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Summary of Significant Accounting Policies - Property and Equipment At Cost and Depreciable Useful Lives (Details) - USD ($)
$ in Millions
12 Months Ended
Jan. 01, 2023
Jan. 02, 2022
Jan. 03, 2021
Property, Plant and Equipment [Line Items]      
Property and equipment $ 166.8 $ 205.1  
Depreciation expense 13.6 16.4 $ 16.8
Land      
Property, Plant and Equipment [Line Items]      
Property and equipment 0.0 0.0  
Work in process      
Property, Plant and Equipment [Line Items]      
Property and equipment 3.0 0.3  
Buildings and improvements      
Property, Plant and Equipment [Line Items]      
Property and equipment $ 0.4 12.9  
Buildings and improvements | Minimum      
Property, Plant and Equipment [Line Items]      
Estimated useful life 15 years    
Buildings and improvements | Maximum      
Property, Plant and Equipment [Line Items]      
Estimated useful life 40 years    
Computer hardware and software      
Property, Plant and Equipment [Line Items]      
Property and equipment $ 126.8 147.9  
Computer hardware and software | Minimum      
Property, Plant and Equipment [Line Items]      
Estimated useful life 3 years    
Computer hardware and software | Maximum      
Property, Plant and Equipment [Line Items]      
Estimated useful life 12 years    
Equipment, furniture and fixtures      
Property, Plant and Equipment [Line Items]      
Property and equipment $ 22.7 26.6  
Estimated useful life 5 years    
Leasehold improvements      
Property, Plant and Equipment [Line Items]      
Property and equipment $ 13.9 $ 17.4  
Leasehold improvements | Headquarters      
Property, Plant and Equipment [Line Items]      
Estimated useful life 15 years    
Leasehold improvements | Maximum | Branches      
Property, Plant and Equipment [Line Items]      
Estimated useful life 5 years