Difficult Choice

Chef and his mother are going travelling. Chef's world consists of $N$ cities (numbered $1$ through $N$) connected by $N-1$ bidirectional roads such that each city can be reached from any other city using roads. For each city, we know its age — the number of years elapsed since the foundation of the city; let's denote the age of city $i$ by $a_i$. First of all, Chef and his mother have to decide