Impairment Of Long-Lived Assets And Other Lease Charges (Details) $ in Millions	12 Months Ended
	Jan. 01, 2023 USD ($) restaurant	Jan. 02, 2022 USD ($)	Jan. 03, 2021 USD ($) restaurant
Impaired Long-Lived Assets Held and Used [Line Items]
Impairment and other lease charges	$ 4.9	$ 4.5	$ 12.8
Impairment charges	2.8	3.9	8.2
Other lease charges	$ 2.1	0.6	$ 4.6
Impairment, Nonoperating		$ 1.9
Asset impairment charges, number of restaurants	15	9	15
Asset Impairment Charges, Number of Restaurant Closures | restaurant			22
Asset Impairment Charges, Right of First Refusal			$ 2.0
Previously Impaired [Member]
Impaired Long-Lived Assets Held and Used [Line Items]
Impairment charges	$ 0.7	$ 0.5	1.2
Initial Impairments [Member]
Impaired Long-Lived Assets Held and Used [Line Items]
Impairment charges	2.1	$ 1.5	$ 5.0
Other Lease Charges
Impaired Long-Lived Assets Held and Used [Line Items]
Long-lived Assets Impairment and Other Lease Charges	$ 1.7
Closed Restaurants [Member]
Impaired Long-Lived Assets Held and Used [Line Items]
Asset Impairment Charges, Number of Restaurant Closures | restaurant	8