There are n cities labeled from $0$ to $n - 1$, connected by $n - 1$ roads, so there is only one route between any two cities. This road network forms a tree structure.

Last year, the Ministry of transport made all roads one-way due to their narrow width. These roads are represented as connections, where each entry connections[i] $= [a_i, b_i]$ means there is a road going from city $a_i$ to city $b_i$ ...