino shaped like a $2 \times 2$ square. It has nowhere to go on a $1 \times 4$ board, so Richard wins.

In test case 4 Richard can choose the straight $1 \times 3$ tromino or the L shaped tromino. In both cases Gabriel fills the $2 \times 3$ board with two copies of the same shape, so Gabriel wins.