To be considered grade AA, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AA eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AA eggs are used, the shells are all discarded, and no mass is lost in the cooking process?

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To be considered grade AA, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AA eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AA eggs are used, the shells are all discarded, and no mass is lost in the cooking process?