Chef and Travel

A country CHEFLAND has $N$ cities numbered $1, 2… N$. All cities are connected to each other by some distance. The distance $D_{ij}$ between two cities $i$ and $j$ for every $1 \leq i, j \leq N$ is *the minimum value obtained by expression* – $ix + jy$ , where $x$ and $y$ are non-negative integers. CHEF wants to travel from his home city $H$ to every city in CHEFLAND and return back to his home c