CUBOIDALOID

Let $p$, $q$ and $r$ be integers. Consider the following set of abc small cubes: {( (p+i) mod A, (q+j) mod B, (r+k) mod C ) | $i$, $j$ and $k$ are integers satisfying 0 i < a , 0 j < b , 0 k < c} A set of small cubes that can be expressed in the above format using some integers $p$, $q$ and $r$, is called a Unique cuboid of size $a×b×c$. Find the number of the sets of Unique cuboids of