Acquisitions (Details) $ in Thousands	3 Months Ended	12 Months Ended
	Apr. 04, 2021 USD ($) numberOfMarkets	Dec. 31, 2023 USD ($) number_of_restaurants	Jan. 01, 2023 USD ($) number_of_restaurants	Jan. 02, 2022 USD ($) number_of_restaurants	Jan. 03, 2021 USD ($)	Nov. 18, 2020 numberOfMarkets	Jul. 31, 2020 number_of_restaurants numberOfMarkets
Business Acquisition
Number of Restaurants | number_of_restaurants		7,240
Goodwill		$ 773,727	$ 773,088	$ 775,278
Number of markets to be sold by NPC | numberOfMarkets							8
NPC consortium bid: number of markets to be purchased by franchisees | numberOfMarkets						7
NPC consortium bid: number of markets to be purchased by Company | numberOfMarkets						1
NPC Consortium bid deposit					$ 43,240
NPC Consortium bid payable					$ 38,361
NPC asset purchase agreement: number of markets to be purchased by FRG | numberOfMarkets	4
NPC asset purchase agreement: number of markets to be purchased by franchisees | numberOfMarkets	4
Acquisitions		$ 0	$ 0	$ 123,069
Acquisitions
Business Acquisition
Restaurants acquired from franchisees | number_of_restaurants		0	0	93
Total consideration paid, net of cash received				$ 127,948
Properties				21,984
Acquired franchise rights				81,239
Total identifiable net assets				104,506
Goodwill				23,442
Business combination, provisional information, initial accounting incomplete, adjustment, financial assets			$ 260
Finance lease assets | Acquisitions
Business Acquisition
Lease assets				25,547
Operating lease assets | Acquisitions
Business Acquisition
Lease assets				44,282
Finance lease liabilities | Acquisitions
Business Acquisition
Lease liabilities				(25,059)
Operating lease liabilities | Acquisitions
Business Acquisition
Lease liabilities				(43,478)
Settlement of NPC-related deposits
Business Acquisition
Acquisitions	$ (4,879)
Other liabilities | Acquisitions
Business Acquisition
Other				$ (9)
Restaurants under construction | Acquisitions
Business Acquisition
Restaurants acquired from franchisees | number_of_restaurants				2
NPC franchised restaurants
Business Acquisition
Number of Restaurants | number_of_restaurants							393