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Transactions with Related Parties (Details)
$ in Thousands
6 Months Ended
Jun. 30, 2024
USD ($)
number_of_restaurants
Jul. 02, 2023
USD ($)
Dec. 31, 2023
USD ($)
Related Party Transaction      
Number of Restaurants | number_of_restaurants 7,261    
Accounts payable $ 25,767   $ 27,370
TimWen | Franchise Rental Expense      
Related Party Transaction      
Operating Costs and Expenses 10,522 $ 10,140  
TimWen | Management Fee Income | General and administrative      
Related Party Transaction      
Other Operating Income 120 121  
QSCC | Patronage Dividends      
Related Party Transaction      
Related Party Transaction, Purchases from Related Party 3,379 0  
QSCC | Patronage Dividends | Other Operating Income (Expense)      
Related Party Transaction      
Related Party Transaction, Purchases from Related Party 2,909    
QSCC | Patronage Dividends | Cost of sales      
Related Party Transaction      
Related Party Transaction, Purchases from Related Party 470    
Yellow Cab | Royalty, Advertising Fund, Lease and Other Income      
Related Party Transaction      
Other Operating Income 7,543 7,411  
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 $ 1,134   1,153
Yellow Cab | Franchised Units      
Related Party Transaction      
Number of Restaurants | number_of_restaurants 86    
AMC | Advertising Funds Expense      
Related Party Transaction      
Related Party Transaction, Purchases from Related Party $ 1,100 $ 1,200  
AMC | Advertising funds restricted liabilities | Advertising Funds Expense      
Related Party Transaction      
Accounts payable $ 0   $ 584