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Goodwill and Other Intangible Assets - Narrative (Details) - USD ($)
3 Months Ended
Apr. 02, 2022
Apr. 03, 2021
Jan. 01, 2022
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]      
Goodwill $ 1,077,800,000   $ 1,116,500,000
Gross carrying value, finite-lived intangible assets 490,600,000   495,000,000.0
Non-amortized trademarks 141,200,000   142,600,000
Accumulated impairment losses $ 0    
Weighted-average amortization period (in years) 12 years    
Aggregate amortization expense $ 7,200,000 $ 6,000,000  
Estimated annual amortization expense for fiscal period 2022 28,300,000    
Estimated annual amortization expense for fiscal period 2023 24,900,000    
Estimated annual amortization expense for fiscal period 2024 19,600,000    
Estimated annual amortization expense for fiscal period 2025 14,100,000    
Estimated annual amortization expense for fiscal period 2026 10,500,000    
Estimated annual amortization expense for fiscal period 2027 9,700,000    
Dealer-FX      
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]      
Goodwill 118,200,000    
Goodwill, purchase accounting adjustments 32,600,000    
Non-amortized trademarks 17,700,000    
Secateurs Pradines      
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]      
Goodwill 10,700,000    
Customer relationships      
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]      
Gross carrying value, finite-lived intangible assets $ 216,800,000   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    
Customer relationships | Dealer-FX      
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]      
Gross carrying value, finite-lived intangible assets $ 28,400,000    
Developed technology      
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]      
Gross carrying value, finite-lived intangible assets $ 36,500,000   36,600,000
Weighted-average amortization period (in years) 5 years    
Developed technology | Dealer-FX      
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]      
Gross carrying value, finite-lived intangible assets $ 14,800,000    
Repair Systems & Information Group      
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]      
Goodwill 743,200,000   778,300,000
Repair Systems & Information Group | Dealer-FX      
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]      
Goodwill 118,200,000    
Commercial & Industrial Group      
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]      
Goodwill 322,200,000   $ 325,800,000
Commercial & Industrial Group | Secateurs Pradines      
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]      
Goodwill 10,700,000    
Commercial & Industrial Group | AutoCrib      
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]      
Goodwill $ 3,300,000