Income Taxes - Summary of Income Tax Contingencies (Details) - USD ($) $ in Thousands	12 Months Ended
Dec. 31, 2025	Dec. 31, 2024	Dec. 31, 2023
Income Tax Disclosure [Abstract]
Balance, beginning of period	$ 5,662	$ 511	$ 512
Adjustments made during purchase accounting window	(167)	0	0
Increases for tax positions related to prior years	37	0	0
Decreases for tax positions related to prior years	(400)	(216)	(1)
Acquired tax positions related to prior years	0	5,433	0
Effects of foreign currency	66		0
Effects of foreign currency		(66)
Balance, end of period	$ 5,198	$ 5,662	$ 511

Adjustments Made During Purchase Accounting Window

No definition available.

Name:	fa_AdjustmentsMadeDuringPurchaseAccountingWindow
Namespace Prefix:	fa_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Unrecognized Tax Benefits Acquired Tax Positions Related To Prior Years

+ References

No definition available.

+ Details

Name:	fa_UnrecognizedTaxBenefitsAcquiredTaxPositionsRelatedToPriorYears
Namespace Prefix:	fa_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- References

No definition available.

+ Details

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

- Definition

Amount of unrecognized tax benefits.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 217
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482663/740-10-55-217

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 15A
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482685/740-10-50-15A

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 10B
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482525/740-10-45-10B

+ Details

Name:	us-gaap_UnrecognizedTaxBenefits
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of decrease in unrecognized tax benefits resulting from foreign currency translation.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 15A
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482685/740-10-50-15A

+ Details

Name:	us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromForeignCurrencyTranslation
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of decrease in unrecognized tax benefits resulting from tax positions taken in prior period tax returns.

+ References

+ Details

Name:	us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromPriorPeriodTaxPositions
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of increase in unrecognized tax benefits resulting from foreign currency translation.

+ References

+ Details

Name:	us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromForeignCurrencyTranslation
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of increase in unrecognized tax benefits resulting from tax positions taken in prior period tax returns.

+ References

+ Details

Name:	us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromPriorPeriodTaxPositions
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration