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Commitments and Contingencies - Additional Information (Details) - USD ($) $ in Millions	Mar. 31, 2022	Feb. 28, 2022	Dec. 31, 2021
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

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- 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