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Default Help! Need to ignore 0s and blank cells in average formula!

I have the following formula - which works - to calculate an average of
numbers that are listed in 3 separate columns:
=AVERAGE(E7:E126,M7:M129,U7:U128)

The problem is that I need the formula to ignore blank cells and cells that
contain a zero. I've tried many different things but just can't get it to
work!

Anyone have any suggestions?
Thanks in advance for your help!
 
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