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The word 一溜烟 is formed by the sequential combination of the numeral 一 (one), the verb 溜 (to slip or glide), and the noun 烟 (smoke), creating a literal meaning of "a glide of smoke" which functions as an idiomatic adverbial phrase to depict rapid motion, metaphorically comparing the speed to the swift dispersal of smoke.

Word Definition - 一溜烟

yī liù yān like a wisp of smoke; (to disappear etc) in an instant