Restaurant Impairments, Closure Costs and Asset Disposals - Narrative (Details) $ in Thousands	12 Months Ended
	Jan. 02, 2024 USD ($) restaurant	Jan. 03, 2023 USD ($) restaurant	Dec. 28, 2021 USD ($) restaurant
Restructuring and Related Activities [Abstract]
Number of restaurants impaired	2	4	6
Number of Restaurants With Lease Related Assets Written Down	4	2	1
Number of Restaurants With Lease Related Assets Written Down, Previously Closed Restaurants	2		1
Write down related to assets held for sale | $			$ 500
Number of restaurants closed	6	5	12
Offset adjustment to closure costs related to lease terminations | $	$ 200	$ (100)	$ 200
Loss on disposal | $	$ 300
Disposal Group, Not Discontinued Operation, Gain (Loss) on Disposal, Statement of Income or Comprehensive Income [Extensible Enumeration]	Restaurant impairments, closure costs and asset disposals
Number of Restaurants Sold		15