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ACCUMULATED OTHER COMPREHENSIVE INCOME - Schedule of Accumulated Other Comprehensive Income (Details) - USD ($)
$ in Millions
 3 Months Ended
Apr. 02, 2023
Jan. 01, 2023
Apr. 03, 2022
Jan. 02, 2022
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Balances at beginning of period $ 1,239.4 $ 1,269.1 $ 1,347.9 $ 1,479.0
Other comprehensive income (loss) before reclassification 7.6 (1.1) 5.8 8.6
Other comprehensive income (loss) before tax 11.7 (2.7) 4.6 7.0
Deferred tax effect 4.5 17.2 (4.7) (2.9)
Other comprehensive income (loss), net of tax 16.2 14.5 (0.1) 4.1
Other comprehensive income (loss) attributable to controlling interest 16.0 14.2 0.0 4.0
Balances at end of period 1,189.1 1,239.4 1,328.6 1,347.9
Continuing Operations        
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Net reclassification for (gain) loss to income 4.2 (1.6) (0.5) (1.1)
Less: other comprehensive income from operations attributable to non-controlling interest 0.1 0.2 (0.1) 0.1
Discontinued Operations        
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Net reclassification for (gain) loss to income (0.1)   (0.7) (0.5)
Less: other comprehensive income from operations attributable to non-controlling interest 0.1 0.1    
Total        
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Balances at beginning of period (288.9) (303.1) (231.3) (235.3)
Balances at end of period (272.9) (288.9) (231.3) (231.3)
Foreign Currency Translation        
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Balances at beginning of period (250.8) (285.9) (192.6) (194.8)
Other comprehensive income (loss) before reclassification 14.6 26.6 (1.6) 6.8
Other comprehensive income (loss) before tax 14.6 26.6 (1.6) 6.8
Deferred tax effect 3.7 8.8 (3.1) (4.5)
Other comprehensive income (loss), net of tax 18.3 35.4 (4.7) 2.3
Other comprehensive income (loss) attributable to controlling interest 18.1 35.1 (4.6) 2.2
Balances at end of period (232.7) (250.8) (197.2) (192.6)
Foreign Currency Translation | Continuing Operations        
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Net reclassification for (gain) loss to income 0.0 0.0 0.0 0.0
Less: other comprehensive income from operations attributable to non-controlling interest 0.1 0.2 (0.1) 0.1
Foreign Currency Translation | Discontinued Operations        
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Net reclassification for (gain) loss to income 0.0   0.0 0.0
Less: other comprehensive income from operations attributable to non-controlling interest 0.1 0.1    
Derivative Instruments        
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Balances at beginning of period (3.9) 16.8 9.5 6.4
Other comprehensive income (loss) before reclassification (7.1) (25.4) 6.4 1.2
Other comprehensive income (loss) before tax (2.3) (27.9) 4.2 (1.4)
Deferred tax effect 0.7 7.2 (1.0) 4.5
Other comprehensive income (loss), net of tax (1.6) (20.7) 3.2 3.1
Other comprehensive income (loss) attributable to controlling interest (1.6) (20.7) 3.2 3.1
Balances at end of period (5.5) (3.9) 12.7 9.5
Derivative Instruments | Continuing Operations        
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Net reclassification for (gain) loss to income 4.9 (2.5) (1.5) (2.1)
Less: other comprehensive income from operations attributable to non-controlling interest 0.0 0.0 0.0 0.0
Derivative Instruments | Discontinued Operations        
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Net reclassification for (gain) loss to income (0.1)   (0.7) (0.5)
Less: other comprehensive income from operations 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 (34.2) (34.0) (48.2) (46.9)
Other comprehensive income (loss) before reclassification 0.1 (2.3) 1.0 0.6
Other comprehensive income (loss) before tax (0.6) (1.4) 2.0 1.6
Deferred tax effect 0.1 1.2 (0.6) (2.9)
Other comprehensive income (loss), net of tax (0.5) (0.2) 1.4 (1.3)
Other comprehensive income (loss) attributable to controlling interest (0.5) (0.2) 1.4 (1.3)
Balances at end of period (34.7) (34.2) (46.8) (48.2)
Defined Benefit Pension | Continuing Operations        
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Net reclassification for (gain) loss to income (0.7) 0.9 1.0 1.0
Less: other comprehensive income from operations attributable to non-controlling interest 0.0 0.0 0.0 0.0
Defined Benefit Pension | Discontinued Operations        
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Net reclassification for (gain) loss to income 0.0   $ 0.0 $ 0.0
Less: other comprehensive income from operations attributable to non-controlling interest $ 0.0 $ 0.0