Can you solve this riddle?

Inspector Donna DiAnsa and police informer Stu Pidgeon sat together at a table in the Greasy Spoon Diner. Across the room, three men sat, talking. "You say those three are known as Slick, Smilely, and Mug," said the inspector, taking out her notebook,"but which is which Stu? My guess is that the one with the cigar is Smiley, the one wearing the hat is Slick, and the one with the mustache is Mug." "Wrong, all wrong."said Stu. Just then, the man with the mustache stood up and said,"It's time we took off Slick." The 2 other men gotup and all three left,without another word.
"Take another guess," said Stu. "which one is which?" "I don't need to guess," Donna DiAnsa said, putting her notebook away, and correctly named all three men. Can you?

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