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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 |  |

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