Reorganization and Realignment Costs System Optimization Costs (Details) $ in Thousands	12 Months Ended
	Jan. 01, 2023 USD ($) number_of_restaurants	Jan. 02, 2022 USD ($) number_of_restaurants	Jan. 03, 2021 USD ($) number_of_restaurants
Restructuring Cost and Reserve
Reorganization and realignment costs	$ 698	$ 8,548	$ 16,030
Consolidated Statements of Operations location:	Reorganization and realignment costs
Acquisitions
Restructuring Cost and Reserve
Restaurants acquired from franchisees | number_of_restaurants	0	93	0
System Optimization Initiative
Restructuring Cost and Reserve
Reorganization and realignment costs	$ 611	$ 6,852	$ 4,327
Restructuring and Related Cost, Expected Benefit Remaining	700
Restructuring and Related Cost, Incurred Cost	544	3,996	4,327
Restructuring and Related Cost, Cost Incurred to Date	50,737
Restructuring Charges, Incurred to Date	84,071
System Optimization Initiative | Severance and related employee costs
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost	4	661	0
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	395	1,570	4,323
Restructuring and Related Cost, Cost Incurred to Date	24,072
System Optimization Initiative | Other
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost	145	1,765	4
Restructuring and Related Cost, Cost Incurred to Date	7,763
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	67	2,856	0
Restructuring and Related Cost, Cost Incurred to Date	2,923
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