Question 16Let $a_1,a_2,\ldots$ be a sequence with $a_1=1$ and $a_{n+1}=\frac{n+2}{n}S_n$ for all $n=1,2,\ldots$, where $S_n=a_1+a_2+\cdots+a_n$. Determine the minimum integer $n$ such that $a_n\ge2021$.