Property, plant and equipment, net - Additional Information (Details) - USD ($) $ in Millions	12 Months Ended
Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Property Plant And Equipment [Line Items]
Depreciation Expense	$ 194.7	$ 194.0	$ 195.6
Loss on disposal of fixed assets	2.5	1.4	5.5
Computer software and development costs
Property Plant And Equipment [Line Items]
Depreciation Expense	$ 33.7	$ 33.4	$ 38.4

Amount of gain (loss) on sale or disposal of property, plant and equipment assets, excluding oil and gas property and timber property.

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=123570139&loc=d3e3602-108585

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 360
-SubTopic 10
-Section 45
-Paragraph 5
-URI http://asc.fasb.org/extlink&oid=123351718&loc=d3e2443-110228

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 360
-SubTopic 10
-Section 50
-Paragraph 3
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=109226691&loc=d3e2941-110230

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration