Count value arrays in multiple columns and return per row sums

I'm trying to tally 7 columns and return the result for each row. But every variation of the formula I've tried has given the wrong result. Usually, it just tallies the entire range and returns the same result for every row.

=ArrayFormula(IF(I3:I>0,COUNT(B3:B,C3:C,D3:D,E3:E,F3:F,G3:G,H3:H),""))

This example should currently return "3,1,1", but it sums the range and returns "4,4,4"

Here's my sheet for reference.