Reorganization and Realignment Costs System Optimization Costs (Details) $ in Thousands	12 Months Ended
	Dec. 31, 2023 USD ($) number_of_restaurants	Jan. 01, 2023 USD ($) number_of_restaurants	Jan. 02, 2022 USD ($) number_of_restaurants
Restructuring Cost and Reserve
Reorganization and realignment costs	$ 9,200	$ 698	$ 8,548
Consolidated Statements of Operations location:	Reorganization and realignment costs
Acquisitions
Restructuring Cost and Reserve
Restaurants acquired from franchisees | number_of_restaurants	0	0	93
System Optimization Initiative
Restructuring Cost and Reserve
Reorganization and realignment costs	$ 136	$ 611	$ 6,852
Restructuring and Related Cost, Expected Benefit Remaining	150
Restructuring reserve	0	0	0
Restructuring and Related Cost, Incurred Cost	76	544	3,996
Restructuring and Related Cost, Cost Incurred to Date	50,813
Restructuring Charges, Incurred to Date	84,207
System Optimization Initiative | Severance and related employee costs
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost	0	4	661
Restructuring and Related Cost, Cost Incurred to Date	18,902
System Optimization Initiative | Professional fees
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost	3	395	1,570
Restructuring and Related Cost, Cost Incurred to Date	24,075
System Optimization Initiative | Other
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost	73	145	1,765
Restructuring and Related Cost, Cost Incurred to Date	7,836
System Optimization Initiative | Other | NPC Transaction Fees
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost			1,350
System Optimization Initiative | Accelerated depreciation and amortization
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost	0	0	0
Restructuring and Related Cost, Cost Incurred to Date	25,398
System Optimization Initiative | NPC lease termination costs
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost	60	67	2,856
Restructuring and Related Cost, Cost Incurred to Date	2,983
System Optimization Initiative | NPC lease termination costs | Write-Off of Lease Assets
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost			1,376
System Optimization Initiative | NPC lease termination costs | Lease Termination Fees
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost			1,480
System Optimization Initiative | Share-based compensation
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost	0	$ 0	$ 0
Restructuring and Related Cost, Cost Incurred to Date	$ 5,013