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Basis of Presentation and Recent Developments (Details) € in Millions, £ in Millions, R$ in Millions, $ in Millions |  |  |  |  |  |  |  | 3 Months Ended | 9 Months Ended |  |  |
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Jul. 19, 2024 USD ($) shares | Apr. 05, 2024 USD ($) shares | Apr. 05, 2024 BRL (R$) shares | Apr. 04, 2024 USD ($) | Apr. 04, 2024 EUR (€) | Mar. 01, 2024 USD ($) shares | Mar. 01, 2024 GBP (£) shares | Jan. 02, 2024 USD ($) shares | Nov. 01, 2023 USD ($) shares | Oct. 02, 2023 USD ($) shares | Jun. 30, 2024 USD ($) | Dec. 31, 2023 USD ($) | Sep. 30, 2023 USD ($) | Sep. 30, 2023 | Apr. 05, 2024 BRL (R$) | Apr. 04, 2024 EUR (€) | Mar. 01, 2024 GBP (£)
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Income Tax Expense Adjustment |  |  |  |  |  |  |  |  |  |  | $ 10.4 | $ 5.3 | $ 7.3 |  |  |  |
Income Tax Expense Adjustment |  |  |  |  |  |  |  |  |  |  | $ 10.4 | $ 5.3 | $ 7.3 |  |  |  |
income tax expense |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Immaterial Error Correction |  |  |  |  |  |  |  |  |  |  |  |  |  | 2.1 million |  |  |
Income tax receivable and payable |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Immaterial Error Correction |  |  |  |  |  |  |  |  |  |  |  | 12.9 million |  |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Immaterial Error Correction |  |  |  |  |  |  |  |  |  |  |  |  |  | 23.5 million |  |  |
Income tax payable |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Immaterial Error Correction |  |  |  |  |  |  |  |  |  |  |  |  |  | 2.4 million |  |  |
Deferred tax asset |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Immaterial Error Correction |  |  |  |  |  |  |  |  |  |  |  |  |  | 4.5 million |  |  |
Tax receivable agreement |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Immaterial Error Correction |  |  |  |  |  |  |  |  |  |  | 2.1 million |  |  |  |  |  |
Left Field Labs |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Aggregate purchase price |  |  |  |  |  |  |  |  |  | $ 13.2 |  |  |  |  |  |  |
Payments to Acquire Businesses, Gross |  |  |  |  |  |  |  |  |  | $ 9.4 |  |  |  |  |  |  |
Shares issued by the Company (shares) | shares |  |  |  |  |  |  |  |  |  | 825,402 |  |  |  |  |  |  |
Deferred acquisition consideration |  |  |  |  |  |  |  |  |  | $ 51.0 |  |  |  |  |  |  |
Business Acquisition, Equity Interest Issued or Issuable, Value Assigned |  |  |  |  |  |  |  |  |  | $ 3.8 |  |  |  |  |  |  |
Movers and Shakers LLC |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Aggregate purchase price |  |  |  |  |  |  |  |  | $ 14.7 |  |  |  |  |  |  |  |
Payments to Acquire Businesses, Gross |  |  |  |  |  |  |  |  | 10.2 |  |  |  |  |  |  |  |
Deferred acquisition consideration |  |  |  |  |  |  |  |  | 35.0 |  |  |  |  |  |  |  |
Business Acquisition, Equity Interest Issued or Issuable, Value Assigned |  |  |  |  |  |  |  |  | $ 4.5 |  |  |  |  |  |  |  |
Movers and Shakers LLC | Common Class A |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Shares issued by the Company (shares) | shares |  |  |  |  |  |  |  |  | 1,000,000 |  |  |  |  |  |  |  |
Team Epiphany |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Aggregate purchase price |  |  |  |  |  |  |  | $ 15.8 |  |  |  |  |  |  |  |  |
Payments to Acquire Businesses, Gross |  |  |  |  |  |  |  | $ 10.8 |  |  |  |  |  |  |  |  |
Shares issued by the Company (shares) | shares |  |  |  |  |  |  |  | 797,916 |  |  |  |  |  |  |  |  |
Deferred acquisition consideration |  |  |  |  |  |  |  | $ 17.0 |  |  |  |  |  |  |  |  |
Business Acquisition, Equity Interest Issued or Issuable, Value Assigned |  |  |  |  |  |  |  | $ 5.0 |  |  |  |  |  |  |  |  |
Sidekick Live Limited |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Aggregate purchase price |  |  |  |  |  | $ 6.0 | £ 4.6 |  |  |  |  |  |  |  |  |  |
Payments to Acquire Businesses, Gross |  |  |  |  |  | $ 5.0 | £ 3.6 |  |  |  |  |  |  |  |  |  |
Shares issued by the Company (shares) | shares |  |  |  |  |  | 195,431 | 195,431 |  |  |  |  |  |  |  |  |  |
Deferred acquisition consideration |  |  |  |  |  | $ 10.0 |  |  |  |  |  |  |  |  |  |  | £ 8.0
Business Acquisition, Equity Interest Issued or Issuable, Value Assigned |  |  |  |  |  | $ 1.0 |  |  |  |  |  |  |  |  |  |  | £ 0.9
What's Next Partners |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Aggregate purchase price |  |  |  | $ 5.0 | € 4.3 |  |  |  |  |  |  |  |  |  |  |  |
Deferred acquisition consideration |  |  |  | $ 9.0 |  |  |  |  |  |  |  |  |  |  |  | € 8.5 |
PROS Agency |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Aggregate purchase price |  | $ 9.0 | R$ 42.1 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Payments to Acquire Businesses, Gross |  | $ 5.0 | R$ 23.3 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Shares issued by the Company (shares) | shares |  | 182,256 | 182,256 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Deferred acquisition consideration |  | $ 14.0 |  |  |  |  |  |  |  |  |  |  |  |  | R$ 72.5 |  |
Business Acquisition, Equity Interest Issued or Issuable, Value Assigned |  | $ 1.0 |  |  |  |  |  |  |  |  |  |  |  |  | R$ 5.3 |  |
Leaders | Subsequent event |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Aggregate purchase price | $ 3.8 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Payments to Acquire Businesses, Gross | $ 2.9 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Shares issued by the Company (shares) | shares | 135,010 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Deferred acquisition consideration | $ 6.6 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition, Equity Interest Issued or Issuable, Value Assigned | $ 0.9 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |

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