Acquisition Narrative (Details) $ / shares in Units, $ in Thousands						3 Months Ended			12 Months Ended
	Jun. 23, 2021 USD ($) restaurant	Jun. 17, 2021 USD ($) restaurant	Aug. 20, 2019 USD ($) restaurant	Jun. 11, 2019 USD ($) restaurant	Apr. 30, 2019 USD ($) restaurant $ / shares shares	Jan. 02, 2022 USD ($)	Oct. 03, 2021 USD ($)	Jul. 04, 2021 USD ($) restaurant	Jan. 02, 2022 USD ($) restaurant	Jan. 03, 2021 USD ($) restaurant	Dec. 29, 2019 USD ($) restaurant
Business Acquisition [Line Items]
Revenue									$ 1,652,370	$ 1,547,502	$ 1,462,765
Restaurants Acquired | restaurant	5	14						19	19
Acquisition of restaurants, net of cash acquired									$ (30,819)	0	(130,646)
Deferred income taxes						$ 1,800			1,800		$ 47,200
Acquisition-related costs							$ 100	$ 300
Business Combination, Retirement of Debt, Net of Cash Acquired					$ 113,800
Business Combination Purchase Price Allocation, Common Stock					$ 145,300
Business Combination Purchase Price Allocation, Common Stock, Per Share | $ / shares					$ 9.81
Payments to Acquire Businesses, Gross	$ 3,216	$ 27,603							$ 30,819
Number Of Businesses Acquired, Fee Owned | restaurant	1	12							13
2019 Acquisitions [Member]
Business Acquisition [Line Items]
Business Acquisition, Pro Forma, General and Administrative Exepnses									$ 4,100
Restaurants Acquired | restaurant									234
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Deferred Tax Liabilities						29			$ 29
Other Revenue from Contract with Customer, Excluding Assessed Tax										10,200
Cambridge Holdings, LLC [Member]
Business Acquisition [Line Items]
Business Combination, Restaurants Acquired | restaurant					132
Business Combination, Construction Of Restaurants Acquired | restaurant					33
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Deferred Tax Liabilities						44,292			$ 44,292
2021 Acquisitions
Business Acquisition [Line Items]
Revenue						$ 12,900
Franchise Rights [Member] | 2019 Acquisitions [Member]
Business Acquisition [Line Items]
Acquired Finite-lived Intangible Assets, Weighted Average Useful Life									28 years 8 months 12 days		32 years 8 months 12 days
Common Stock [Member] | Cambridge Holdings, LLC [Member]
Business Acquisition [Line Items]
Business Acquisition, Equity Interest Issued or Issuable, Number of Shares | shares					7,400,000
Convertible Preferred Stock, Shares Issued upon Conversion | shares					7,500,000
Business Combination, Share Restriction					2 years
Series C Preferred Stock [Member] | Cambridge Holdings, LLC [Member]
Business Acquisition [Line Items]
Business Acquisition, Equity Interest Issued or Issuable, Number of Shares | shares					10,000
NEW YORK | 2019 Acquisitions [Member]
Business Acquisition [Line Items]
Restaurants Acquired | restaurant			1	13	220				234
Acquisition of restaurants, net of cash acquired			$ (1,108)	$ (15,788)	$ (259,083)				$ (275,979)	$ (3,400)	$ (8,300)
Number Of Businesses Acquired, Fee Owned | restaurant			0	0	14				14	2	6
Restaurant sales
Business Acquisition [Line Items]
Revenue									$ 1,652,370	$ 1,547,502	$ 1,452,516
Restaurant sales | 2019 Acquisitions [Member]
Business Acquisition [Line Items]
Revenue									288,900	201,900
Other revenue
Business Acquisition [Line Items]
Revenue									$ 0	$ 0	$ 10,249