CubesOnATable

You have exactly 150 unit cubes. You also have a small square table. The horizontal surface of the table is divided into a grid of 10x10 unit squares. Let's label the cells of this grid (0,0) through (9,9).

We can now naturally extend the 2-dimensional grid into a 3-dimensional grid of unit cube cells going upwards from the table. Each cell of this grid will have coordinates (x,y,z) with 0 <= x,y <= 9 and with 0 <= z. (Cells with z = 0 touch the surface of the table.)

Place some of your cubes onto the table, as follows:

• Each cube must exactly fill one of the cube cells of the grid defined above.
• The set of cubes must be stable. That is, if you have a cube at (x,y,z+1), you must also have a cube at (x,y,z).
• The total surface area of your creation must be surface. A face of a cube counts as surface if and only if it has a cube on one side and air on the other side.

If there is no solution, return an empty int[]. If your solution consists of cubes (x1,y1,z1), (x2,y2,z2), and so on, return the following int[]: { x1, y1, z1, x2, y2, z2, ... }. If there are multiple solutions, you may construct and return any of them. The order of cubes in your output may be arbitrary.