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Income Taxes - Income Tax Expense (Benefit) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2023	Jan. 02, 2022	Jan. 03, 2021
Current provision (benefit)
Federal	$ 47.2	$ 43.0	$ 25.3
State	14.8	10.8	7.0
Foreign	47.8	57.5	39.1
Total current provision (benefit)	109.8	111.3	71.4
Deferred provision (benefit)
Federal	(39.0)	(39.7)	(0.5)
State	0.3	(0.1)	2.3
Foreign	48.1	17.0	(5.4)
Total deferred provision (benefit)	9.4	(22.8)	(3.6)
Provision (benefit) for income taxes	$ 119.2	$ 88.5	$ 67.8

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