Suppose we run the Multistage Algorithm on the data of Exercise $6\mathrm{.}3\mathrm{.}1,$ with the same support threshold of $4.$ The first pass is the same as in that exercise, and for the second pass, we hash pairs to nine buckets, using the hash function that hashes $\{$i$,$ j$\}$ to bucket i $+$ j mod $9.$ Determine the counts of the buckets on the second pass. Does the second pass reduce the set of candidate pairs? Note that all items are frequent, so the only reason a pair would not be hashed on the second pass is if it hashed to an infrequent bucket on the first pass.