I'm looking for a tight bound for Turan number $ex_2(n,K_{1,t,t})$, where $K_{1,t,t}$ is the complete 3-partite graph with parts of size 1, t, and t.

The motivation is that we now $ex_2(n,K_{t,t})=O(n^{2-\frac{1}{t}})$ for complete bipartite graph with parts of size t and t. And $ex_2(n,K_{t,t,t})=O(n^2)$. Therefore there should be a bound of $ex_2(n,K_{1,t,t})$ between $n^{2-\frac{1}{t}}$ and $n^2$. I wonder if there is some result in this area.