Reorganization and Realignment Costs System Optimization Costs (Details) $ in Thousands	3 Months Ended		9 Months Ended		12 Months Ended
	Oct. 02, 2022 USD ($)	Oct. 03, 2021 USD ($)	Oct. 02, 2022 USD ($) number_of_restaurants	Oct. 03, 2021 USD ($) number_of_restaurants	Jan. 02, 2022 number_of_restaurants
Restructuring Cost and Reserve
Reorganization and realignment costs	$ 8	$ 345	$ 628	$ 7,381
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	7	295	$ 548	$ 5,870
Restructuring and Related Cost, Expected Benefit Remaining	700		700
Restructuring and Related Cost, Incurred Cost	(10)	277	497	3,031
Restructuring and Related Cost, Cost Incurred to Date	50,690		50,690
Restructuring Charges, Incurred to Date	84,008		84,008
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	0	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	(28)	277	346	1,016
Restructuring and Related Cost, Cost Incurred to Date	24,023		24,023
System Optimization Initiative | Other
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost	18	0	151	1,354
Restructuring and Related Cost, Cost Incurred to Date	7,769		7,769
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	18	51	2,839
Restructuring and Related Cost, Cost Incurred to Date	2,907		2,907
System Optimization Initiative | NPC lease termination costs | Write-Off of Lease Assets
Restructuring Cost and Reserve
Restructuring and Related Cost, Incurred Cost			1,359
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