For $r\ge 3$ let $d_r(e)$ be the minimal $d$ such that$${\mathrm{ex}}_r(n,\mathcal{F})=o(n^2),$$where $\mathcal{F}$ is the family of $r$-uniform hypergraphs on $d$ vertices with $e$ edges.Prove that$$d_r(e)=(r-2)e+3$$for all $r,e\ge 3$.