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DIVESTITURES - Additional Information (Detail)
$ in Millions
3 Months Ended 12 Months Ended
Nov. 02, 2020
USD ($)
country
May 30, 2019
USD ($)
Jul. 03, 2021
USD ($)
Jan. 01, 2022
USD ($)
Jan. 02, 2021
USD ($)
Dec. 28, 2019
USD ($)
Dec. 31, 2021
USD ($)
Nov. 30, 2020
country
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                
Number of countries | country               5
(Loss) gain on sales of businesses       $ (0.6) $ (13.5) $ 17.0    
Commercial Electronic Security                
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                
(Loss) gain on sales of businesses         4.2      
Convergent Security Solutions | Discontinued Operations, Disposed of by Sale                
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                
Agreement for divesture of interest in consolidated subsidiaries             $ 3,200.0  
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 from sales of businesses, net of cash sold $ 60.9              
(Loss) gain on sales of businesses         (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]                
(Loss) gain on sales of businesses         (17.7)      
Small Business in Security Segment | Commercial Electronic Security                
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                
(Loss) gain on sales of businesses     $ (1.0)          
Other Divestures                
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                
(Loss) gain on sales of businesses         $ 4.1 3.0    
Sargent & Greenleaf                
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                
Proceeds from sales of businesses, net of cash sold   $ 79.0            
Pre-tax gain on divestiture   $ 17.0            
Pretax income           $ 4.6