Revenue Recognition (Details) - USD ($) $ in Thousands	3 Months Ended
	Apr. 02, 2024	Apr. 04, 2023	Jan. 02, 2024
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction [Line Items]
Expected unredeemed percent	14.00%
Estimated redemption period	24 months
Gift card liability, current	$ 2,067		$ 2,222
Revenue recognized for redemption of gift cards	$ 900	$ 1,000
Period in which initial fees received from franchisees will be recognized as revenue	20 years
Loyalty program deferred revenue	$ 800		900
Accrued Expenses and Other Current Liabilities
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction [Line Items]
Gift card liability, current	2,100		2,200
Other Long-term Liabilities
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction [Line Items]
Gift card liability, non-current	$ 800		$ 1,000