Segment Reporting - Segment Reporting Information by Operating Segment (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Segment Reporting Information [Line Items]
Revenue, net	$ 2,073.3	$ 1,953.5	$ 1,795.4
Depreciation and amortization	219.1	202.1	168.6
Operating income (loss)	103.0	(52.2)	75.0
Property, plant and equipment, net	718.1	685.6	558.1
Goodwill	1,321.4	1,284.3	1,047.5
Intangible assets, net	969.8	987.6	597.0
Total assets	3,723.4	3,604.7
Additions to property, plant and equipment	152.0	114.0	101.3
Continued Operations
Segment Reporting Information [Line Items]
Total assets	3,723.4	3,604.7	2,864.4
North America | Revision of Prior Period, Adjustment
Segment Reporting Information [Line Items]
Operating income (loss)		(2.1)	(1.5)
Rest of World | Revision of Prior Period, Adjustment
Segment Reporting Information [Line Items]
Operating income (loss)		(6.9)	(6.5)
Operating Segments | North America
Segment Reporting Information [Line Items]
Revenue, net	1,562.9	1,493.2	1,269.8
Depreciation and amortization	156.9	142.4	113.1
Operating income (loss)	146.0	130.0	91.2
Property, plant and equipment, net	554.2	550.7	433.2
Goodwill	994.1	982.1	673.1
Intangible assets, net	748.1	759.7	358.8
Additions to property, plant and equipment	113.5	87.0	70.7
Operating Segments | North America | Continued Operations
Segment Reporting Information [Line Items]
Total assets	2,744.4	2,729.7	1,874.5
Operating Segments | Rest of World
Segment Reporting Information [Line Items]
Revenue, net	510.4	460.3	518.4
Depreciation and amortization	60.7	58.4	55.2
Operating income (loss)	1.5	(118.3)	22.6
Property, plant and equipment, net	163.3	134.1	123.8
Goodwill	327.3	302.2	374.4
Intangible assets, net	217.3	222.9	237.2
Additions to property, plant and equipment	38.5	27.2	30.2
Operating Segments | Rest of World | Continued Operations
Segment Reporting Information [Line Items]
Total assets	938.0	841.3	941.6
All Other
Segment Reporting Information [Line Items]
Revenue, net	0.0	0.0	7.2
Depreciation and amortization	1.5	1.3	0.3
Operating income (loss)	(44.5)	(63.9)	(38.8)
Property, plant and equipment, net	0.6	0.8	1.1
Goodwill	0.0	0.0	0.0
Intangible assets, net	4.4	5.0	1.0
Additions to property, plant and equipment	0.0	(0.2)	0.4
All Other | Revision of Prior Period, Adjustment
Segment Reporting Information [Line Items]
Operating income (loss)		9.0	8.0
All Other | Continued Operations
Segment Reporting Information [Line Items]
Total assets	$ 41.0	$ 33.7	$ 48.3