Product Pain

For a given array $B_1, B_2, \ldots, B_M$ of length at least $3$, let's define its **weight** as the largest value of $(B_i-B_j)\cdot(B_j-B_k)$ over all possible triples $(i, j, k)$ with $1 \le i, j, k \le M$ and $i \neq j, j \neq k, k \neq i$. You are given a sorted array $A_1, A_2, \ldots, A_N$ (that is, $A_1 \le A_2 \le \ldots \le A_N$). Calculate the sum of weights of all contiguous subarray