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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 ($)
Jan. 02, 2022
USD ($)
number_of_restaurants
Jan. 03, 2021
USD ($)
Dec. 29, 2019
USD ($)
Jun. 30, 2021
USD ($)
ft²
Nov. 30, 2018
USD ($)
ft²
Related Party Transaction              
Number of Restaurants | number_of_restaurants     6,949        
Franchised Units              
Related Party Transaction              
Number of Restaurants | number_of_restaurants     6,541        
QSCC              
Related Party Transaction              
Area of Real Estate Property | ft²           18,774 14,493
Annual Base Rental           $ 250 $ 217
Proceeds from Rents Received     $ 217 $ 217 $ 217    
QSCC | Cost of sales | Patronage Dividends              
Related Party Transaction              
Related Party Transaction, Other Revenues from Transactions with Related Party     279 0 504    
TimWen              
Related Party Transaction              
Related Party Transaction, Expenses from Transactions with Related Party     18,687 16,130 16,660    
TimWen | Cost of sales | Franchise Rental Expense              
Related Party Transaction              
Related Party Transaction, Expenses from Transactions with Related Party     18,906 16,339 16,867    
TimWen | General and administrative | Management Fee Income              
Related Party Transaction              
Related Party Transaction, Other Revenues from Transactions with Related Party     $ 219 $ 209 207    
Yellow Cab | Franchised Units              
Related Party Transaction              
Number of Restaurants | number_of_restaurants     84        
Significant Changes, Franchises Purchased During Period | number_of_restaurants 54            
Yellow Cab | Royalty, Advertising Fund, Lease, and Other Income              
Related Party Transaction              
Related Party Transaction, Other Revenues from Transactions with Related Party   $ 1,090 $ 9,869   $ 0    
Yellow Cab | Accounts Receivable and Advertising Funds Restricted Assets | Royalty, Advertising Fund, Lease, and Other Income              
Related Party Transaction              
Accounts Receivable, Related Parties, Current     $ 974