You are excavating what remains of a very old Indian temple. The architecture of the temple is very curious: you found a line of $$$N$$$ towers of different heights (no two towers have the same height), all spaced by one meter (the radius of each tower is supposed to be negligible).

During the excavations, you find something which might explain this curious architecture: the tomb of the architect. You find the following epitaph on the tomb:

You wonder how to compute this sum, this "enlightenment score" of the temple.

You are given a positive integer $$$N$$$ corresponding to the number of towers, and an array $$$H$$$ of $$$N$$$ distinct non-negative integers corresponding to the heights of the towers. $$$H_0$$$ is the height of the leftmost tower, $$$H_1$$$ is the height of the tower to the right of $$$H_0$$$, and so on. Finally, $$$H_{N-1}$$$ is the height of the rightmost tower. Observe that the distance between any two towers, in meters, is the absolute value of the difference of their respective indices in the array $$$H$$$. Let $$$p$$$ denote the index of the tallest tower in $$$H$$$ and define, for every $$$i\neq p$$$, $$$$$$ d(i) =\min\{ |i-j|\mbox{: for every $j$ such that $H_j \gt H_i$\}.} $$$$$$ Note that $$$d(p)$$$ is not defined. The "enlightenment score" of the temple is then given by $$$$$$ \sum_{i=0 , i\neq p}^{N-1} d(i). $$$$$$