Superlative form of dirty; the most unclean, soiled, or contaminated; also can mean the most morally corrupt or unfair.
From Old English dryge meaning 'dry,' which evolved to mean 'earth' and 'soil,' eventually becoming 'dirty.' The -iest suffix forms the superlative (most extreme version) of an adjective.
It's fascinating that 'dirty' can mean physically unclean OR morally wrong—we use the same word for mud on your shirt and cheating in a game! This shows how humans think of moral corruption as a kind of filth that needs washing away.
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