Water Supply

The country of Chefland has $N$ cities, with its capital being at city $1$. Unfortunately, the only source of water in the entire country is the capital, and so water must be sent via pipes to all the other cities. For each city $i \gt 1$, there is a *unique* city $p_i \lt i$ such that there is a pipe connecting cities $i$ and $p_i$. Note that this ensures every city is connected to city $1$ v