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Acquisitions (Details) $ in Millions | 3 Months Ended | 12 Months Ended
--- | --- | ---
Jan. 02, 2022 USD ($) | Oct. 03, 2021 USD ($) employee
Business Acquisition [Line Items] |  |
Contingent earn-out liability | $ 65.8 |
Minimum |  |
Business Acquisition [Line Items] |  |
Significant unobservable input, earn-out period | 3 years |
Minimum | Existing customer contracts |  |
Business Acquisition [Line Items] |  |
Useful life of intangible assets | 1 year |
Minimum | Trade names |  |
Business Acquisition [Line Items] |  |
Useful life of intangible assets | 3 years |
Maximum |  |
Business Acquisition [Line Items] |  |
Significant unobservable input, earn-out period | 5 years |
Maximum | Existing customer contracts |  |
Business Acquisition [Line Items] |  |
Useful life of intangible assets | 10 years |
Maximum | Trade names |  |
Business Acquisition [Line Items] |  |
Useful life of intangible assets | 5 years |
Hoare Lea |  |
Business Acquisition [Line Items] |  |
Number of employees | employee |  | 900
Business acquisitions |  |
Business Acquisition [Line Items] |  |
Fair value of acquisition purchase price |  | $ 151.7
Initial cash payments |  | 101.4
Contingent earn-out liability |  | 50.3
Aggregate maximum of contingent consideration |  | $ 74.0
Business acquisitions | Minimum |  |
Business Acquisition [Line Items] |  |
Earn-out period |  | 3 years
Business acquisitions | Maximum |  |
Business Acquisition [Line Items] |  |
Earn-out period |  | 4 years
All acquisitions |  |
Business Acquisition [Line Items] |  |
Aggregate maximum of contingent consideration | $ 119.4 |

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