Accounting Policies (Accumulated Other Comprehensive Loss) (Details) - USD ($) $ in Millions	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity, including portion attributable to noncontrolling interest	$ 6,422.6	$ 6,408.2	$ 2,615.4	$ 2,420.4
Accumulated Foreign Currency Adjustment Attributable to Parent
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity, including portion attributable to noncontrolling interest	(356.1)	(201.8)
Accumulated Gain (Loss), Net, Cash Flow Hedge
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity, including portion attributable to noncontrolling interest	17.3	21.0
Accumulated other comprehensive income (loss), tax	5.1	6.6
Accumulated Defined Benefit Plans Adjustment Attributable to Parent
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity, including portion attributable to noncontrolling interest	13.3	14.3
Accumulated other comprehensive income (loss), tax	(4.1)	(4.2)
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity, including portion attributable to noncontrolling interest	$ (352.1)	$ (195.1)	$ (163.3)	$ (237.8)