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Acquisitions and Disposition - Acquisitions Narrative (Details) - USD ($)
$ in Millions
3 Months Ended 12 Months Ended
May 02, 2022
Mar. 07, 2022
Apr. 05, 2021
Nov. 18, 2020
Jan. 14, 2020
Jan. 01, 2023
Oct. 02, 2022
Apr. 03, 2022
Jan. 02, 2022
Oct. 03, 2021
Jul. 04, 2021
Apr. 04, 2021
Jun. 28, 2020
Jan. 01, 2023
Jan. 02, 2022
Jan. 03, 2021
Business Acquisition [Line Items]                                
Payment for contingent consideration liability, financing activities                           $ 3.3 $ 1.6 $ 0.0
Gain on insurance settlement                           0.0 19.0 0.0
Goodwill impairment charge           $ 10.3 $ 30.7             41.0 0.0 147.7
Disposal Group, Not Discontinued Operations | Russian Operations                                
Business Acquisition [Line Items]                                
Discontinued Operation, Income (Loss) from Discontinued Operation During Phase-out Period, before Income Tax, Attributable to Parent                           1.4 3.2 2.4
Softworld, Inc.                                
Business Acquisition [Line Items]                                
Ownership percentage acquired (percent)     100.00%                          
Purchase price of acquisition     $ 215.0                          
Purchase price paid at closing     220.4                          
Additional consideration payable     2.6                          
Intangible assets acquired     79.4                          
Net working capital adjustment     (6.0)             $ (6.0)            
Pro forma revenues                             4,940.9 4,626.5
Pro forma net earnings (loss)                             157.7 (70.8)
Amortization of intangible assets                 $ 2.0 2.0 $ 2.0 $ 2.0        
Gain on insurance settlement                 $ 19.0              
Pro forma information, revenue of acquiree since acquisition date, actual                             98.0  
Pro forma information, earnings or loss of acquiree since acquisition date, actual                             4.7  
Softworld, Inc. | Customer relationships                                
Business Acquisition [Line Items]                                
Intangible assets acquired     $ 54.9                          
Acquired finite-lived intangible assets, weighted average useful life (years)     10 years                          
Softworld, Inc. | Non-compete agreements                                
Business Acquisition [Line Items]                                
Intangible assets acquired     $ 1.4                          
Acquired finite-lived intangible assets, weighted average useful life (years)     5 years                          
Softworld, Inc. | Trade names                                
Business Acquisition [Line Items]                                
Intangible assets acquired     $ 23.1                          
Acquired finite-lived intangible assets, weighted average useful life (years)     10 years                          
Greenwood/Asher                                
Business Acquisition [Line Items]                                
Ownership percentage acquired (percent)       100.00%                        
Purchase price of acquisition       $ 3.5                        
Purchase price paid at closing       5.2                        
Contingent consideration, liability       $ 2.1   3.3               3.3    
Expense related to earnout liability                           1.0 2.5  
Payment for contingent consideration liability, financing activities               $ 0.7                
Payment for contingent consideration liability               $ 2.3                
Insight                                
Business Acquisition [Line Items]                                
Ownership percentage acquired (percent)         100.00%                      
Purchase price of acquisition         $ 34.5                      
Purchase price paid at closing         38.1                      
Contingent consideration, liability         $ 1.6                      
Expense related to earnout liability                             0.1 $ 0.1
Payment for contingent consideration liability, financing activities                             1.6  
Payment for contingent consideration liability                   $ 1.8            
Payments for previous acquisition                         $ 0.1      
Pediatric Therapeutic Services                                
Business Acquisition [Line Items]                                
Ownership percentage acquired (percent) 100.00%                              
Purchase price of acquisition $ 82.1                              
Purchase price paid at closing 85.7                              
Additional consideration payable 1.1                              
Employee retention credits             $ 0.1                  
Intangible assets acquired 40.3                              
Pro forma information, revenue of acquiree since acquisition date, actual                           28.5    
Pro forma information, earnings or loss of acquiree since acquisition date, actual                           3.8    
Pediatric Therapeutic Services | Customer relationships                                
Business Acquisition [Line Items]                                
Intangible assets acquired $ 29.8                              
Acquired finite-lived intangible assets, weighted average useful life (years) 15 years                              
Pediatric Therapeutic Services | Non-compete agreements                                
Business Acquisition [Line Items]                                
Intangible assets acquired $ 1.2                              
Acquired finite-lived intangible assets, weighted average useful life (years) 5 years                              
Pediatric Therapeutic Services | Trade names                                
Business Acquisition [Line Items]                                
Intangible assets acquired $ 9.3                              
Acquired finite-lived intangible assets, weighted average useful life (years) 15 years                              
RocketPower                                
Business Acquisition [Line Items]                                
Ownership percentage acquired (percent)   100.00%                            
Purchase price of acquisition   $ 59.3                            
Purchase price paid at closing   61.8                            
Additional consideration payable   1.1                            
Contingent consideration, liability   0.6                            
Intangible assets acquired   15.8                            
Pro forma information, revenue of acquiree since acquisition date, actual                           24.3    
Pro forma information, earnings or loss of acquiree since acquisition date, actual                           (43.5)    
Possible future contingent consideration   31.8                            
Goodwill expected to be deductible           $ 27.5               27.5    
Goodwill impairment charge                           $ 41.0    
RocketPower | Customer relationships                                
Business Acquisition [Line Items]                                
Intangible assets acquired   $ 7.5                            
Acquired finite-lived intangible assets, weighted average useful life (years)   3 years                            
RocketPower | Non-compete agreements                                
Business Acquisition [Line Items]                                
Intangible assets acquired   $ 1.7                            
Acquired finite-lived intangible assets, weighted average useful life (years)   6 years                            
RocketPower | Trade names                                
Business Acquisition [Line Items]                                
Intangible assets acquired   $ 6.6                            
Acquired finite-lived intangible assets, weighted average useful life (years)   10 years                            
Acquisition-related Costs | Softworld, Inc.                                
Business Acquisition [Line Items]                                
Net Income (Loss)                             $ 1.3