Parsing Greek Words

In the Epistle of Diognetus, we find the word: ἀφυλάκτως.

The context is:  οὐ πολὺ πλέον αὐτῶν καταφρονεῖτε; οὐ πολὺ μᾶλλον αὐτοὺς χλευάζετε καὶ ὑβρίζετε, τοὺς μὲν λιθίνους καὶ ὀστρακίνους σέβοντες ἀφυλάκτως, τοὺς δὲ ἀργυρέους καὶ χρυσοῦς ἐγκλείοντες ταῖς νυξί, καὶ ταῖς ἡμέραις φύλακας παρακαθιστάντες, ἵνα μὴ κλαπῶσιν;

Which Michael Holmes translates as:

“Are you not mocking and insulting them [the gods] much more when you leave unguarded the stone or pottery gods you worship but lock up the silver and gold ones at night and post guards by them during the day, lest they be stolen?”

But my question is, how are we to parse ἀφυλάκτως? Logos parses it as Accusative, Plural, Masculine, but according to Perseus, it could also be parsed as an Adverb (they also mention that if a noun, it could be feminine but that irrelevant here). Holmes’ translation seems to assume an adverbial usage, but that’s the translation, which isn’t exactly “literal” (though the meaning is rightly conveyed). It could be translated as a noun with something like:

“Are you not mocking and insulting them [the gods], by worshipping the unguarded ones made of stone and pottery, but locking up those made of silver and gold at night, and posting guards for them by day, to prevent them from being stolen?”

If it is parsed as a noun, then this is an excellent example of Y1 Hyperbaton appearing in relation to a μένδέ construction where the strong contrastive focus is clearly evidence. If its parsed as an adverb, then well, its not an example of anything.

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