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Acquisition Purchase Price Allocation, Acquisitions (Details) - USD ($)
$ in Thousands
12 Months Ended
Jan. 02, 2022
Jan. 01, 2023
Jan. 03, 2021
Business Acquisition [Line Items]      
Goodwill, Acquired During Period $ 1,832    
Goodwill $ 124,451 $ 107,751 $ 122,619
2021 Acquisitions      
Business Acquisition [Line Items]      
Inventory   229  
Land and building   20,376  
Restaurant equipment   850  
Restaurant equipment - subject to capital lease   29  
Right-of-use assets   2,997  
Leasehold improvements   550  
Franchise fees   411  
Franchise rights   6,025  
Goodwill   1,832  
Finance lease obligations for restaurant equipment   (35)  
Operating lease liabilities   (2,900)  
Accounts payable   (29)  
Net assets acquired   30,819  
Deferred taxes   $ 484