1 AC-3 puts back on the queue every arc (X ,X ) whenever any value is deleted from the domain of Xi, even if each value of Xk is consistent with several remaining values of Xi.

Suppose that, for every arc (Xk,Xi), we keep track of the number of remaining values of Xi that are consistent with each value of Xk. Explain how to update these numbers efficiently and hence show that arc consistency can be enforced in total time O(n2d2).