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Commitments and Contingencies - Additional Information (Details) - USD ($) $ in Millions | Sep. 30, 2024 | Dec. 31, 2023
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Commitments and Contingencies Disclosure [Abstract] |  |
Indemnity liability | $ 4.3 | $ 5.2

X
- Definition Indemnity Liabilities + References No definition available. + Details
Name: | fa_IndemnityLiability
Namespace Prefix: | fa_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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- References No definition available. + Details
Name: | us-gaap_CommitmentsAndContingenciesDisclosureAbstract
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration