Restructuring Costs (Details) $ in Millions	3 Months Ended				12 Months Ended
	Oct. 01, 2023 USD ($)	Oct. 02, 2022 USD ($)	Jul. 03, 2022 USD ($)	Apr. 03, 2022 USD ($)	Dec. 31, 2023 USD ($) employee	Jan. 01, 2023 USD ($) employee	Jan. 02, 2022 USD ($) employee
Restructuring Cost and Reserve [Line Items]
Restructuring and other charges (credits)					$ 31.4	$ 23.7	$ (10.5)
Restructuring charges (credits)					$ 7.7	(4.8)	(11.3)
Restructuring and Related Cost, Expected Number of Positions Eliminated | employee					110
Inventory write-down							0.8
Restructuring Reserve [Roll Forward]
Restructuring charges	$ (0.5)	$ (2.6)	$ (1.3)	$ (1.1)
Other nonoperating income (expense), litigation reserve		$ (19.9)		(8.6)	$ 0.0	(28.5)	0.0
Cost of sales					3,371.1	$ 3,121.8	2,466.6
Facility Idling
Restructuring Reserve [Roll Forward]
Restructuring charges							$ 0.7
Employee Severance
Restructuring Cost and Reserve [Line Items]
Reduction in severance related reserves, workforce | employee						110	350
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance				$ 17.7	9.8	$ 17.7	$ 43.4
Restructuring charges					7.7	(4.8)	(12.0)
Payments for Restructuring					(2.3)	(3.1)	(13.7)
Restructuring Reserve, Ending Balance					15.2	9.8	$ 17.7
Start Up Costs
Restructuring Reserve [Roll Forward]
Restructuring charges	2.8				11.5
Unplanned Outage Costs
Restructuring Reserve [Roll Forward]
Restructuring charges	$ 1.9				1.9
Asset Write-offs
Restructuring Reserve [Roll Forward]
Restructuring charges					10.3
Unusual or Infrequent Item, or Both
Restructuring Reserve [Roll Forward]
Cost of sales					23.7
Other Current Liabilities [Member]
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance					5.4
Restructuring Reserve, Ending Balance					10.9	5.4
Other Noncurrent Liabilities [Member]
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance					4.4
Restructuring Reserve, Ending Balance					$ 4.3	$ 4.4