A polycube is a solid made by gluing together unit cubes (one unit on each edge) on one or more
faces. The figure in the lowerleft is not a polycube because some cubes are attached along an
edge.
For this problem, the polycube will be formed from unit cubes centered at integer lattice points in
3space. The polycube will be built up one cube at a time, starting with a cube centered at (0,0,0). At
each step of the process (after the first cube), the next cube must have a face in common with a cube
previously included and not be the same as a block previously included. For example, a 1by1by5
block (as shown above in the upperleft polycube) could be built up as:
(0,0,0) (0,0,1) (0,0,2) (0,0,3) (0,0,4)
and a 2by2by2 cube (upperright figure) could be built as:
(0,0,0) (0,0,1) (0,1,1) (0,1, 0) (1,0,0) (1,0,1) (1,1,1) (1,1, 0)
Since the surface of the polycube is made up of unit squares, its area is an integer.
Write a program which takes as input a sequence of integer lattice points in 3space and determines
whether is correctly forms a polycube and, if so, what the surface area of the polycube is.

Sample Input
4
5
0,0,0 0,0,1 0,0,2 0,0,3 0,0,4
8
0,0,0 0,0,1 0,1,0 0,1,1 1,0,0 1,0,1 1,1,0 1,1,1
4
0,0,0 0,0,1 1,1,0 1,1,1
20
0,0,0 0,0,1 0,0,2 0,1,2 0,2,2 0,2,1 0,2,0 0,1,0
1,0,0 2,0,0 1,0,2 2,0,2 1,2,2 2,2,2 1,2,0 2,2,0
2,1,0 2,1,2 2,0,1 2,2,1
