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Transactions with Related Parties Related Party Transaction Summary (Details) $ in Thousands	12 Months Ended
	Dec. 29, 2024 USD ($) number_of_restaurants	Dec. 31, 2023 USD ($)	Jan. 01, 2023 USD ($)	Jun. 30, 2021 USD ($) ft²	Nov. 30, 2018 USD ($) ft²
Related Party Transaction
Number of Restaurants \| number_of_restaurants	7,240
Accounts receivable, net	$ 86,836	$ 104,797
Accounts payable	$ 28,455	27,370
Franchised Units
Related Party Transaction
Number of Restaurants \| number_of_restaurants	6,846
Advertising funds restricted liabilities
Related Party Transaction
Accounts payable	$ 83,035	101,796
QSCC
Related Party Transaction
Proceeds from Rents Received	277	231	$ 198
Area of Real Estate Property \| ft²				18,774	14,493
Annual Base Rent				$ 250	$ 217
QSCC \| Patronage Dividends
Related Party Transaction
Related Party Transaction, Purchases from Related Party	3,493	363	427
QSCC \| Other Operating Income (Expense) \| Patronage Dividends
Related Party Transaction
Related Party Transaction, Purchases from Related Party	2,909
QSCC \| Cost of sales \| Patronage Dividends
Related Party Transaction
Related Party Transaction, Purchases from Related Party	584	363	427
TimWen
Related Party Transaction
Operating Costs and Expenses	21,172	20,653	19,694
TimWen \| Franchise Rental Expense
Related Party Transaction
Operating Costs and Expenses	21,409	20,894	19,927
TimWen \| General and administrative \| Management Fee Income
Related Party Transaction
Other Operating Income	$ 237	241	233
Yellow Cab \| Franchised Units
Related Party Transaction
Number of Restaurants \| number_of_restaurants	89
Yellow Cab \| Royalty, Advertising Fund, Lease, and Other Income
Related Party Transaction
Other Operating Income	$ 15,417	14,757	13,404
Yellow Cab \| Accounts Receivable and Advertising Funds Restricted Assets \| Royalty, Advertising Fund, Lease, and Other Income
Related Party Transaction
Accounts receivable, net	1,132	1,153
AMC \| Advertising Funds Expense
Related Party Transaction
Related Party Transaction, Purchases from Related Party	2,010	2,366	$ 0
AMC \| Advertising funds restricted liabilities \| Advertising Funds Expense
Related Party Transaction
Accounts payable	$ 17	$ 584