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Acquisitions (Details)
£ / shares in Units, £ in Millions, $ in Millions
3 Months Ended 12 Months Ended
Jan. 03, 2023
employee
program
Sep. 23, 2022
employee
£ / shares
Jan. 01, 2023
USD ($)
Oct. 02, 2022
USD ($)
acquisition
Jan. 23, 2023
GBP (£)
Dec. 31, 2022
GBP (£)
Dec. 30, 2022
USD ($)
Dec. 28, 2022
GBP (£)
Dec. 28, 2022
USD ($)
Business Acquisition [Line Items]                  
Pence per share expected to be acquired | £ / shares   £ 2.22              
Number of acquisitions | acquisition       4          
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            
RPS Group PLC                  
Business Acquisition [Line Items]                  
Number of employees | employee   5,000              
RPS Group PLC | Foreign Exchange Forward                  
Business Acquisition [Line Items]                  
Notional amount           £ 714.0 $ 774.8 £ 714.0 $ 775.4
RPS Group PLC | Subsequent Event | Foreign Exchange Forward                  
Business Acquisition [Line Items]                  
Notional amount | £         £ 714.0        
Amyx, Inc. | Subsequent Event                  
Business Acquisition [Line Items]                  
Number of employees | employee 500                
Number of government programs acquired | program 30                
Business acquisitions                  
Business Acquisition [Line Items]                  
Fair value of acquisition purchase price       $ 88.3          
Aggregate maximum of contingent consideration       47.0          
Initial cash payments       44.0          
Receivables related to estimated post-closing adjustments       2.5          
Payables related to promissory note       15.5          
Contingent earn-out liability       $ 31.3          
Business acquisitions | Minimum                  
Business Acquisition [Line Items]                  
Earn-out period       3 years          
Business acquisitions | Maximum                  
Business Acquisition [Line Items]                  
Earn-out period       5 years          
All acquisitions                  
Business Acquisition [Line Items]                  
Aggregate maximum of contingent consideration     $ 120.9            
Contingent earn-out liability     $ 69.0