Other Income (Details) $ in Thousands	12 Months Ended
	Jan. 01, 2023 USD ($)	Jan. 02, 2022 USD ($) restaurant	Jan. 03, 2021 USD ($) transaction restaurant
Other Income and Expenses [Abstract]
Other Operating Income (Expense), Net	$ 926	$ 1,186	$ 1,271
Sale and Leaseback Transaction, Gain (Loss), Net	425	22	(189)
Property, Plant and Equipment, Disposals	1,200	1,200	1,000
Gain on insurance recoveries		$ (1,300)	$ (2,100)
Number Of Restaurants Subject To Insurance Recovery | restaurant		2	4
Number Of Sale-leaseback Transactions In Gain Position | transaction			12
Gain on Sale of Litigation Claim	(2,500)	$ (1,100)
Sales-type and Direct Financing Leases, Profit (Loss)	$ 400