Let $p$ be a fixed prime number. Jomland has $p$ cities labelled $0,1,\dots,p-1$. Navi is a traveller and JomAirlines only has flights between two cities with labels $a$ and $b$ (flights are available in both directions) iff there exist positive integers $x$ and $y$ such that \[ \begin{cases} a \equiv x^2 + 2025xy + y^2\pmod{p}\\ b \equiv 20x^2 + xy + 25y^2\pmod{p} \end{cases} \]Prove that: i) There exist infinitely many primes $p$ such that there exist $2$ cities where Navi cannot start from one city and get to the other through a sequence of flights; ii) There exist infinitely many primes $p$ such that for any $2$ cities, Navi can start from one city and get to the other through a sequence of flights. (Proposed by Ivan Chan Guan Yu)