$($a$)$ Write code to apply k$-$means to cluster the data points with the initial centroids as follows. Display the resulting cluster labels of the data points, cluster centroids, number of iterations performed, and inertia. $[10]$

$$ Data points: $(0,1),(5,2),(4,1),(4,2),(2,1),(6,3),$ and $(1,3)$

$$ Initial centroids of C$0$ and C$1$: $(2,1)$ and $(4,3)$