KMO 2023 Problem 6

For positive integer $n\geq 3$ and real numbers $a_1,...,a_n,b_1,...,b_n$ , prove the following. $$\sum_{i=1}^n a_i(b_i-b_{i+3})\leq\frac{3n}{8}\sum_{i=1}^n((a_i-a_{i+1})^2+(b_i-b_{i+1})^2)$$ ( $a_{n+1}=a_1$ , and for $i=1,2,3$ $b_{n+i}=b_i$ .)