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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