Pension Plans and Postretirement Benefits (Net Periodic Pension Benefit (Income) Expense) (Details) - Pension Plan - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Domestic
Components of net period pension benefit expense
Service cost - benefits earned during the period (in millions)	$ 9.3	$ 9.3	$ 8.5
Pension non-service (income)/expense (in millions):
Interest cost on benefit obligation	21.6	26.5	32.4
Expected return on plan assets	(55.8)	(56.0)	(64.8)
Amortization of prior service cost	(3.6)	(6.0)	(6.0)
Amortization of actuarial loss	26.3	22.5	30.6
Settlements/Curtailment	0.0	0.0	0.0
Defined Benefit Plan, Net Periodic Benefit Cost (Credit), Total	(11.5)	(13.0)	(7.8)
Foreign
Components of net period pension benefit expense
Service cost - benefits earned during the period (in millions)	1.3	1.1	0.9
Pension non-service (income)/expense (in millions):
Interest cost on benefit obligation	0.7	0.9	1.2
Expected return on plan assets	(1.0)	(1.1)	(1.4)
Amortization of prior service cost	0.1	0.1	0.1
Amortization of actuarial loss	0.4	0.3	0.3
Settlements/Curtailment	0.0	0.0	(0.5)
Defined Benefit Plan, Net Periodic Benefit Cost (Credit), Total	$ 0.2	$ 0.2	$ (0.3)