ONLY THE WORD EXPLANATION NEEDED NO CODE PLEASE. Also include PSEUDOCODE $-($pointers are not allowed$)$

You are consulting for an oil company, which is planning a large

pipeline $($called the huge pipeline$)$ running horizontally from east to west through an oil field of n wells. From each well, a spur pipeline is to be connected directly to the main pipeline along a shortest path $($going to either the north or the south$).$ Suppose that there are n wells, represented by n points p$1,$ p$2,...,$ pn in the plane. We are given the x$-$ and y$-$coordinates of the n wells pi $=($xi$,$ yi$)$ for i $=1,2,3,..,$ n$.$ Note that the wells are not given in any sorted order. Our goal is to pick an optimal location for the main pipeline $($i$.$e$.,$ find the y$-$coordinate of the main pipeline$)$ such that the total sum of the lengths of the spur pipelines is minimized. For simplicity, we assume that no two wells have the same x$-$coordinate or y$-$coordinate.

Design an O$($n$)$ time algorithm to compute an optimal location for the main pipeline. The answer is not the median of the sorted y$-$coordinates