1984 AIME Problem 4

Let S be a list of positive integers - not necessarily distinct - in which the number 68 appears. The arithmetic mean of the numbers in S is 56. However, if 68 is removed, the arithmetic mean of the numbers is 55. What's the largest number that can appear in S?

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.