1989 AIME Problem 11

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^{}_{}.)

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.