Income Taxes (Income Tax Expense (Benefit) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Current
Federal	$ 43.0	$ 25.3	$ 66.0
State	10.8	7.0	10.6
Foreign	57.5	39.1	28.4
Total current	111.3	71.4	105.0
Deferred
Federal	(39.7)	(0.5)	(37.0)
State	(0.1)	2.3	(2.3)
Foreign	17.0	(5.4)	5.7
Total deferred	(22.8)	(3.6)	(33.6)
Provision for income taxes	$ 88.5	$ 67.8	$ 71.4