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Goodwill and Other Intangible Assets - Narrative (Detail) - USD ($)
3 Months Ended 12 Months Ended
Jul. 02, 2022
Apr. 02, 2022
Dec. 31, 2022
Jan. 01, 2022
Jan. 02, 2021
Feb. 26, 2021
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]            
Goodwill     $ 1,045,300,000 $ 1,116,500,000 $ 982,400,000  
Goodwill associated with acquisition, purchase accounting adjustment     33,100,000      
Goodwill and intangible assets, accumulated impairment loss     $ 0      
Weighted-average amortization period (in years)     12 years      
Aggregate amortization expense     $ 28,700,000 29,200,000 23,400,000  
Estimated annual amortization expense for fiscal period 2023     26,600,000      
Estimated annual amortization expense for fiscal period 2024     20,700,000      
Estimated annual amortization expense for fiscal period 2025     14,800,000      
Estimated annual amortization expense for fiscal period 2026     11,300,000      
Estimated annual amortization expense for fiscal period 2027     10,000,000      
Repair Systems  & Information Group            
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]            
Goodwill     730,000,000.0 778,300,000 638,800,000  
Goodwill associated with acquisition, purchase accounting adjustment     32,600,000      
Commercial & Industrial Group            
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]            
Goodwill     302,900,000 325,800,000 $ 331,200,000  
Goodwill associated with acquisition, purchase accounting adjustment     500,000      
Dealer-FX            
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]            
Goodwill     118,200,000     $ 118,200,000
Goodwill associated with acquisition, purchase accounting adjustment   $ 32,600,000 32,600,000      
Dealer-FX | Repair Systems  & Information Group            
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]            
Goodwill     118,200,000      
Secateurs Pradines            
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]            
Goodwill     10,200,000      
Goodwill associated with acquisition, purchase accounting adjustment $ 500,000   500,000      
Secateurs Pradines | Commercial & Industrial Group            
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]            
Goodwill     10,200,000      
AutoCrib            
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]            
Goodwill       $ 18,300,000    
AutoCrib | Commercial & Industrial Group            
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]            
Goodwill     $ 3,300,000