# A Meeting of Dragons

Calculus Level 5

Dragons are meeting in a convention center for a brainstorm. The delegates have to be selected to provide the maximum efficiency of the brainstorm session. A dragon has any (integer) amount of heads, and for any $$N$$, any amount of $$N$$-headed dragons is available if needed. The problem is that the size of the convention center is limited so no more than $$1000$$ heads can fit into the assembly hall. The intellectual power of a dragon pack is the product of head numbers of dragons in the pack. How many dragons are there in an optimal pack of dragons at the convention center?

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