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DIVESTITURES - Operating Results of Divested Businesses (Detail) - USD ($)
$ in Millions
 12 Months Ended
Jan. 01, 2022
Jan. 02, 2021
Dec. 28, 2019
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]      
Earnings from discontinued operations before income taxes $ 70.2 $ 47.2 $ 35.6
Income taxes on discontinued operations (18.7) (1.6) 34.0
Depreciation and amortization 60.5 63.9 64.1
Cash and cash equivalents included in Current assets held for sale 144.9 139.1  
Total assets 3,183.4 3,148.1  
Convergent Security Solutions | Discontinued Operations, Disposed of by Sale      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]      
Net Sales 1,635.5 1,476.9 1,529.3
Cost of sales 1,024.8 914.3 957.2
Selling, general and administrative 481.8 461.1 472.7
Other, net and restructuring charges 58.7 54.3 63.8
Earnings from discontinued operations before income taxes 70.2 47.2 35.6
Income taxes on discontinued operations (18.7) (1.6) 34.0
Net earnings from discontinued operations 88.9 48.8 1.6
Depreciation and amortization 60.5 63.9 64.1
Capital expenditures 17.9 15.6 30.1
Stock-based compensation 6.0 5.3 $ 3.2
Cash and cash equivalents included in Current assets held for sale 144.9 139.1  
Accounts and notes receivable, net 434.8 347.7  
Inventories, net 142.5 98.5  
Other current assets 41.0 44.0  
Property, plant and equipment, net 74.0 80.7  
Goodwill and other intangibles, net 2,072.3 2,169.3  
Other assets 273.9 268.8  
Total assets 3,183.4 3,148.1  
Accounts payable and accrued expenses 388.3 390.6  
Other long-term liabilities 130.4 162.9  
Total liabilities $ 518.7 $ 553.5