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Commitments and Contingencies - Additional Information (Details) - USD ($) $ in Millions	Sep. 30, 2024	Dec. 31, 2023
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

X

- References

No definition available.

+ Details

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