Joined Subarrays on Tree

Alice thought of a function $F$, which takes an arbitrary array of integers $A = (A_1, A_2, \ldots, A_M)$ as the only argument and is defined in the following way: - Consider all pairs of subarrays $(A_i, A_{i+1}, \ldots, A_j)$ and $(A_k, A_{k+1}, \ldots, A_l)$ such that: - $1 \le i \le j \lt k \le l \le M$ - both subarrays are non-decreasing - $A_j \le A_k$ - If there is no such