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Stock-Based Compensation and Other Stock Plans - Other Stock Plans Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021
Directors' Fee Plan
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items]
Percentage of non-employee directors fee	100.00%
Number of shares issued (in shares)	621	1,235	1,836
Deferred shares received (in shares)	309	922	1,364
Number of shares reserved for issuance (in shares)	195,730
Non-employee Directors | Restricted Stock
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items]
Shares granted (in shares)	6,525	6,858	7,380
Vesting period	1 year
Employees Stock Purchase Plan
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items]
Number of shares issued (in shares)	18,452	82,286	25,425
Number of shares reserved for issuance (in shares)	578,823
Employee contributions for purchase of common stock	$ 2.8
Compensation expense	$ 0.2	$ 9.6	$ 1.1
Franchisee Stock Purchase Plan
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items]
Number of shares issued (in shares)	44,937	143,388	55,980
Number of shares reserved for issuance (in shares)	225,225
Compensation expense	$ 0.4	$ 16.7	$ 1.9
Franchisee contributions for purchase of common stock	$ 6.3

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