a sample of 121 integers is given, each between 1 and 1000 inclusive, with repetitions allowed. the sample has a unique mode (most frequent value). let $d$ be the difference between the mode and the arithmetic mean of the sample. what is the largest possible value of $\lfloor d\rfloor$? (for real $x$, $\lfloor x\rfloor$ is the greatest integer less than or equal to $x$.)