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A3. Ordering a multiset

Given a multiset of real numbers {a1, ...,an} find expressions e1, ...,en such that {a1, ...,an} = {e1, ...,en}, and {ei} is a non-increasing sequence, where each expression is formed from the ai, the max function, and elementary arithmetic operations.
I will not post the answer to this problem, because I plan to publish it if it is not already known. If it is a known result, I would appreciate a reference.

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