Consider a connected undirected graph G with distinct edge costs. Design a linear$-$time algorithm to find a minimum bottleneck spanning tree, which is a spanning tree T that minimizes the maximum edge cost max$($e in T$)$ ce$.$ You can assume access to a subroutine FindMedian that, given as input an unsorted list of n numbers, computes the median in O$($n$)$ time.

please provide a brief justification $($one or two sentences$)$ for the correctness and running time of the algorithm.