Array Formula Question

I have a list of words.

I need to count how many of those words are made using ONLY the letters D, O, and G (not case sensitive).

For example, if the list of words was:

dog, toe, go, dot, got, god, get, doe, Do

the formula should return the value 4 (dog, go, god, Do).

I know I could hash this out with regex in a VBA macro, but I was hoping there was an easier way to get this done with a formula (there's no regex in an excel formula, right?).

I've tried using some pretty ugly array formulas, where I sort of "brute force" every possible combination, such as...

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but it just gives me either a 1 or a 0.

I'm working on Excel 2007 if it matters.

Any help is appreciated, thanks!