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Transactions with Related Parties Related Party Transaction Summary (Details) $ in Thousands		3 Months Ended	12 Months Ended
	Jan. 07, 2021 number_of_restaurants	Jan. 03, 2021 USD ($) number_of_restaurants	Jan. 03, 2021 USD ($) number_of_restaurants	Dec. 29, 2019 USD ($)	Dec. 30, 2018 USD ($)	Nov. 30, 2018 USD ($) ft²	Jan. 01, 2017 USD ($) ft²
Related Party Transaction
Number of Restaurants \| number_of_restaurants		6,828	6,828
Franchised Units
Related Party Transaction
Number of Restaurants \| number_of_restaurants		6,467	6,467
QSCC
Related Party Transaction
Area of Real Estate Property \| ft²						14,493	14,333
Annual Base Rental						$ 217	$ 215
QSCC \| Cost of sales \| Patronage Dividends
Related Party Transaction
Related Party Transaction, Other Revenues from Transactions with Related Party			$ 0	$ 504	$ 470
QSCC \| Franchise rental income \| Lease Income
Related Party Transaction
Related Party Transaction, Other Revenues from Transactions with Related Party			217	217	215
TimWen
Related Party Transaction
Related Party Transaction, Expenses from Transactions with Related Party			16,130	16,660	13,044
TimWen \| Cost of sales \| Franchise Rental Expense
Related Party Transaction
Related Party Transaction, Expenses from Transactions with Related Party			16,339	16,867	13,256
TimWen \| General and administrative \| Management Fee Income
Related Party Transaction
Related Party Transaction, Other Revenues from Transactions with Related Party			$ 209	207	212
Yellow Cab \| Royalty, Advertising Fund, Lease, and Other Income
Related Party Transaction
Related Party Transaction, Other Revenues from Transactions with Related Party		$ 1,090		$ 0	$ 0
Yellow Cab \| Franchised Units
Related Party Transaction
Number of Restaurants \| number_of_restaurants		24	24
Yellow Cab \| Accounts Receivable \| Royalty, Advertising Fund, Lease, and Other Income
Related Party Transaction
Accounts Receivable, Related Parties, Current		$ 298	$ 298
Yellow Cab \| Subsequent Event \| Franchised Units
Related Party Transaction
Significant Changes, Franchises Purchased During Period \| number_of_restaurants	54