Segment Reporting - Segment Reporting Information by Operating Segment (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021
Segment Reporting Information [Line Items]
Revenue, net	$ 2,215.1	$ 2,073.3	$ 1,953.5
Depreciation and amortization	242.8	219.1	202.1
Operating income (loss)	127.9	103.0	(52.2)
Property, plant and equipment, net	714.4	718.1	685.6
Goodwill	1,293.0	1,321.4	1,284.3
Intangible assets, net	894.7	969.8	987.6
Total segment assets	3,667.0	3,723.4
Additions to property, plant and equipment	207.7	152.0	114.0
Continued Operations
Segment Reporting Information [Line Items]
Total segment assets	3,667.0	3,723.4	3,604.7
Operating Segments | North America
Segment Reporting Information [Line Items]
Revenue, net	1,685.6	1,562.9	1,493.2
Depreciation and amortization	179.6	156.9	142.4
Operating income (loss)	203.7	146.0	130.0
Property, plant and equipment, net	547.8	554.2	550.7
Goodwill	997.2	994.1	982.1
Intangible assets, net	720.0	748.1	759.7
Additions to property, plant and equipment	160.0	113.5	87.0
Operating Segments | North America | Continued Operations
Segment Reporting Information [Line Items]
Total segment assets	2,746.1	2,744.4	2,729.7
Operating Segments | Europe
Segment Reporting Information [Line Items]
Revenue, net	265.3	247.6	240.5
Depreciation and amortization	38.9	39.4	39.1
Operating income (loss)	(28.4)	(10.2)	(124.0)
Property, plant and equipment, net	101.9	107.0	86.5
Goodwill	186.8	204.0	180.5
Intangible assets, net	116.1	145.3	146.5
Additions to property, plant and equipment	26.4	25.9	20.8
Operating Segments | Europe | Continued Operations
Segment Reporting Information [Line Items]
Total segment assets	526.8	579.1	515.4
Other
Segment Reporting Information [Line Items]
Revenue, net	264.2	263.8	221.3
Depreciation and amortization	24.3	22.8	20.6
Operating income (loss)	(47.4)	(32.8)	(58.2)
Property, plant and equipment, net	64.7	56.9	48.4
Goodwill	109.0	123.3	121.7
Intangible assets, net	58.6	76.4	81.4
Additions to property, plant and equipment	21.3	12.6	6.2
Other | Continued Operations
Segment Reporting Information [Line Items]
Total segment assets	394.1	399.9	359.6
Eliminations
Segment Reporting Information [Line Items]
Revenue, net	0.0	(1.0)	(1.5)
Depreciation and amortization	0.0	0.0	0.0
Operating income (loss)	0.0	0.0	0.0
Property, plant and equipment, net	0.0	0.0	0.0
Goodwill	0.0	0.0	0.0
Intangible assets, net	0.0	0.0	0.0
Additions to property, plant and equipment	0.0	0.0	0.0
Eliminations | All Other Products To Europe
Segment Reporting Information [Line Items]
Revenue, net		1.0	1.5
Eliminations | Continued Operations
Segment Reporting Information [Line Items]
Total segment assets	$ 0.0	$ 0.0	$ 0.0