--description--

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 colored using up to $c$ colors, so that no two adjacent vertices have the same color. The compound graph above is an example of a configuration of type $(2,2,6)$, in fact of type $(2,2,c)$ for all $c ≥ 4$

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 $N(25,75,1984)$.

--hints--

coloredConfigurations() should return 61190912.

assert.strictEqual(coloredConfigurations(), 61190912);

--seed--

--seed-contents--

function coloredConfigurations() {

  return true;
}

coloredConfigurations();

--solutions--

// solution required