Dispositions - Narrative (Details) - USD ($) $ in Thousands	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019	Aug. 16, 2021
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Description and timing of disposal	On June 30, 2021, the Company's Board of Directors approved a stock purchase agreement, which was subsequently entered into by the Company on July 1, 2021, for the sale of all of the outstanding capital stock of Taco Cabana, Inc., including nearly all related assets and liabilities, for a cash purchase price of $85.0 million subject to reduction for (i) closing adjustments of approximately $4.6 million and (ii) certain other working capital adjustments as set forth in the stock purchase agreement. The transaction was completed August 16, 2021 and the Company recognized a gain on the sale of Taco Cabana of $25.0 million during the year ended January 2, 2022, which is included within income from discontinued operations, net of tax, in the consolidated statements of operations.
Cash purchase price of disposition				$ 85,000
Closing adjustments				$ 4,600
Gain on sale of Taco Cabana	$ 24,979	$ 0	$ 0
Discontinued Operations
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Gain on sale of Taco Cabana	24,979	$ 0	$ 0
Recorded expected insurance proceeds	900
Discontinued Operations | Transition Services
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Other Income	$ 500