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Commitments and Contingencies - Additional Information (Details) - USD ($) $ in Millions	Dec. 31, 2022	Dec. 31, 2021
Loss Contingencies [Line Items]
Indemnity liability	$ 4.4	$ 7.9
Total liability		5.5
Total insurance receivable		$ 2.1

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

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_LossContingenciesLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration