What is the formula for listing all non empty cells in a range of cells

I'm trying to gather all of the non empty cells in a n x n range of cells, then output them in a single column that I can drag the fill handle to automatically grab the next valid value. I'm running office 2016 so no FILTER Function.The values need to be collected by top to bottom, and then left to right, so for example:

A1A2A3B1B2B3... and so on

See, below for a basic demonstration of what I have and what I need to output.