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Revenue Contract Balances (Details) - USD ($)
$ in Thousands
9 Months Ended
Oct. 02, 2022
Oct. 03, 2021
Jan. 02, 2022
Contract balances      
Deferred franchise fees at beginning of period $ 97,186 $ 97,785  
Revenue recognized during the period (7,193) (14,001)  
New deferrals due to cash received and other 10,143 15,273  
Deferred franchise fees at end of period 100,136 $ 99,057  
Deferred franchise fees, current 8,467   $ 9,084
Deferred franchise fees, noncurrent 91,669   88,102
Accounts and notes receivable, net | Short-term Contract with Customer      
Contract balances      
Receivables, Net, Current 68,936   49,168
Advertising funds restricted assets | Short-term Contract with Customer      
Contract balances      
Receivables, Net, Current $ 68,251   $ 65,497