For two distinct points p$1=($x$1,$ y$1)$ and p$2=($x$2,$ y$2)$ in the plane, we say that p$2$ dominates p$1$ if x$1$ x$2$ and y$1$ y$2.$ For a set P $=\{$p$1,$ p$2,...,$ pn$\}$ of n points in the plane, a point pi in P is called a maximal point in P if pi is not dominated by any other point in P $.$ Suppose for a set P $=\{$p$1,$ p$2,...,$ pn$\}$ of n distinct points in the plane, the points in P are not given in any sorted order. When we studied the divide$-$and$-$conquer strategy, an O$($n log n$)$ time algorithm for computing all the maximal points in P was presented in class. Here, you are asked to prove that the problem of computing all the maximal points in P $($and reporting such points in the increasing order of their x$-$coordinates$)$ has a lower bound of $($n log n$)$ time.