I'm looking for a reference in a published paper or book of the following fact.
Consider an element $\sigma \in A_n$, where $A_n$ is the alternating group on $n$ elements, and $n\geq 3$. Then $\sigma$ can be written as the product of at most $\lfloor \frac{n}{2} \rfloor$ three-cycles.
I already know that this is true (it is just an induction on $n$ with some cases depending on the cycle-type of the element $\sigma$). However, I would be grateful if somebody can help me find a reference for this. When I look around I find a lot of material about $A_n$ being generated by $3$-cycles, but nothing about this "minimal number".
Thank you very much for your help.