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Cash and Receivables Accounts and Notes Receivable (Details) - USD ($)
$ in Thousands
12 Months Ended
Jan. 01, 2023
Jan. 02, 2022
Accounts, Notes, Loans and Financing Receivable    
Accounts receivable, gross, current $ 100,270 $ 104,744
Accounts receivable, allowance for doubtful accounts, current (1,707) (3,229)
Accounts receivable, net, current 98,563 101,515
Notes receivable from franchisees, gross, current 22,503 23,000
Notes receivable from franchisees, allowance for doubtful accounts, current (4,640) (4,975)
Notes receivable from franchisees, net, current 17,863 18,025
Accounts and notes receivable, gross, current 122,773 127,744
Accounts and financing receivable, allowance for doubtful accounts, current (6,347) (8,204)
Accounts and notes receivable, net, current 116,426 119,540
Notes receivable from franchisees, gross, noncurrent 3,888 4,514
Notes receivable from franchisees, allowance for doubtful accounts, noncurrent 0 (315)
Notes receivable from franchisees, net, noncurrent 3,888 4,199
Accounts and Notes Receivable, Net    
Accounts, Notes, Loans and Financing Receivable    
Income taxes receivable 3,236 11,901
Sales-type and direct financing leases, lease receivable 8,263 6,266
Indonesia franchisee    
Accounts, Notes, Loans and Financing Receivable    
Notes receivable from franchisees, gross, current 1,153 1,795
Brazil JV    
Accounts, Notes, Loans and Financing Receivable    
Notes receivable from franchisees, gross, current 13,087 12,925
Notes receivable from franchisees, gross, noncurrent 3,888 4,200
India franchisee    
Accounts, Notes, Loans and Financing Receivable    
Notes receivable from franchisees, gross, current   335
Notes receivable from franchisees, gross, noncurrent   315
Notes receivable from franchisees, allowance for doubtful accounts, current and noncurrent   $ (650)
Notes receivable from franchisees, payment received $ 350