Roads in Chefland

In Chefland, there are $N$ cities (numbered $1$ through $N$). Initially, there are no roads between them. The Mayor of Chefland has ordered engineers to build roads across Chefland in such a way that each city is reachable from all other cities. For each pair of distinct cities $i$ and $j$, the cost of building a road between these cities is equal to ($i \wedge j$), where $\wedge$ denotes the b