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Transactions with Related Parties (Details) $ in Thousands	6 Months Ended
Transactions with Related Parties (Details) $ in Thousands	Jun. 28, 2026 USD ($) number_of_restaurants	Jun. 29, 2025 USD ($)	Dec. 28, 2025 USD ($)
Related Party Transaction
Number of Restaurants \| number_of_restaurants	7,180
Accounts payable	$ 21,440		$ 30,450
TimWen \| Franchise Rental Expense
Related Party Transaction
Operating Costs and Expenses	10,126	$ 10,344
TimWen \| Management Fee Income
Related Party Transaction
Other Operating Income	118	115
Yellow Cab \| Royalty, Advertising Fund, Lease and Other Income
Related Party Transaction
Other Operating Income	7,822	7,588
Accounts receivable, net, current	$ 1,338		1,045
Yellow Cab \| Franchised Units
Related Party Transaction
Number of Restaurants \| number_of_restaurants	87
AMC \| Advertising Funds Expense
Related Party Transaction
Related Party Transaction, Purchases from Related Party	$ 0	$ 600
Accounts payable	$ 0		$ 0