Consider graphs built with the units $A$: and $B$: , where the units are glued along the vertical edges as in the graph .

A configuration of type $(a,b,c)$ is a graph thus built of $a$ units $A$ and $b$ units $B$, where the graph's vertices are coloured using up to $c$ colours, so that no two adjacent vertices have the same colour.
The compound graph above is an example of a configuration of type $(2,2,6)$, in fact of type $(2,2,c)$ for all $c\ge 4$.

Let $N(a,b,c)$ be the number of configurations of type $(a,b,c)$.
For example, $N(1,0,3)=24$, $N(0,2,4)=92928$ and $N(2,2,3)=20736$.

Find the last $8$ digits of $N(25,75,1984)$.