--description--

The minimum number of cubes to cover every visible face on a cuboid measuring 3 x 2 x 1 is twenty-two.

If we add a second layer to this solid it would require forty-six cubes to cover every visible face, the third layer would require seventy-eight cubes, and the fourth layer would require one-hundred and eighteen cubes to cover every visible face.

However, the first layer on a cuboid measuring 5 x 1 x 1 also requires twenty-two cubes; similarly, the first layer on cuboids measuring 5 x 3 x 1, 7 x 2 x 1, and 11 x 1 x 1 all contain forty-six cubes.

We shall define $C(n)$ to represent the number of cuboids that contain $n$ cubes in one of its layers. So $C(22) = 2$, $C(46) = 4$, $C(78) = 5$, and $C(118) = 8$.

It turns out that 154 is the least value of $n$ for which $C(n) = 10$.

Find the least value of $n$ for which $C(n) = 1000$.

--hints--

cuboidLayers() should return 18522.

assert.strictEqual(cuboidLayers(), 18522);

--seed--

--seed-contents--

function cuboidLayers() {

  return true;
}

cuboidLayers();

--solutions--

// solution required