Count cells if any criteria are met, not multiple criteria

So I need to count the number of values in a column (G), only if the cells in columns A-F have a value in them. If any (or multiple) cell in A-F has a value in it, (G) should be counted. I have attached a dummy file with a sample of what I'm looking for with this.

I've tried COUNTIFS and SUMPRODUCT functions with no luck, I'm sure it's just that I'm not sure how to format it to make it work.

Helper columns are okay as long as I can hide them later I can make pretty much anything work with this workbook.

I am using one cell to total the count of these and the cell range in the actual sheet is: S2:X21, each cell will either be blank or have a 1 in them. The cells counted in the actual cell are AG2:AG21. This value will be calculated in cell AK9. This is a large work file so I would love to make it work as soon as possible.

Any help is appreciated. Thank you!