Income Taxes - Provision for Income Taxes From Continuing Operations (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Current tax expense:
U.S. federal	$ 3.5	$ 8.2	$ 4.7
U.S. state and local	2.1	5.9	3.0
Foreign	7.9	9.0	11.0
Total current	13.5	23.1	18.7
Deferred tax (benefit) expense:
U.S. federal	(11.8)	(36.0)	(19.4)
U.S. state and local	(0.7)	(12.3)	(1.6)
Foreign	34.1	(8.8)	2.7
Total deferred	21.6	(57.1)	(18.3)
Total provision	$ 35.1	$ (34.0)	$ 0.4