Problem $3.$ Given the following points, show a K$-$means cluster and a hierarchical cluster. Show the calculation. The distance threshold for a K$-$means cluster is $2\mathrm{.}5.$ You can use an excel sheet to perform the distance based computation. Please show the whole process. Do not use mental calculations for clustering. Also mark the outliers for K$-$means cluster. Calculate the centroids at least two times. For the K$-$means cluster, take two seeds in the beginning, and use Excel sheet for the calculation. Please do not do manual calculations. It will consume too much time unnecessarily. Note that distances between two seed points and all eight given points have to be calculated before you decide which point will go to which cluster. For hierarchical cluster also, use Excel sheet for calculating the distance between the points. Since there are $8$ points and distances between each pair of points has to be calculated, total number of distances to be calculated are C$(8,2)=(8$ x $7)/2=28.$ Each time you fuse one pair with currently shortest distance, a new centroid is calculated. Fusion will join the population of both children clusters. You will also have to calculate the distance of this new centroid after fusion against all the remaining points$/$clusters and again find the pair with the shortest distance. The process continues until there is just one large cluster. $(1,1\mathrm{.}5),(2,4),(3,5),(4,6),(7,7),(6,8),(8,11),(9,12)$