Suppose that S is a finite set of positive integers. If the greatest integer in S is removed from S then the average value (arithmetic mean) of the integers remaining is 32 If the least integer in S is also removed, then the average value of the integers remaining is 35 If the greatest integer is then returned to the set, the average value of the integers rises to 40 The greatest integer in the original set S is 72 greater than the least integer in S What is the average value of all the integers in the set S?

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