Impairment Of Long-Lived Assets And Other Lease Charges (Details) $ in Millions	12 Months Ended
	Dec. 31, 2023 USD ($) restaurant	Jan. 01, 2023 USD ($) restaurant	Jan. 02, 2022 USD ($)
Impaired Long-Lived Assets Held and Used [Line Items]
Impairment and other lease charges	$ 7.6	$ 4.9	$ 4.5
Impairment charges	1.7	2.8	3.9
Other lease charges	$ 5.9	$ 2.1	$ 0.6
Asset impairment charges, number of restaurants	3	15	9
Impairment, Intangible Asset, Finite-Lived, Statement of Income or Comprehensive Income [Extensible Enumeration]	Impairment and other lease charges
Previously Impaired [Member]
Impaired Long-Lived Assets Held and Used [Line Items]
Impairment charges	$ 1.0	$ 0.7	$ 0.5
Initial Impairments [Member]
Impaired Long-Lived Assets Held and Used [Line Items]
Impairment charges	0.7	2.1	1.5
Other Lease Charges
Impaired Long-Lived Assets Held and Used [Line Items]
Long-lived Assets Impairment and Other Lease Charges	$ 5.7	$ 1.7
Closed Restaurants [Member]
Impaired Long-Lived Assets Held and Used [Line Items]
Asset Impairment Charges, Number of Restaurant Closures | restaurant	8	8
Non-Operating Properties
Impaired Long-Lived Assets Held and Used [Line Items]
Impairment charges			$ 1.9