Frobenius coin problem: 2025, b, c

Let $b$ and $c$ be positive integers with $2025 < b < c$. Suppose the integers $2025$, $b$, and $c$ have no common factors. Let $S$ be the set of all integers of the form $2025x + by + cz$ where $x, y, z$ are non-negative integers. Let $T$ be the set of all positive integers not in $S$; $T$ is finite.

Let $t_o$ denote the number of odd integers in $T$ and $t_e$ the number of even integers in $T$. How large can $|t_o - t_e|$ be? Prove your result and give an explicit choice of $b$ and $c$ that achieves this maximum.