Leases - Maturities of lease liabilities (Details) - USD ($) $ in Thousands	Sep. 30, 2022	Jan. 01, 2022
Leases [Abstract]
Finance Lease, 2022	$ 214
Finance Lease, 2023	106
Finance Lease, Liability, Payment, Due, Total	320
Finance Lease, Less: Imputed interest	(5)
Finance Leases, Present value of minimum lease payments	315
Operating Lease, 2022	1,895
Operating Lease, 2023	6,041
Operating Lease, 2024	5,264
Operating Lease, 2025	2,032
Operating Lease, 2026	1,523
Operating Lease, Thereafter	383
Lessee, Operating Lease, Liability, to be Paid, Total	17,138
Operating Lease, Less: Imputed interest	(1,270)
Operating Lease, Present value of minimum lease payments	15,868	$ 15,000
2022	2,109
2023	6,147
2024	5,264
2025	2,032
2026	1,523
Thereafter	383
Total minimum lease payments	$ 17,458

Lease Liability Payments Due

No definition available.

Name:	fa_LeaseLiabilityPaymentsDue
Namespace Prefix:	fa_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Lease Liability Payments Due After Year Five

+ References

No definition available.

+ Details

Name:	fa_LeaseLiabilityPaymentsDueAfterYearFive
Namespace Prefix:	fa_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Lease Liability Payments Due Year Five

+ References

No definition available.

+ Details

Name:	fa_LeaseLiabilityPaymentsDueYearFive
Namespace Prefix:	fa_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Lease Liability Payments Due Year Four

+ References

No definition available.

+ Details

Name:	fa_LeaseLiabilityPaymentsDueYearFour
Namespace Prefix:	fa_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Lease Liability Payments Due Year Three

+ References

No definition available.

+ Details

Name:	fa_LeaseLiabilityPaymentsDueYearThree
Namespace Prefix:	fa_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Lease Liability Payments Due Year Two

+ References

No definition available.

+ Details

Name:	fa_LeaseLiabilityPaymentsDueYearTwo
Namespace Prefix:	fa_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Lease Liability Payments Remainder Of Fiscal Year

+ References

No definition available.

+ Details

Name:	fa_LeaseLiabilityPaymentsRemainderOfFiscalYear
Namespace Prefix:	fa_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Present value of lessee's discounted obligation for lease payments from finance lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 6
-URI https://asc.fasb.org/extlink&oid=128292326&loc=SL77918701-209980

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=123391704&loc=SL77918627-209977

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payments for finance lease.

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for finance lease to be paid in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for finance lease to be paid in remainder of current fiscal year.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 6
-URI https://asc.fasb.org/extlink&oid=128292326&loc=SL77918701-209980

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payments in excess of discounted obligation for lease payments for finance lease.

+ References

+ Details

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

- References

No definition available.

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease.

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease due after fifth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease having initial or remaining lease term in excess of one year to be paid in remainder of current fiscal year.

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payments in excess of discounted obligation for lease payments for operating lease.

+ References

+ Details

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

- Definition

Present value of lessee's discounted obligation for lease payments from operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=123391704&loc=SL77918627-209977

+ Details

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