graff: kcott raised the most important points. To expand on that a bit...
Kind sorta almost ... the question/problem feels more at the fizz-buzz stage, the OP has a good idea (almost) its just translating it into code, and working through the hurdles, thats the issue
For example, if he can get $max to affect add_max ... then notice the issue with the update you mentioned
then its just a matter of adding a update limit clause
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