Impairment of Long-Lived Assets (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2023	Jan. 01, 2023	Jan. 02, 2022
Impairment of Long-Lived Assets
Impairment of long-lived assets	$ 1,401	$ 6,420	$ 2,251
Company-operated restaurants
Impairment of Long-Lived Assets
Impairment of long-lived assets	1,316	5,485	1,862
Restaurants leased or subleased to franchisees
Impairment of Long-Lived Assets
Impairment of long-lived assets	0	242	189
Surplus properties
Impairment of Long-Lived Assets
Impairment of long-lived assets	$ 85	$ 693	$ 200