Fixed Weight

A permutation of length $N$ is an array of $N$ integers $(P_1,P_2, \dots,P_N)$ where every integer from $1$ to $N$ (inclusive) appears in it exactly once. The weight of a subsegment containing the elements $(P_l,P_{l+1}, \dots,P_r)$ is defined as follows: $$W(l, r) = (r-l+1)\cdot \min\limits_{l\le i \le r} (P_i)$$ where $1\le l \le r \le N$ and $\min\limits_{l\le i \le r} (P_i)$ denotes the mini