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Goodwill and Other Intangible Assets - Narrative (Details) - USD ($)
 3 Months Ended 9 Months Ended
Oct. 01, 2022
Jul. 02, 2022
Apr. 02, 2022
Oct. 02, 2021
Oct. 01, 2022
Oct. 02, 2021
Jan. 01, 2022
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]              
Goodwill $ 1,010,600,000       $ 1,010,600,000   $ 1,116,500,000
Gross Carrying Value 479,800,000       479,800,000   495,000,000.0
Non-amortized trademarks 128,300,000       128,300,000   142,600,000
Goodwill impairment loss   $ 0          
Accumulated impairment losses 0       $ 0    
Weighted-average amortization period (in years)         12 years    
Aggregate amortization expense 7,200,000     $ 6,400,000 $ 21,600,000 $ 18,700,000  
Estimated annual amortization expense for fiscal period 2022 28,400,000       28,400,000    
Estimated annual amortization expense for fiscal period 2023 26,200,000       26,200,000    
Estimated annual amortization expense for fiscal period 2024 20,700,000       20,700,000    
Estimated annual amortization expense for fiscal period 2025 14,400,000       14,400,000    
Estimated annual amortization expense for fiscal period 2026 11,000,000       11,000,000    
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 207,600,000       $ 207,600,000   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 35,100,000       $ 35,100,000   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 717,500,000       717,500,000   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 280,700,000       280,700,000   $ 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