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Reportable Segments - Reportable Segments - Schedule of Adjusted EBITDA Reconciled to Net Income (Parenthetical) (Details) $ in Millions	3 Months Ended
	Mar. 31, 2024 USD ($)
Sterling
Segment Reporting Information [Line Items]
Transaction and acquisition-related charges	$ 11.1

X

- Definition

This element represents acquisition-related costs incurred to effect a business combination which costs have been expensed during the period. Such costs include finder's fees; advisory, legal, accounting, valuation, and other professional or consulting fees; general administrative costs, including the costs of maintaining an internal acquisitions department; and may include costs of registering and issuing debt and equity securities.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 805
-SubTopic 10
-Section 25
-Paragraph 23
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479405/805-10-25-23

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

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

X

- Details

Name:	us-gaap_StatementBusinessSegmentsAxis=fa_SterlingCheckCorpMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: