ACCUMULATED OTHER COMPREHENSIVE INCOME (Details) - USD ($) $ in Millions	3 Months Ended
	Apr. 03, 2022	Jan. 02, 2022	Apr. 04, 2021	Jan. 03, 2021
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balances at beginning of period	$ 1,347.9	$ 1,479.0	$ 1,444.2	$ 1,415.8
Other comprehensive income (loss) income before reclassification	5.8	8.6	28.9	4.8
Other comprehensive income (loss) before tax	4.6	7.0	33.0	8.6
Deferred tax effect	(4.7)	(2.9)	(8.0)	8.0
Other comprehensive income (loss), net of tax	(0.1)	4.1	25.0	16.6
Other comprehensive income (loss) attributable to controlling interest	0.0	4.0	25.1	16.2
Balances at end of period	1,328.6	1,347.9	1,494.6	1,444.2
Continuing Operations
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Net reclassifications for (gain) loss to income	(0.5)	(1.1)	4.2	3.7
Less: other comprehensive income (loss) attributable to non-controlling interest	(0.1)		(0.1)	0.1
Discontinued Operations
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Net reclassifications for (gain) loss to income	(0.7)	(0.5)	(0.1)	0.1
Less: other comprehensive income (loss) attributable to non-controlling interest		0.1		0.3
Total
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balances at beginning of period	(231.3)	(235.3)	(268.5)	(284.7)
Balances at end of period	(231.3)	(231.3)	(243.4)	(268.5)
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balances at beginning of period	(192.6)	(194.8)	(202.3)	(226.6)
Other comprehensive income (loss) income before reclassification	(1.6)	6.8	22.2	19.4
Other comprehensive income (loss) before tax	(1.6)	6.8	22.2	19.4
Deferred tax effect	(3.1)	(4.5)	(5.0)	5.3
Other comprehensive income (loss), net of tax	(4.7)	2.3	17.2	24.7
Other comprehensive income (loss) attributable to controlling interest	(4.6)	2.2	17.3	24.3
Balances at end of period	(197.2)	(192.6)	(185.0)	(202.3)
Foreign Currency Translation | Continuing Operations
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Net reclassifications for (gain) loss to income	0.0	0.0	0.0	0.0
Less: other comprehensive income (loss) attributable to non-controlling interest	(0.1)		(0.1)	0.1
Foreign Currency Translation | Discontinued Operations
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Net reclassifications for (gain) loss to income	0.0	0.0	0.0	0.0
Less: other comprehensive income (loss) attributable to non-controlling interest		0.1		0.3
Derivative Instruments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balances at beginning of period	9.5	6.4	(3.6)	3.6
Other comprehensive income (loss) income before reclassification	6.4	1.2	5.8	(12.4)
Other comprehensive income (loss) before tax	4.2	(1.4)	8.8	(9.7)
Deferred tax effect	(1.0)	4.5	(2.4)	2.5
Other comprehensive income (loss), net of tax	3.2	3.1	6.4	(7.2)
Other comprehensive income (loss) attributable to controlling interest	3.2	3.1	6.4	(7.2)
Balances at end of period	12.7	9.5	2.8	(3.6)
Derivative Instruments | Continuing Operations
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Net reclassifications for (gain) loss to income	(1.5)	(2.1)	3.1	2.6
Less: other comprehensive income (loss) attributable to non-controlling interest	0.0		0.0	0.0
Derivative Instruments | Discontinued Operations
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Net reclassifications for (gain) loss to income	(0.7)	(0.5)	(0.1)	0.1
Less: other comprehensive income (loss) attributable to non-controlling interest		0.0		0.0
Defined Benefit Pension
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balances at beginning of period	(48.2)	(46.9)	(62.6)	(61.7)
Other comprehensive income (loss) income before reclassification	1.0	0.6	0.9	(2.2)
Other comprehensive income (loss) before tax	2.0	1.6	2.0	(1.1)
Deferred tax effect	(0.6)	(2.9)	(0.6)	0.2
Other comprehensive income (loss), net of tax	1.4	(1.3)	1.4	(0.9)
Other comprehensive income (loss) attributable to controlling interest	1.4	(1.3)	1.4	(0.9)
Balances at end of period	(46.8)	(48.2)	(61.2)	(62.6)
Defined Benefit Pension | Continuing Operations
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Net reclassifications for (gain) loss to income	1.0	1.0	1.1	1.1
Less: other comprehensive income (loss) attributable to non-controlling interest	0.0		0.0	0.0
Defined Benefit Pension | Discontinued Operations
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Net reclassifications for (gain) loss to income	$ 0.0	0.0	$ 0.0	0.0
Less: other comprehensive income (loss) attributable to non-controlling interest		$ 0.0		$ 0.0