4. For a positive integer $n$, if $(x y-5 x+3 y-15)^{n}$ is expanded and like terms are combined, $x^{i} y^{j}(i, j=0,1$, $\cdots, n)$ after combining have at least 2021 terms, then the minimum value of $n$ is $\qquad$.
The expansion of $(x y-5 x+3 y-15)^{n}=(x+3)^{n}(y-5)^{n}$ has $(n+1)^{2}$ terms, so $(n+1)^{2} \geqslant 2021 \Rightarrow n+1 \geqslant 45 \Rightarrow n \geqslant 44$.