Summary of Significant Accounting Policies - Property and Equipment At Cost and Depreciable Useful Lives (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Property, Plant and Equipment [Line Items]
Property and equipment	$ 205.1	$ 222.3
Depreciation expense	16.4	16.8	$ 25.3
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	0.3	0.4
Buildings and improvements
Property, Plant and Equipment [Line Items]
Property and equipment	$ 12.9	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	$ 147.9	152.3
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	$ 26.6	34.8
Estimated useful life	5 years
Leasehold improvements
Property, Plant and Equipment [Line Items]
Property and equipment	$ 17.4	$ 21.9
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