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Income Taxes - Provision for Income Taxes From Continuing Operations (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2023	Jan. 02, 2022	Jan. 03, 2021
Current tax expense:
U.S. federal	$ 1.3	$ 1.0	$ 6.6
U.S. state and local	1.4	2.1	5.9
Foreign	61.5	10.4	10.6
Total current	64.2	13.5	23.1
Deferred tax (benefit) expense:
U.S. federal	(2.5)	(11.9)	(35.8)
U.S. state and local	0.7	(0.7)	(12.3)
Foreign	(70.3)	34.2	(9.0)
Total deferred	(72.1)	21.6	(57.1)
Total provision	$ (7.9)	$ 35.1	$ (34.0)

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