Dutch Mathematical Olympiad

Albert makes a sequence of numbers, the first $2023$ of which are exactly the numbers $1$ through $2023$, in some order. To determine each subsequent number, Albert takes the median of the $2023$ previous numbers. You find the median of $2023$ numbers by sorting them by size and taking exactly the middle number from that sequence. How many different values can the three thousandth number of Albert's sequence have?