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Acquisitions - Narrative (Details) £ / shares in Units, $ / shares in Units, $ in Thousands, £ in Millions |  | 3 Months Ended | 5 Months Ended | 9 Months Ended | 12 Months Ended |
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Jan. 23, 2023 USD ($) employee | Jan. 23, 2023 GBP (£) employee | Jul. 02, 2023 USD ($) $ / shares | Apr. 02, 2023 USD ($) program employee | Jul. 03, 2022 USD ($) | Jul. 02, 2023 USD ($) $ / shares | Jul. 02, 2023 USD ($) | Jul. 03, 2022 USD ($) | Oct. 02, 2022 USD ($) acquisition | Sep. 23, 2022 £ / shares
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |
Pence per share expected to be acquired | £ / shares |  |  |  |  |  |  |  |  |  | £ 2.22
Acquisition and integration expenses |  |  | $ 2,107 |  | $ 0 |  | $ 25,812 | $ 0 |  |
Payables related to promissory note |  |  |  |  |  |  | $ 0 | $ 14,578 |  |
Number of acquisitions | acquisition |  |  |  |  |  |  |  |  | 4 |
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 |  |  | 1 year | 1 year |  |  |
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 |  |  | 8 years |  |  | 8 years | 8 years |  |  |
RPS Group PLC |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |
Number of employees | employee | 5,000 | 5,000 |  |  |  |  |  |  |  |
Total purchase price | $ 784,000 | £ 633 |  |  |  |  |  |  |  |
Acquisition and integration expenses |  |  | $ 2,100 |  |  |  | $ 25,800 |  |  |
Net purchase price | 675,000 |  |  |  |  |  |  |  |  |
Revenue |  |  | 220,400 |  |  | $ 389,900 |  |  |  |
Net income (loss) |  |  | $ 700 |  |  | $ (1,000) |  |  |  |
Diluted earnings per share (in dollars per share) | $ / shares |  |  | $ 0.01 |  |  | $ 0.02 |  |  |  |
Intangible amortization |  |  | $ 10,400 |  |  | $ 18,100 |  |  |  |
RPS Group PLC | Foreign Exchange Forward |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |
Foreign currency forward contract, asset fair value | $ 109,300 |  |  |  |  |  |  |  | $ 19,900 |
Amyx, Inc. |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |
Number of employees | employee |  |  |  | 500 |  |  |  |  |  |
Total purchase price |  |  |  | $ 120,900 |  |  |  |  |  |
Number of government programs acquired | program |  |  |  | 30 |  |  |  |  |  |
Payables related to promissory note |  |  |  | $ 100,000 |  |  |  |  |  |
Contingent earn-out liability |  |  |  | 12,200 |  |  |  |  |  |
Aggregate maximum of contingent consideration |  |  |  | 25,000 |  |  |  |  |  |
Receivables (payables) related to estimated post-closing adjustments |  |  |  | $ (8,700) |  |  |  |  |  |
Business acquisitions |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |
Total purchase price |  |  |  |  |  |  |  |  | 88,300 |
Payables related to promissory note |  |  |  |  |  |  |  |  | 15,500 |
Contingent earn-out liability |  |  |  |  |  |  |  |  | 31,300 |
Aggregate maximum of contingent consideration |  |  |  |  |  |  |  |  | 47,000 |
Initial cash payments |  |  |  |  |  |  |  |  | 44,000 |
Receivables (payables) related to estimated post-closing adjustments |  |  |  |  |  |  |  |  | $ 2,500 |
Business acquisitions | Minimum |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |
Earn-out period |  |  |  |  |  |  |  |  | 3 years |
Business acquisitions | Maximum |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |
Earn-out period |  |  |  |  |  |  |  |  | 5 years |
All acquisitions |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |
Contingent earn-out liability |  |  | 76,600 |  |  | 76,600 | 76,600 |  |  |
Aggregate maximum of contingent consideration |  |  | $ 120,300 |  |  | $ 120,300 | 120,300 |  |  |
Reduction in contingent earn-out liabilities |  |  |  |  |  |  | $ 8,500 |  |  |

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