Random walk on $\mathbb Z_{2025}$ with uniform nonzero steps

Let $Z_1,Z_2,\dots$ be a sequence of independent and identically distributed random variables having discrete uniform distribution over $\{1,2,\dots,2024\}$. Let $Y_n=\sum_{i=1}^nZ_i$, $n\ge2$. Further, let $X_n$ be the remainder when $Y_n$ is divided by $2025$. Then, which of the following statements is true?