Given a collection D of documents. For any keyword $($or index term$)$ w$,$ the document frequency d f subscript w is the number of documents in D that contain w$.$ We sort all keywords in decreasing order of their document frequencies. Let r subscript w denote the rank, i$.$e$.,$ the position of w in the sorted list. Assume that we have the following Zipf$$s Law:

d f subscript w space equals space A over r subscript w

Here, A is constant. Suppose that there are N distinct keywords. Under the above Zipf$$s Law, what is the size of the inverted indices for D$?$