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Commitments and Contingencies - Additional Information (Details) - USD ($) $ in Millions | Mar. 31, 2022 | Feb. 28, 2022 | Dec. 31, 2021
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Commitments and Contingencies Disclosure [Abstract] |  |  |
Indemnity liability | $ 2.5 |  | $ 7.9
Total liability settlement and related to administrative fees |  | $ 5.5 |
Total insurance recoverable asset | $ 2.2 |  |

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

X
- Definition Total insurance recoverable asset + References No definition available. + Details
Name: | fa_TotalInsuranceRecoverableAsset
Namespace Prefix: | fa_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | instant

X
- Definition Total lability settlement and related to administrative fees + References No definition available. + Details
Name: | fa_TotalLabilitySettlementAndRelatedToAdministrativeFees
Namespace Prefix: | fa_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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