--description--

Let $f(n)$ represent the number of ways one can fill a $3×3×n$ tower with blocks of $2×1×1$. You're allowed to rotate the blocks in any way you like; however, rotations, reflections etc of the tower itself are counted as distinct.

For example (with $q = 100\,000\,007$):

$$\begin{align} & f(2) = 229, \\ & f(4) = 117\,805, \\ & f(10)\bmod q = 96\,149\,360, \\ & f({10}^3)\bmod q = 24\,806\,056, \\ & f({10}^6)\bmod q = 30\,808\,124. \end{align}$$

Find $f({10}^{10000})\bmod 100\,000\,007$.

--hints--

buildingTower() should return 96972774.

assert.strictEqual(buildingTower(), 96972774);

--seed--

--seed-contents--

function buildingTower() {

  return true;
}

buildingTower();

--solutions--

// solution required