--description--

An $m×n$ maze is an $m×n$ rectangular grid with walls placed between grid cells such that there is exactly one path from the top-left square to any other square. The following are examples of a 9×12 maze and a 15×20 maze:

Let $C(m, n)$ be the number of distinct $m×n$ mazes. Mazes which can be formed by rotation and reflection from another maze are considered distinct.

It can be verified that $C(1, 1) = 1$, $C(2, 2) = 4$, $C(3, 4) = 2415$, and $C(9, 12) = 2.5720\mathrm{e}\,46$ (in scientific notation rounded to 5 significant digits).

Find $C(100, 500)$ and write your answer as a string in scientific notation rounded to 5 significant digits.

When giving your answer, use a lowercase e to separate mantissa and exponent. E.g. if the answer is 1234567891011 then the answer format would be the string 1.2346e12.

--hints--

amazingMazes() should return a string.

assert.isString(amazingMazes());

amazingMazes() should return the string 6.3202e25093.

assert.strictEqual(amazingMazes(), '6.3202e25093');

--seed--

--seed-contents--

function amazingMazes() {

  return true;
}

amazingMazes();

--solutions--

// solution required