Topcoder: SRM 638 (Div. 1)

First Problem
Div 1. (300) - ShadowSculpture
Summary:
You are given a 3D array describing a 3D figure. Then a shadow is casted from the 3D figure to XY, YZ, and ZX planes (or in other words, XY, YZ and ZX contains the projection of the 3D object). Given the projections, output whether there is a possible 3D object satisfying the required projections, given that the object must be 6-connected (which means if two cubes are a part of the 3D object, then they must share a face).