Commitments and Contingencies (Details)			12 Months Ended
	Oct. 02, 2019	Jun. 07, 2018 USD ($) item	Jan. 03, 2023 USD ($)	Dec. 28, 2021 USD ($)
Commitments and Contingencies
Purchase obligations			$ 129,900,000	$ 139,500,000
Purchase obligations due within terms recorded			3 years
Minimum payments for real estate and leases			$ 252,400,000	151,600,000
Outstanding standby letters of credit			31,500,000	29,900,000
Total accrued liability for self-insured plans			71,900,000	$ 67,600,000
Wage citation		$ 4,200,000
Number of restaurants receiving janitorial services | item		8
Deferred consideration			11,300,000
Liability for contingent consideration provision			28,600,000
Payments required under event of an actual or constructive termination of employment			3,300,000
Accrued potential bonuses			2,000,000.0
Annual founder's retirement benefit for ten years after termination of full time employment			$ 650,000
Number of years annual founder's retirement benefit after termination of full time employment			10 years
Number of months annual founder's retirement benefit after termination of full time employment			6 months
FRC Acquisition
Commitments and Contingencies
Number of years for providing finance to achieve the targets	5 years