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Goodwill and Other Intangible Assets - Narrative (Details) - USD ($)
 3 Months Ended 6 Months Ended
Jul. 02, 2022
Jul. 03, 2021
Jul. 02, 2022
Jul. 03, 2021
Jan. 01, 2022
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]          
Goodwill $ 1,046,000,000   $ 1,046,000,000   $ 1,116,500,000
Goodwill impairment loss     0    
Gross Carrying Value 487,200,000   487,200,000   495,000,000.0
Non-amortized trademarks 135,000,000.0   135,000,000.0   142,600,000
Accumulated impairment losses 0   $ 0    
Weighted-average amortization period (in years)     12 years    
Aggregate amortization expense 7,200,000 $ 6,300,000 $ 14,400,000 $ 12,300,000  
Estimated annual amortization expense for fiscal period 2022 28,400,000   28,400,000    
Estimated annual amortization expense for fiscal period 2023 25,800,000   25,800,000    
Estimated annual amortization expense for fiscal period 2024 19,600,000   19,600,000    
Estimated annual amortization expense for fiscal period 2025 14,100,000   14,100,000    
Estimated annual amortization expense for fiscal period 2026 10,900,000   10,900,000    
Estimated annual amortization expense for fiscal period 2027 9,700,000   9,700,000    
Customer relationships          
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]          
Gross Carrying Value 212,600,000   $ 212,600,000   217,800,000
Weighted-average amortization period (in years)     14 years    
Customer relationship contractual term, minimum (in years)     3 years    
Customer relationship contractual term, maximum (in years)     5 years    
Developed technology          
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]          
Gross Carrying Value 35,900,000   $ 35,900,000   36,600,000
Weighted-average amortization period (in years)     5 years    
Dealer-FX          
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]          
Goodwill 118,200,000   $ 118,200,000    
Goodwill, purchase accounting adjustments     32,600,000    
Non-amortized trademarks 17,700,000   17,700,000    
Dealer-FX | Customer relationships          
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]          
Gross Carrying Value 28,400,000   28,400,000    
Dealer-FX | Developed technology          
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]          
Gross Carrying Value 14,800,000   14,800,000    
Secateurs Pradines          
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]          
Goodwill 10,200,000   10,200,000    
Goodwill, purchase accounting adjustments (500,000)        
Repair Systems & Information Group          
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]          
Goodwill 731,000,000.0   731,000,000.0   778,300,000
Repair Systems & Information Group | Dealer-FX          
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]          
Goodwill 118,200,000   118,200,000    
Commercial & Industrial Group          
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]          
Goodwill 302,600,000   302,600,000   $ 325,800,000
Commercial & Industrial Group | Secateurs Pradines          
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]          
Goodwill 10,200,000   10,200,000    
Commercial & Industrial Group | AutoCrib          
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]          
Goodwill $ 3,300,000   $ 3,300,000