Goodwill and Other Intangible Assets - Other Intangible Assets (Details) - USD ($) $ in Millions	Oct. 01, 2022	Jan. 01, 2022
Finite-Lived Intangible Assets [Line Items]
Gross	$ 296.5	$ 320.7
Accumulated Amortization	166.2	173.0
Net	130.4	147.6
Software
Finite-Lived Intangible Assets [Line Items]
Gross	202.1	196.8
Accumulated Amortization	119.8	102.1
Net	82.3	94.7
Trademarks and trade names
Finite-Lived Intangible Assets [Line Items]
Gross	14.3	14.3
Accumulated Amortization	5.6	4.6
Net	8.7	9.7
Customer lists and other
Finite-Lived Intangible Assets [Line Items]
Gross	80.2	109.6
Accumulated Amortization	40.8	66.4
Net	$ 39.4	$ 43.3