Clustering $(20$ pts$)$: Consider the following approach to grouping n distinct objects p$1$ pn on which a distance function d$($pi$,$ pj$)$ is defined such that d$($pi$,$ pi$)=0,$ d$($pi$,$ pj$)>0$ if i $/$:$=$ j $($that is$,$ pi and pj are distinct objects$),$ and d$($pi$,$ pj$)=$ d$($pj$,$ pi$)($distances are symmetric.$)$ The clusteringapproach is as follows: divide the n points into k clusters such that we minimize the maximum distance between any two points in the same cluster. That is$,$ we seeklow$-$diameter clusters. Supposewewant to know whether, for a particular set of n objects, and a bound B$,$ the objects can be partitioned into k sets such that no two points in the same set are further than B apart. Prove that this decision problem is NP$-$complete.