what level is higher in this contest: $ O $ or $ A $? some solutions?

A polygon may be described by an ordered tuple of vectors with vanishing sum. Let $P$ and $Q$ be denoted by $\left(p_i\right)_{i=1}^m$ and $\left(q_j\right)_{j=1}^n$. It is easy to see that $f(P,Q) = \frac{1}{2}\sum_{i=1}^m \sum_{j=1}^n \left|p_i \cdot q_j\right|$. This is certainly a symmetric function. (The convexity requirement is essential and it is related to the factor $\frac{1}{2}$ in front of the summation.)