System Optimization (Gains) Losses, Net Summary of Disposition Activity (Details) $ in Thousands	12 Months Ended
	Jan. 03, 2021 USD ($) number_of_restaurants	Dec. 29, 2019 USD ($) number_of_restaurants	Dec. 30, 2018 USD ($) number_of_restaurants	Jan. 01, 2017
Plant, Property and Equipment
Company-operated restaurant ownership percentage				5.00%
Number of restaurants classified as held for sale | number_of_restaurants	43	0
Proceeds from sales of restaurants	$ 6,091	$ 3,448	$ 3,223
System optimization gains, net	$ 3,148	$ 1,283	$ 463
Sale of franchise-operated restaurants to franchisees
Plant, Property and Equipment
Number of restaurants sold to franchisees | number_of_restaurants	54	37	96
Sale of company-owned restaurants to franchisees
Plant, Property and Equipment
Number of restaurants sold to franchisees | number_of_restaurants	1	0	3
Proceeds from sales of restaurants	$ 50	$ 0	$ 1,436
Net assets sold	(34)	0	(1,370)
Goodwill related to sales of restaurants	0	0	(208)
Net favorable leases	0	0	220
Other	0	0	11
Gain on sales of restaurants, net, before post-closing adjustments	16	0	89
Post-closing adjustments on sales of restaurants	362	1,087	445
System optimization gains, net	378	1,087	534
Recognition of deferred gain on sale of property	368	911	1,029
Cash Proceeds from Post Closing Adjustments, Net of Payments			6
Sale of other assets
Plant, Property and Equipment
Proceeds from sales of restaurants	6,041	3,448	1,781
System optimization gains, net	$ 2,770	$ 196	$ (71)