Reorganization and Realignment Costs System Optimization Costs (Details) $ in Thousands	3 Months Ended		6 Months Ended		12 Months Ended
	Jul. 03, 2022 USD ($)	Jul. 04, 2021 USD ($)	Jul. 03, 2022 USD ($) number_of_restaurants	Jul. 04, 2021 USD ($) number_of_restaurants	Jan. 02, 2022 number_of_restaurants
Restructuring Cost and Reserve
Reorganization and realignment costs	$ 156	$ 2,102	$ 620	$ 7,036
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	134	897	$ 541	$ 5,575
Restructuring and Related Cost, Expected Benefit Remaining	700		700
Restructuring and Related Cost, Incurred Cost	117	1,165	507	2,754
Restructuring and Related Cost, Cost Incurred to Date	50,700		50,700
Restructuring Charges, Incurred to Date	84,001		84,001
System Optimization Initiative | Acquisitions
Restructuring Cost and Reserve
Restaurants acquired from franchisees | number_of_restaurants					93
System Optimization Initiative | Severance and related employee costs
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost	0	661	0	661
Restructuring and Related Cost, Cost Incurred to Date	18,898		18,898
System Optimization Initiative | Professional fees
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost	80	504	374	739
Restructuring and Related Cost, Cost Incurred to Date	24,051		24,051
System Optimization Initiative | Other
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost	37	0	133	1,354
Restructuring and Related Cost, Cost Incurred to Date	7,751		7,751
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	0
Restructuring and Related Cost, Cost Incurred to Date	25,398		25,398
System Optimization Initiative | NPC lease termination costs
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost	17	(268)	34	2,821
Restructuring and Related Cost, Cost Incurred to Date	2,890		2,890
System Optimization Initiative | NPC lease termination costs | Write-Off of Lease Assets
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost			1,341
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	$ 0
Restructuring and Related Cost, Cost Incurred to Date	$ 5,013		$ 5,013