Derivative Instruments and Hedging Activities - Schedule of Fair value gains and losses of derivative contracts (Details) - Not Designated as Hedging Instrument - Other Expense, Net - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Derivative [Line Items]
Interest rate cap derivatives	$ (0.2)	$ 1.5	$ 16.0
Foreign currency derivatives	32.1	(2.1)	(1.8)
Cross currency swaps	$ (24.0)	$ 6.0	$ 0.0