Supplemental Financial Statement Information - Other Non-operating Income (Expense) (Details) - USD ($) $ in Millions	3 Months Ended		12 Months Ended
	Oct. 02, 2022	Apr. 03, 2022	Dec. 31, 2023	Jan. 01, 2023	Jan. 02, 2022
Disaggregation of Revenue [Line Items]
Rent, royalty income and other income			$ 2.6	$ 2.3	$ 1.1
Gains from disposal of property, plant and equipment, net			0.3	0.2	2.9
Income (loss) from equity method investments			(1.6)	12.6	0.1
Joint venture restructuring credit (charge)			0.0	0.9	0.0
Net gain (loss) on sale of businesses			0.0	0.0	13.8
Other nonoperating income (expense), litigation reserve	$ (19.9)	$ (8.6)	0.0	(28.5)	0.0
Other			0.0	0.0	0.3
Other income (loss), net			1.3	(12.5)	18.2
Gain (loss) on asset sales and sale of business, net			(0.6)	(105.4)	13.8
Supplier Finance Program, Obligation, Current			$ 15.6	$ 23.7
Supplier Finance Program, Obligation, Current, Statement of Financial Position [Extensible Enumeration]			Accounts payable	Accounts payable
Flowform Products
Disaggregation of Revenue [Line Items]
Net gain (loss) on sale of businesses					$ 13.8