--description--

Let $n$ be a positive integer. An integer triple ($a$, $b$, $c$) is called a factorisation triple of $n$ if:

• $1 ≤ a ≤ b ≤ c$
• $a \times b \times c = n$.

Define $f(n)$ to be $a + b + c$ for the factorisation triple ($a$, $b$, $c$) of $n$ which minimises $\frac{c}{a}$. One can show that this triple is unique.

For example, $f(165) = 19$, $f(100\,100) = 142$ and $f(20!) = 4\,034\,872$.

Find $f(43!)$.

--hints--

factorisationTriples() should return 1177163565297340400.

assert.strictEqual(factorisationTriples(), 1177163565297340400);

--seed--

--seed-contents--

function factorisationTriples() {

  return true;
}

factorisationTriples();

--solutions--

// solution required