Income Taxes (Provision for Income Taxes) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Current
Federal	$ 18.2	$ 7.1	$ 1.8
State	10.6	2.7	1.1
Foreign	54.6	63.5	35.9
Total	83.4	73.3	38.8
Deferred
Federal	1.2	(2.0)	20.4
State	(2.7)	(0.3)	2.6
Foreign	(13.4)	(14.2)	(0.6)
Total	(14.9)	(16.5)	22.4
Total	$ 68.5	$ 56.8	$ 61.2