CN-LEAGUE 2020 Problem 2

Let $n\geq3$ be a given integer, and let $a_1,a_2,\cdots,a_{2n},b_1,b_2,\cdots,b_{2n}$ be $4n$ nonnegative reals, such that $$a_1+a_2+\cdots+a_{2n}=b_1+b_2+\cdots+b_{2n}>0,$$ and for any $i=1,2,\cdots,2n,$ $a_ia_{i+2}\geq b_i+b_{i+1},$ where $a_{2n+1}=a_1,$ $a_{2n+2}=a_2,$ $b_{2n+1}=b_1.$ Detemine the minimum of $a_1+a_2+\cdots+a_{2n}.$