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Transactions with Related Parties (Details)
$ in Thousands
9 Months Ended
Sep. 28, 2025
USD ($)
number_of_restaurants
Sep. 29, 2024
USD ($)
Dec. 29, 2024
USD ($)
Related Party Transaction      
Number of Restaurants | number_of_restaurants 7,363    
Accounts payable $ 27,195   $ 28,455
TimWen | Franchise Rental Expense      
Related Party Transaction      
Operating Costs and Expenses 15,960 $ 16,065  
TimWen | Management Fee Income | General and administrative      
Related Party Transaction      
Other Operating Income 174 179  
QSCC | Patronage Dividends      
Related Party Transaction      
Patronage dividends   3,493  
QSCC | Patronage Dividends | Cost of sales      
Related Party Transaction      
Patronage dividends 118 584  
QSCC | Patronage Dividends | Other Operating Income (Expense)      
Related Party Transaction      
Patronage dividends   2,909  
Yellow Cab | Royalty, Advertising Fund, Lease and Other Income      
Related Party Transaction      
Other Operating Income 11,491 11,397  
Yellow Cab | Accounts and notes receivable, net and Advertising funds restricted assets | Royalty, Advertising Fund, Lease and Other Income      
Related Party Transaction      
Accounts receivable, net, current $ 1,050   1,132
Yellow Cab | Franchised Units      
Related Party Transaction      
Number of Restaurants | number_of_restaurants 89    
AMC | Advertising Funds Expense      
Related Party Transaction      
Related Party Transaction, Purchases from Related Party $ 800 $ 1,600  
AMC | Advertising funds restricted liabilities | Advertising Funds Expense      
Related Party Transaction      
Accounts payable $ 15   $ 17