Maximum Length of a Constrained Sequence

Consider a decreasing sequence of $n$ positive integers $x_1>x_2>\cdots>x_n$ that satisfies the following conditions: The average of the first $3$ terms in the sequence is $2025$. For all $4 \le k \le n,$ the average of the first $k$ terms is $1$ less than the average of the first $k - 1$ terms. What is the greatest possible value of ${n?}$