Segment Information (Narrative) (Details) $ in Millions	12 Months Ended
	Jan. 01, 2022 USD ($) segment	Jan. 02, 2021 USD ($)	Dec. 28, 2019
Segment Reporting Information [Line Items]
Number of operating segments (in segment) | segment	4
Assets	$ 10,281.6	$ 4,589.0
Commercial Systems
Segment Reporting Information [Line Items]
Assets	1,229.1	1,319.6
Industrial Systems
Segment Reporting Information [Line Items]
Assets	$ 832.6	$ 837.5
Geographic Concentration Risk | Sales Revenue, Net | United States
Segment Reporting Information [Line Items]
Concentration risk	62.10%	64.80%	64.00%