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Acquisitions (Details)
$ in Millions
3 Months Ended 12 Months Ended
Jan. 02, 2022
USD ($)
Oct. 03, 2021
USD ($)
employee
Business Acquisition [Line Items]    
Contingent earn-out liability $ 65.8  
Minimum    
Business Acquisition [Line Items]    
Significant unobservable input, earn-out period 3 years  
Minimum | Existing customer contracts    
Business Acquisition [Line Items]    
Useful life of intangible assets 1 year  
Minimum | Trade names    
Business Acquisition [Line Items]    
Useful life of intangible assets 3 years  
Maximum    
Business Acquisition [Line Items]    
Significant unobservable input, earn-out period 5 years  
Maximum | Existing customer contracts    
Business Acquisition [Line Items]    
Useful life of intangible assets 10 years  
Maximum | Trade names    
Business Acquisition [Line Items]    
Useful life of intangible assets 5 years  
Hoare Lea    
Business Acquisition [Line Items]    
Number of employees | employee   900
Business acquisitions    
Business Acquisition [Line Items]    
Fair value of acquisition purchase price   $ 151.7
Initial cash payments   101.4
Contingent earn-out liability   50.3
Aggregate maximum of contingent consideration   $ 74.0
Business acquisitions | Minimum    
Business Acquisition [Line Items]    
Earn-out period   3 years
Business acquisitions | Maximum    
Business Acquisition [Line Items]    
Earn-out period   4 years
All acquisitions    
Business Acquisition [Line Items]    
Aggregate maximum of contingent consideration $ 119.4