Suppose we are given the following dataset

$\{(0,4),(1,3),(2,6),(3,3),(5,5),(5,6),(9,9)\}.$

We apply $k-$means, with $k=3,$ to cluster the dataset using the Manhattan distance for computing the distances between centroids and pairs in the dataset. The Manhattan distance between $(x_1,y_1)$ and $(x_2,y_2)$ is defined as

$|x_1-x_2|+|y_1-y_2|$

Suppose that the initial clusters of $k-$means are $C_1,C_2$ and $C_3$ with

$\{(1,3),(3,3),(5,6)\}$

$\{(0,4),(2,6)\}$

$\{(5,5),(9,9)\}$

and that the centroids for $C_1,C_2$ and $C_3$ are $(3,4),(1,5)$ and $(7,7),$ respectively. If we then run $k-$means for two iterations, what are the new clusters and what are their respective centroids? PLEASE UPLOAD A HANDWRITTEN ANSWER