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Default MAXIF style function

I need a function that works just like COUNTIF or SUMIF but is MAXIF instead.

Basically

A B
Dog 5
Dog 6
Cat 7
Bird 2
Cat 5

I want to look for Dog in Column A and get the max value associate with
those rows in Column B. I am thinking I can do this with an Array Function,
but can't seem to get my head arround it.
 
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