Problem $1.[3$ points$]$ Take the following points in a twodimensional space: $(8,4),(3,3),(4,5),(0,1),(10,2),(3,7),(0,9),(8,1),(4,3),(9,4).$ For this exercise, use the Manhattan distance metric. Beginning with centroids at $(1,1)$ and $(8,8),$ do two iterations of the $2-$means clustering algorithm, that is:

allocate the points to centroids, then find new centroids.

again, allocate the points to centroids, and then the new centroids

If a point is equidistant between the centroids, assign it to the centroid that starts at $(1,1).$ What are the resulting centroids and resulting clusters?