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

• $1\le a\le b\le c$
• $a\cdot b\cdot c=n$.

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

For example, $f(165)=19$, $f(100100)=142$ and $f(20!)=4034872$.

Find $f(43!)$.