Min-Fund Country

There is a country which has $n$ houses and $m$ bi-directional roads between these houses, where the $i^{th}$ road connects house $u_i$ to $v_i$. A subset of these houses $S$ is called a *city* if any house in $S$ is reachable from any other house in $S$. Formally, a subset of houses $S$ is a city if $x$ and $y$ are reachable from each other for all $x, y \in S$. The funding required for a city $S