Firdavs and Planet F

Firdavs is living on planet F. There are $N$ cities (numbered $1$ through $N$) on this planet; let's denote the value of city $i$ by $v_i$. Firdavs can travel directly from each city to any other city. When he travels directly from city $x$ to city $y$, he needs to pay $f(x, y) = |v_y-v_x|+y-x$ coins (this number can be negative, in which case he receives $-f(x, y)$ coins). Let's define a simple