13040 - Flyovers of Khaka

[Hikari9]

Problem description says:
"So the Government has decided to let Bodi travel each road only once and build some flyovers, which connects two notable places, so that he can complete his visit to all the notable places while going through every road in Khakha city."

I'm confused. Is this euler path creation, hamiltonian path creation or both? I don't think it's hamiltonian, because it says everything is connected already. I tried forcing the euler path through greedily adding cheapest flyovers while odd degrees exceed 2, but it gets WA. Help please? :C