Pension Plans and Postretirement Benefits (Funded Status) (Details) - USD ($) $ in Millions	Jan. 02, 2022	Jan. 03, 2021
Amounts recognized in the consolidated balance sheets:
Assets for Plan Benefits, Defined Benefit Plan	$ 123.7	$ 67.9
Pension Plan | Domestic
Funded Status and Amounts Recognized in Balance Sheets [Abstract]
Funded status	65.0	7.7
Amounts recognized in the consolidated balance sheets:
Assets for Plan Benefits, Defined Benefit Plan	118.9	67.9
Accrued pension obligation long-term	(44.4)	(51.6)
Accrued pension obligation short-term	(3.7)	(2.7)
Other long-term liabilities	(5.8)	(5.9)
Net amount recognized	65.0	7.7
Amounts recognized in accumulated other comprehensive loss:
Net prior service cost (credit)	(3.0)	(6.6)
Net loss	397.7	454.2
Net amount recognized, before tax effect	394.7	447.6
Pension Plan | Foreign
Funded Status and Amounts Recognized in Balance Sheets [Abstract]
Funded status	(7.3)	(16.0)
Amounts recognized in the consolidated balance sheets:
Assets for Plan Benefits, Defined Benefit Plan	4.8	0.0
Accrued pension obligation long-term	(11.7)	(15.5)
Accrued pension obligation short-term	(0.4)	(0.5)
Other long-term liabilities	0.0	0.0
Net amount recognized	(7.3)	(16.0)
Amounts recognized in accumulated other comprehensive loss:
Net prior service cost (credit)	0.6	0.8
Net loss	3.4	10.6
Net amount recognized, before tax effect	$ 4.0	$ 11.4