Question: What is the minimum and maximum number of maximal frequent itemsets and closed frequent itemsets one can generate from this lattice?

I've been able to calculate the number of maximal and closed frequent nodes with a given list of transactions, but I'm not quite understanding this theoretical side of it. With a 5-itemset lattice, what are the min and max amount of those nodes? All maximal frequent itemsets are closed, but not all closed are maximal. Any guidance would be appreciated.

AB ANC AD AE BD BE CD CE DE ADE BCD BDE CDE ABCD ABCE ABDE ACDE DCDE BCDE AB ANC AD AE BD BE CD CE DE ADE BCD BDE CDE ABCD ABCE ABDE ACDE DCDE BCDE