--description--

In a standard 52 card deck of playing cards, a set of 4 cards is a Badugi if it contains 4 cards with no pairs and no two cards of the same suit.

Let $f(n)$ be the number of ways to choose $n$ cards with a 4 card subset that is a Badugi. For example, there are $2\,598\,960$ ways to choose five cards from a standard 52 card deck, of which $514\,800$ contain a 4 card subset that is a Badugi, so $f(5) = 514800$.

Find $\sum f(n)$ for $4 ≤ n ≤ 13$.

--hints--

badugi() should return 862400558448.

assert.strictEqual(badugi(), 862400558448);

--seed--

--seed-contents--

function badugi() {

  return true;
}

badugi();

--solutions--

// solution required