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Business Acquisitions - Purchase Price (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2023	Jan. 02, 2022	Jan. 03, 2021	Oct. 02, 2022
Business Acquisition [Line Items]
Cash paid	$ 99.6	$ 3,723.3	$ 29.0
Goodwill Acquired	78.5	$ 5,905.5
ETM
Business Acquisition [Line Items]
Cash paid	87.7
Goodwill Acquired	32.6
Acquired intangible assets	20.9
NL Acoustics
Business Acquisition [Line Items]
Interest acquired				80.00%
Cash paid	11.9
Goodwill Acquired	11.6
Acquired intangible assets	3.8
Total
Business Acquisition [Line Items]
Cash paid	99.6
Goodwill Acquired	44.2
Acquired intangible assets	$ 24.7

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