Rearranging All Data To Three Columns

I have a worksheet that contains data in the first three columns and then the 4th column is empty and then there's data in the next three columns and then an empty column etc. How can I cut the data from columns E to G and I to K and M to O etc....and paste it directly below the data in columns A to C? I dont know how many columns of data there are in the worksheet and every set of 3 columns of data (eg. E to G) varies in size. I recorded the following macro of what I want to do.

Sub rearrange()
Range("E1:G1").Select
Range(Selection, Selection.End(xlDown)).Select
Selection.Cut
Range("A95").Select
ActiveSheet.Paste
Range("I1:K1").Select
Range(Selection, Selection.End(xlDown)).Select
Selection.Cut
Range("A203").Select
ActiveSheet.Paste
Range("M1:O1").Select
Range(Selection, Selection.End(xlDown)).Select
Selection.Cut
Range("A386").Select
ActiveSheet.Paste
End Sub