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Summary of Significant Accounting Policies - Narrative (Details) - USD ($)
$ in Millions
12 Months Ended
Jan. 02, 2022
Jan. 03, 2021
Dec. 29, 2019
Accounting Policies [Abstract]      
Fiscal period duration 364 days 371 days 364 days
Advertising expense $ 7.5 $ 8.1 $ 9.4
Accounting Policies [Line Items]      
Depreciation expense 16.4 16.8 $ 25.3
Intangible assets, accumulated amortization 30.1 17.1  
Accounts payable 687.2 536.8  
Accrued payroll and related taxes 318.4 293.0  
Workers Compensation      
Accounting Policies [Line Items]      
Liability for claims 1.0    
Cloud Computing Arrangements      
Accounting Policies [Line Items]      
Amortization of intangible assets 2.2 1.0  
Intangible assets, accumulated amortization 3.2 1.0  
Prepaid Expenses and Other Current Assets | Cloud Computing Arrangements      
Accounting Policies [Line Items]      
Short-term hosted software 2.7 2.9  
Other Noncurrent Assets | Cloud Computing Arrangements      
Accounting Policies [Line Items]      
Long-term hosted software 13.9 7.2  
Book overdrafts      
Accounting Policies [Line Items]      
Accounts payable 5.4 9.3  
Accrued payroll and related taxes $ 39.1 $ 11.0  
PersolKelly Pte. Ltd.      
Accounting Policies [Line Items]      
Equity method investment, ownership percentage 49.00% 49.00%