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DIVESTITURES - Summary of Components of Income from Discontinued Operations, Net of Tax (Details) - USD ($) $ in Millions	3 Months Ended				6 Months Ended
	Apr. 03, 2022	Jan. 02, 2022	Apr. 04, 2021	Jan. 03, 2021	Apr. 03, 2022	Apr. 04, 2021
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Income from discontinued operations, net of tax	$ 41.1	$ 38.8	$ 40.3	$ 57.2	$ 79.9	$ 97.5
Income (loss) from discontinued operations, net of tax attributable to noncontrolling interest	0.1		0.0		0.5	(0.2)
Net income from discontinued operations attributable to controlling interest	41.0		40.3		79.4	97.7
Discontinued Operations, Held-for-sale or Disposed of by Sale
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Income from discontinued operations before income taxes	56.9		56.8		106.1	137.9
Income tax expense from discontinued operations	15.8		16.5		26.2	40.4
Income from discontinued operations, net of tax	41.1		40.3		79.9	97.5
Income (loss) from discontinued operations, net of tax attributable to noncontrolling interest	0.1		0.0		0.5	(0.2)
Net income from discontinued operations attributable to controlling interest	41.0		40.3		79.4	97.7
Discontinued Operations, Held-for-sale or Disposed of by Sale \| HHI
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Income from discontinued operations before income taxes	71.0		69.6		130.9	163.7
Discontinued Operations, Held-for-sale or Disposed of by Sale \| Other
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Income from discontinued operations before income taxes	(3.1)		(1.0)		(3.4)	(1.3)
Discontinued Operations, Held-for-sale or Disposed of by Sale \| Corporate Debt
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Income from discontinued operations before income taxes	$ 11.0		$ 11.8		$ 21.4	$ 24.5