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Summary of Significant Accounting Policies - Narrative (Details) - USD ($)
$ in Millions
12 Months Ended
Jan. 01, 2023
Jan. 02, 2022
Jan. 03, 2021
Feb. 14, 2022
Accounting Policies [Abstract]        
Fiscal period duration 364 days 364 days 371 days  
Advertising expense $ 6.4 $ 7.5 $ 8.1  
Accounting Policies [Line Items]        
Depreciation expense 13.6 16.4 16.8  
Intangible assets, accumulated amortization 44.9 28.6    
Accounts payable 723.3 687.2    
Accrued payroll and related taxes 315.8 318.4    
Workers Compensation        
Accounting Policies [Line Items]        
Liability for claims 1.0      
Cloud Computing Arrangements        
Accounting Policies [Line Items]        
Amortization of intangible assets 4.2 2.2 $ 1.0  
Intangible assets, accumulated amortization 7.3 3.2    
Prepaid Expenses and Other Current Assets | Cloud Computing Arrangements        
Accounting Policies [Line Items]        
Short-term hosted software 2.7 2.7    
Other Noncurrent Assets | Cloud Computing Arrangements        
Accounting Policies [Line Items]        
Long-term hosted software 21.0 13.9    
Book overdrafts        
Accounting Policies [Line Items]        
Accounts payable 0.4 5.4    
Accrued payroll and related taxes $ 67.6 $ 39.1    
PersolKelly Pte. Ltd.        
Accounting Policies [Line Items]        
Equity method investment, ownership percentage   49.00%   49.00%