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Cash and Receivables Accounts and Notes Receivable (Details) - USD ($)
$ in Thousands
12 Months Ended
Jan. 02, 2022
Jan. 03, 2021
Dec. 29, 2019
Accounts, Notes, Loans and Financing Receivable      
Accounts receivable, gross, current $ 104,744 $ 97,399  
Accounts receivable, allowance for doubtful accounts, current (3,229) (3,739)  
Accounts receivable, net current 101,515 93,660  
Notes receivable from franchisees, gross, current 23,000 21,227  
Notes receivable from franchisees, allowance for doubtful accounts, current (4,975) (4,996)  
Notes receivable from franchisees, net, current 18,025 16,231  
Accounts and notes receivables, gross, current 127,744 118,626  
Accounts and notes receivable, allowance for doubtful accounts, current (8,204) (8,735)  
Accounts and notes receivable, net, current 119,540 109,891  
Notes receivable from franchisees, gross, noncurrent 4,514 6,759  
Notes receivable from franchisees, allowance for doubtful accounts, noncurrent (315) (629)  
Notes receivable from franchisees, net, noncurrent 4,199 6,130  
Increase (Decrease) in Accounts Receivable 5,613 16,243 $ (16,935)
Rent Receivable      
Accounts, Notes, Loans and Financing Receivable      
Increase (Decrease) in Accounts Receivable   5,226  
Accounts and Notes Receivable Net      
Accounts, Notes, Loans and Financing Receivable      
Income taxes receivable 11,901 5,399  
Sales-type and direct financing leases, lease receivable 6,266 5,965  
India franchisee      
Accounts, Notes, Loans and Financing Receivable      
Notes receivable from franchisees, gross, current 335 356  
Notes receivable from franchisees, gross, noncurrent 315 629  
Notes receivable from franchisees, allowance for doubtful accounts, current and noncurrent (650) (985)  
Indonesia franchisee      
Accounts, Notes, Loans and Financing Receivable      
Notes receivable from franchisees, gross, current 1,795 831  
Notes receivable from franchisees, gross, noncurrent   1,780  
Brazil JV      
Accounts, Notes, Loans and Financing Receivable      
Notes receivable from franchisees, gross, current 12,925 12,775  
Notes receivable from franchisees, gross, noncurrent $ 4,200 $ 4,350