Count the number of cells in a range containing one of the following (1) a text string (2) a blank (3) a zero

[diversification]

I'm having a heck of a time writing a formula that counts how many of the cells are one of the following things: (1) a text string (2) a blank (3) a zero. To be clear, by "zero" I mean that the cell = 0.

Example: Let's say that this is our range of cells, starting with Cell A1. If we have the following cells, I'd like a formula to identify that there are 5 matches to the criteria I mentioned.

5
21458
h249fks9
4100@15
0
214100
78
?????

I've tried COUNTIF, COUNTIFS, SUMPRODUCT, ISTEXT, ISNUMBER, ISBLANK, AGGREGATE, and various combinations therein, and I cannot get it. Can anyone help me write something that'll work?

 

[Fluff]

How about

Fluff.xlsm
	A	B	C
1
2	5		5
3	21458
4
5	h249fks9
6	4100@15
7	0
8	214100
9	78
10	?????
Data

Cell Formulas
Range	Formula
C2	C2	=SUM(COUNTIFS(A2:A10,{"?*","",0}))