Acquisition Narrative (Details) $ / shares in Units, $ in Thousands					3 Months Ended				12 Months Ended
	Aug. 20, 2019 USD ($) restaurant	Jun. 11, 2019 USD ($) restaurant	Apr. 30, 2019 USD ($) restaurant $ / shares shares	Feb. 13, 2018 USD ($) restaurant	Jan. 03, 2021 USD ($)	Sep. 27, 2020 USD ($)	Jun. 28, 2020 USD ($) restaurant	Mar. 29, 2020 USD ($)	Jan. 03, 2021 USD ($) restaurant	Dec. 29, 2019 USD ($)	Dec. 30, 2018 USD ($)
Business Acquisition [Line Items]
Revenue									$ 1,547,502	$ 1,462,765	$ 1,179,307
Restaurants Acquired | restaurant							233		44
Acquisition of restaurants, net of cash acquired									$ 0	(130,646)	(38,102)
Business Combination, Bargain Purchase, Gain Recognized, Amount									0	0	230
Deferred income taxes					$ 47,200				47,200	500
Acquisition-related costs					2,800	$ 2,800	$ 2,600	$ 2,600
Business Combination, Retirement of Debt, Net of Cash Acquired			$ 113,800
Business Combination, Share Restriction			2 years
Business Combination Purchase Price Allocation, Common Stock			$ 145,300
Business Combination Purchase Price Allocation, Common Stock, Per Share | $ / shares			$ 9.81
Business Acquisition, Pro Forma General And Administrative Expenses											1,400
2019 Acquisitions [Member]
Business Acquisition [Line Items]
Business Acquisition, Pro Forma, General and Administrative Exepnses									$ 4,100	1,400
Restaurants Acquired | restaurant									234
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Deferred Tax Liabilities					29				$ 29
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
2018 Acquisitions [Member]
Business Acquisition [Line Items]
Restaurants Acquired | restaurant									44
Acquisition of restaurants, net of cash acquired									$ (38,102)
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Deferred Tax Liabilities					$ 346				$ 346
Off-Market Favorable Lease [Member] | 2018 Acquisitions [Member]
Business Acquisition [Line Items]
Acquired Finite-lived Intangible Assets, Weighted Average Useful Life									17 years 2 months 12 days
Above Market Leases [Member] | 2018 Acquisitions [Member]
Business Acquisition [Line Items]
Acquired Finite-lived Intangible Assets, Weighted Average Useful Life									18 years 3 months 18 days
Franchise Rights [Member]
Business Acquisition [Line Items]
Business Combination, Bargain Purchase, Gain Recognized, Amount				$ 300
Franchise Rights [Member] | 2019 Acquisitions [Member]
Business Acquisition [Line Items]
Acquired Finite-lived Intangible Assets, Weighted Average Useful Life									32 years 8 months 12 days
Franchise Rights [Member] | 2018 Acquisitions [Member]
Business Acquisition [Line Items]
Acquired Finite-lived Intangible Assets, Weighted Average Useful Life									31 years 7 months 6 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
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)
NEW YORK | 2018 Acquisitions [Member]
Business Acquisition [Line Items]
Restaurants Acquired | restaurant				1
Acquisition of restaurants, net of cash acquired				$ 0
Restaurant sales
Business Acquisition [Line Items]
Revenue									1,547,502	1,452,516	1,179,307
Restaurant sales | 2019 Acquisitions [Member]
Business Acquisition [Line Items]
Revenue									288,900	201,900
Restaurant sales | 2018 Acquisitions [Member]
Business Acquisition [Line Items]
Revenue										52,900	16,900
Other revenue
Business Acquisition [Line Items]
Revenue									$ 0	10,249	$ 0
Other Income | 2019 Acquisitions [Member]
Business Acquisition [Line Items]
Revenue										$ 10,200