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Goodwill and Other Intangible Assets - Narrative (Detail) - USD ($) $ in Millions | 12 Months Ended
--- | ---
Jan. 01, 2022 | Jan. 02, 2021 | Dec. 28, 2019
Acquired Finite And Indefinite Lived Intangible Assets [Line Items] |  |  |
Goodwill | $ 1,116.5 | $ 982.4 | $ 913.8
Gross carrying value, finite-lived intangible assets | 495.0 | 440.8 |
Non-amortized trademarks | $ 142.6 | 129.6 |
Weighted-average amortization period (in years) | 12 years |  |
Aggregate amortization expense | $ 29.2 | 23.4 | 22.3
Estimated annual amortization expense for fiscal period 2022 | 28.0 |  |
Estimated annual amortization expense for fiscal period 2023 | 24.5 |  |
Estimated annual amortization expense for fiscal period 2024 | 18.8 |  |
Estimated annual amortization expense for fiscal period 2025 | 14.0 |  |
Estimated annual amortization expense for fiscal period 2026 | 10.8 |  |
Repair Systems & Information Group |  |  |
Acquired Finite And Indefinite Lived Intangible Assets [Line Items] |  |  |
Goodwill | 778.3 | 638.8 | 615.1
Dealer-FX |  |  |
Acquired Finite And Indefinite Lived Intangible Assets [Line Items] |  |  |
Goodwill | 150.8 |  |
Dealer-FX | Repair Systems & Information Group |  |  |
Acquired Finite And Indefinite Lived Intangible Assets [Line Items] |  |  |
Goodwill | 150.8 |  |
Sigmavision Limited |  |  |
Acquired Finite And Indefinite Lived Intangible Assets [Line Items] |  |  |
Goodwill |  | 5.6 |
Cognitran Limited |  |  |
Acquired Finite And Indefinite Lived Intangible Assets [Line Items] |  |  |
Goodwill |  | 14.5 |
Increase in goodwill associated with acquisition, purchase accounting adjustment |  | 3.1 |
AutoCrib |  |  |
Acquired Finite And Indefinite Lived Intangible Assets [Line Items] |  |  |
Goodwill | 18.3 | 18.3 |
Non-amortized trademarks | 17.7 | 7.4 |
Power Hawk Technologies Inc |  |  |
Acquired Finite And Indefinite Lived Intangible Assets [Line Items] |  |  |
Goodwill |  |  | $ 6.4
Patents |  |  |
Acquired Finite And Indefinite Lived Intangible Assets [Line Items] |  |  |
Gross carrying value, finite-lived intangible assets | $ 45.7 | 43.2 |
Weighted-average amortization period (in years) | 14 years |  |
Patents | Sigmavision Limited |  |  |
Acquired Finite And Indefinite Lived Intangible Assets [Line Items] |  |  |
Gross carrying value, finite-lived intangible assets |  | 0.3 |
Customer relationships |  |  |
Acquired Finite And Indefinite Lived Intangible Assets [Line Items] |  |  |
Gross carrying value, finite-lived intangible assets | $ 217.8 | 191.5 |
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 | AutoCrib |  |  |
Acquired Finite And Indefinite Lived Intangible Assets [Line Items] |  |  |
Gross carrying value, finite-lived intangible assets | $ 28.4 | 4.6 |
Developed technology |  |  |
Acquired Finite And Indefinite Lived Intangible Assets [Line Items] |  |  |
Gross carrying value, finite-lived intangible assets | $ 36.6 | 21.8 |
Weighted-average amortization period (in years) | 5 years |  |
Developed technology | AutoCrib |  |  |
Acquired Finite And Indefinite Lived Intangible Assets [Line Items] |  |  |
Gross carrying value, finite-lived intangible assets | $ 14.8 | $ 1.7 |

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