DIVESTITURES - Additional Information (Detail) $ in Millions			12 Months Ended
	Nov. 02, 2020 USD ($) country	May 30, 2019 USD ($)	Jan. 02, 2021 USD ($) country		Dec. 28, 2019 USD ($)		Dec. 29, 2018 USD ($)
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Number Of Countries | country			5
Gain (Loss) on Disposition of Business			$ (13.5)	[1]	$ 17.0	[2]	$ (0.8)	[2]
Commercial Electronic Security
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Gain (Loss) on Disposition of Business			4.2
Sargent & Greenleaf
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Proceeds (payments) from sales of businesses, net of cash sold		$ 79.0
Pre-tax gain on divestiture		$ 17.0
Pretax income					$ 4.6		$ 11.7
Small Business in Security Segment
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Number Of Countries | country	5
Proceeds (payments) from sales of businesses, net of cash sold	$ 60.9
Gain (Loss) on Disposition of Business	$ 13.5
Small Business in Security Segment | Oil & Gas Product Line
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Gain (Loss) on Disposition of Business			$ 17.7

[1] See Note A, Significant Accounting Policies - Restatement, for discussion regarding the impacts of the Restatement.

[2] See Note A, Significant Accounting Policies - Restatement, for discussion regarding the impacts of the Restatement.