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Commitments and Contingencies - Additional Information (Details) - USD ($) $ in Millions	Dec. 31, 2023	Dec. 31, 2022	Dec. 31, 2021
Loss Contingencies [Line Items]
Indemnity liability	$ 5.2	$ 4.4
Total liability			$ 5.5
Total insurance receivable			$ 2.1

X

- Definition

Indemnity Liabilities

+ References

No definition available.

+ Details

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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

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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

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 460
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482425/460-10-50-3

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 450
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-Name Accounting Standards Codification
-Section 50
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-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483076/450-20-50-1

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 450
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-Name Accounting Standards Codification
-Section 50
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-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483076/450-20-50-4

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 450
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-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483076/450-20-50-4

Reference 5: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 450
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-Name Accounting Standards Codification
-Section 50
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-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483076/450-20-50-9

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 450
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 9
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483076/450-20-50-9

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