Planting Trees

Kerim is an environment-friendly guy. Today, he accepted Samir's challenge of planting 20 million trees by 2020. Currently, there are $N$ trees (numbered $1$ through $N$) planted at distinct positions on a line; for each valid $i$, the position of the $i$-th tree is $A_i$. A set of trees is *beautiful* if for each tree in this set (let's denote its position by $x$), there is a tree at the posit