Accelerated amortization of deferred financing costs.

No definition available.

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

- Definition

Amortizing principal payment repayment.

+ References

No definition available.

+ Details

Name:	fa_AmortizingPrincipalPaymentRepayment
Namespace Prefix:	fa_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Debt Instrument Interest Rate Reduced During Period

+ References

No definition available.

+ Details

Name:	fa_DebtInstrumentInterestRateReducedDuringPeriod
Namespace Prefix:	fa_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Description of borrowing capacity not subject to net leverage ratio covenant.

+ References

No definition available.

+ Details

Name:	fa_DescriptionOfBorrowingCapacityNotSubjectToNetLeverageRatioCovenant
Namespace Prefix:	fa_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Revolving credit facility quarterly payments, percentage.

+ References

No definition available.

+ Details

Name:	fa_RevolvingCreditFacilityQuarterlyPaymentsPercentage
Namespace Prefix:	fa_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount, before unamortized (discount) premium and debt issuance costs, of long-term debt. Includes, but is not limited to, notes payable, bonds payable, commercial loans, mortgage loans, convertible debt, subordinated debt and other types of debt.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (b)(1)
-URI http://asc.fasb.org/extlink&oid=123466204&loc=SL6031897-161870

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(16))
-URI http://asc.fasb.org/extlink&oid=120400017&loc=d3e572229-122910

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(16))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

+ Details

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

- Definition

The average effective interest rate during the reporting period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=124435984&loc=d3e28551-108399

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 1F
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=123466505&loc=SL123495355-112611

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22(a)(1))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_DebtInstrumentInterestRateDuringPeriod
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

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

- Definition

Date when the debt instrument is scheduled to be fully repaid, in YYYY-MM-DD format.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22(a)(2))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 1B
-Subparagraph (d)
-URI http://asc.fasb.org/extlink&oid=123466505&loc=SL123495323-112611

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)
-URI http://asc.fasb.org/extlink&oid=123874694&loc=d3e19207-110258

+ Details

Name:	us-gaap_DebtInstrumentMaturityDate
Namespace Prefix:	us-gaap_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

- Definition

Description of the maturity date of the debt instrument including whether the debt matures serially and, if so, a brief description of the serial maturities.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22(a)(2))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Difference between the fair value of payments made and the carrying amount of debt which is extinguished prior to maturity.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 50
-Section 40
-Paragraph 4
-URI http://asc.fasb.org/extlink&oid=123467658&loc=d3e12355-112629

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 50
-Section 40
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=123467658&loc=d3e12317-112629

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=123570139&loc=d3e3602-108585

+ Details

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

- Definition

Amount of current borrowing capacity under the credit facility considering any current restrictions on the amount that could be borrowed (for example, borrowings may be limited by the amount of current assets), but without considering any amounts currently outstanding under the facility.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19(b),22(b))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Date the credit facility terminates, in YYYY-MM-DD format.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19(b),22(b))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_LineOfCreditFacilityExpirationDate1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

- Definition

Maximum borrowing capacity under the credit facility without consideration of any current restrictions on the amount that could be borrowed or the amounts currently outstanding under the facility.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19(b),22(b))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Indebtedness divided by net capital.

+ References

No definition available.

+ Details

Name:	us-gaap_RatioOfIndebtednessToNetCapital1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	instant

- Definition

The cash outflow for debt initially having maturity due after one year or beyond the normal operating cycle, if longer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 15
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=123570139&loc=d3e3291-108585

+ Details

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

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=fa_TermLoanDueJanuaryThirtyOneTwoThousandTwentySevenMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_VariableRateAxis=us-gaap_LondonInterbankOfferedRateLIBORMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=fa_TermLoanDueJanuaryThirtyOneTwoThousandTwentyEightMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=fa_SuccessorFirstLienMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=fa_SuccessorRevolverMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Long-term Debt - Additional Information (Details) $ in Thousands			1 Months Ended		3 Months Ended		6 Months Ended
	Jun. 30, 2021 USD ($)	Sep. 30, 2020	Feb. 28, 2021 USD ($)	Feb. 28, 2020 USD ($)	Jun. 30, 2022 USD ($)	Jun. 30, 2021 USD ($)	Jun. 30, 2022 USD ($)	Jun. 30, 2021 USD ($)
Debt Instrument [Line Items]
Loss on extinguishment of debt			$ 13,900		$ 0	$ 0	$ 0	$ 13,938
Description of borrowing capacity not subject to net leverage ratio covenant				In the event the Company’s outstanding indebtedness under the Successor Revolver exceeds 35% of the aggregate principal amount of the revolving commitments then in effect, it is required to maintain a consolidated first lien leverage ratio no greater than 7.75 to 1:00.			the Company had no outstanding amounts under the Successor Revolver, and therefore was not subject to the consolidated first lien leverage ratio covenant and was compliant with all other covenants under the agreement.
Additional interest expense related to deferred financing costs	$ 3,700
Minimum [Member]
Debt Instrument [Line Items]
Debt instrument, net leverage ratio				7.75
Maximum [Member]
Debt Instrument [Line Items]
Debt instrument, net leverage ratio				1.00
Term Loan due January 31, 2027 [Member]
Debt Instrument [Line Items]
Total debt			$ 766,600	$ 670,000
Maturity date			Jan. 31, 2027	Jan. 31, 2027			Jan. 31, 2027
Amortizing Principal Payment Repayment	44,300
Repayments of Credit Facility	$ 200,000
Debt instrument interest rate reduced during period	0.25%
Term Loan due January 31, 2027 [Member] \| LIBOR [Member] \| Minimum [Member]
Debt Instrument [Line Items]
Interest rate	2.75%		3.00%	3.25%
Term Loan due January 31, 2027 [Member] \| LIBOR [Member] \| Maximum [Member]
Debt Instrument [Line Items]
Interest rate	3.00%		3.25%	3.50%
Term Loan due January 31, 2028 [Member]
Debt Instrument [Line Items]
Total debt				$ 145,000
Maturity date				Jan. 31, 2028
Term Loan due January 31, 2028 [Member] \| LIBOR [Member]
Debt Instrument [Line Items]
Interest rate				8.50%
Successor First Lien [Member]
Debt Instrument [Line Items]
Revolving credit facility quarterly payments, percentage		0.25%
Successor Revolver [Member]
Debt Instrument [Line Items]
Maturity date				Jan. 31, 2025
Current borrowing capacity under successor revolver				$ 75,000	$ 100,000		$ 100,000
Maximum borrowing capacity under successor revolver				$ 75,000
Debt instrument, maturity date, description	the maturity date from January 31, 2025 to July 31, 2026.
Extended maturity date under successor revolver	Jul. 31, 2026