The Biggest Restaurant

Chef Ada is building a new restaurant in the following way: - First, $N$ points $X_1, X_2, \ldots, X_N$ are chosen on the $x$-axis. - Then, $N$ columns (numbered $1$ through $N$) are made. For simplicity, the columns are represented as vertical segments; for each valid $i$, the height of the $i$-th segment is $H_i$. - Ada assigns a column to each of the points $X_1, X_2, \ldots, X_N$ in an arbitra