SUPPLEMENTAL EQUITY AND COMPREHENSIVE INCOME INFORMATION - Change in Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Changes in Accumulated other comprehensive loss (net of tax)
Beginning balance	$ 1,484.9	$ 1,204.0	$ 955.1
Net current-period other comprehensive income (loss), net of tax	66.7	(1.5)	333.9
Ending balance	1,924.4	1,484.9	1,204.0
Foreign Currency Translation
Changes in Accumulated other comprehensive loss (net of tax)
Beginning balance	(248.1)	(245.1)
Other comprehensive income (loss) before reclassifications, net of tax	30.7	(3.0)
Reclassifications to net income, net of tax
Net current-period other comprehensive income (loss), net of tax	30.7	(3.0)
Ending balance	(217.4)	(248.1)	(245.1)
Pension and Other Postretirement Benefits
Changes in Accumulated other comprehensive loss (net of tax)
Beginning balance	(92.7)	(101.8)
Other comprehensive income (loss) before reclassifications, net of tax	27.9	6.2
Reclassifications to net income, net of tax	4.4	2.9
Net current-period other comprehensive income (loss), net of tax	32.3	9.1
Ending balance	(60.4)	(92.7)	(101.8)
Cash Flow Hedges
Changes in Accumulated other comprehensive loss (net of tax)
Beginning balance	(8.8)	(1.2)
Other comprehensive income (loss) before reclassifications, net of tax	5.4	(7.5)
Reclassifications to net income, net of tax	(1.7)	(0.1)
Net current-period other comprehensive income (loss), net of tax	3.7	(7.6)
Ending balance	(5.1)	(8.8)	(1.2)
Accumulated other comprehensive loss
Changes in Accumulated other comprehensive loss (net of tax)
Beginning balance	(349.6)	(348.1)	(682.0)
Other comprehensive income (loss) before reclassifications, net of tax	64.0	(4.3)
Reclassifications to net income, net of tax	2.7	2.8
Net current-period other comprehensive income (loss), net of tax	66.7	(1.5)	333.9
Ending balance	$ (282.9)	$ (349.6)	$ (348.1)