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Commitments and Contingencies (Details)
 12 Months Ended
Oct. 02, 2019
Jun. 07, 2018
USD ($)
item
Jan. 02, 2024
USD ($)
Jan. 03, 2023
USD ($)
Commitments and Contingencies        
Purchase obligations     $ 101,400,000 $ 129,900,000
Purchase obligations due within terms recorded     3 years  
Minimum payments for real estate and leases     $ 414,800,000 252,400,000
Outstanding standby letters of credit     33,500,000 31,500,000
Total accrued liability for self-insured plans     71,500,000 $ 71,900,000
Wage citation   $ 4,200,000    
Number of restaurants receiving janitorial services | item   8    
Liability for contingent consideration provision     25,500,000  
Payments required under event of an actual or constructive termination of employment     3,400,000  
Accrued potential bonuses     2,600,000  
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