f $G$ is generated by 2 elements, and has a free subgroup $L$ of rank $n+1$, where $|G:L|=n$, then $G$ is free of rank $2$.

Question

A question from a past exam paper I am trying to solve:

If $G$ is generated by 2 elements, and has a free subgroup $L$ of rank $n+1$, where $|G:L|=n$, then $G$ is free of rank $2$.

I am not sure how to go about this. I understand how to prove the sort of converse, that if $G$ were free of rank $2$ and $L$ a subgroup of index $n$ then $L$ free of rank $1 + n(2-1) = n + 1$ (Neilsen-Schreier) but I can't seem to get started with this.

Any hints or help would be appreciated.