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Summary of Significant Accounting Policies (Details)		3 Months Ended								12 Months Ended
Summary of Significant Accounting Policies (Details)	Mar. 01, 2019 item	Jan. 01, 2019 USD ($)	Oct. 02, 2018 USD ($)	Jul. 03, 2018 USD ($)	Apr. 03, 2018 USD ($)	Jan. 02, 2018 USD ($)	Oct. 03, 2017 USD ($)	Jul. 04, 2017 USD ($)	Apr. 04, 2017 USD ($)	Jan. 01, 2019 USD ($)	Jan. 02, 2018 USD ($)	Jan. 03, 2017 USD ($)
Description of Business
Number of company-owned upscale, casual, full-service dining restaurants \| item	218
Number of International locations operating under licensing agreements \| item	21
Number of bakery production facilities \| item	2
Basis of Presentation
Length of fiscal year										P364D	P364D	P371D
Contra revenue		$ 585,155,000	$ 575,160,000	$ 587,319,000	$ 584,697,000	$ 571,815,000	$ 555,392,000	$ 569,869,000	$ 563,426,000	$ 2,332,331,000	$ 2,260,502,000	$ 2,275,719,000
Cash and Cash Equivalents
Amounts receivable from credit card processors		17,300,000				$ 13,800,000				$ 17,300,000	$ 13,800,000
Conversion period, credit card sales										P3D	P3D
Concentration of Credit Risk
Maximum amount of money market deposit insured by FDIC		250,000								$ 250,000
Fair Value of Financial Instruments
Fair value of deemed landlord financing liabilities		117,000,000								117,000,000
Carrying value of deemed landlord financing liabilities		$ 118,600,000								$ 118,600,000
Buildings and land improvements \| Minimum
Property and equipment
Useful life										25 years
Buildings and land improvements \| Maximum
Property and equipment
Useful life										30 years
Leasehold improvements \| Minimum
Property and equipment
Useful life										10 years
Leasehold improvements \| Maximum
Property and equipment
Useful life										30 years
Furnishings, fixtures and equipment \| Minimum
Property and equipment
Useful life										3 years
Furnishings, fixtures and equipment \| Maximum
Property and equipment
Useful life										15 years
Computer software and equipment
Property and equipment
Useful life										5 years
Classifying complimentary meals as contra revenue versus other operating expense
Basis of Presentation
Contra revenue			5,700,000	5,900,000	6,000,000					$ 23,300,000
Classifying complimentary meals as contra from from cost of sales to operating expenses
Basis of Presentation
Other operating expense			1,400,000	1,500,000	1,500,000					5,800,000
Classifying complimentary meals from labor to operating expenses
Basis of Presentation
Other operating expense			$ 1,100,000	$ 1,100,000	$ 1,100,000					$ 4,400,000