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Leases (Additional Information) (Details) - USD ($) $ in Millions | 1 Months Ended | 11 Months Ended | 12 Months Ended |
--- | --- | --- | --- | ---
Jan. 31, 2020 | Dec. 31, 2020 | Dec. 31, 2021 | Dec. 31, 2022
Lessee, Lease, Description [Line Items] |  |  |  |
Rent expense under operating leases | $ 0.5 | $ 5.3 | $ 6.1 |
Maximum |  |  |  |
Lessee, Lease, Description [Line Items] |  |  |  |
Lease Term of contract |  |  |  | 8 years
Lease term of contract in majority |  |  |  | 5 years
Renewal lease terms |  |  |  | 5 years
Minimum |  |  |  |
Lessee, Lease, Description [Line Items] |  |  |  |
Lease Term of contract |  |  |  | 1 year
Lease term of contract in majority |  |  |  | 3 years
Renewal lease terms |  |  |  | 1 year

X
- Definition Term of lessee's operating lease and finance lease. + References No definition available. + Details
Name: | fa_LesseeOperatingAndFinanceLeaseTermOfContract
Namespace Prefix: | fa_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | instant

X
- Definition Lessee operating and finance lease term of contract in majority. + References No definition available. + Details
Name: | fa_LesseeOperatingAndFinanceLeaseTermOfContractInMajority
Namespace Prefix: | fa_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | instant

X
- Definition Term of lessee's operating and Finance lease renewal. + References No definition available. + Details
Name: | fa_LesseeOperatingAndFinancingLeaseRenewalTerm
Namespace Prefix: | fa_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | instant

X
- Definition Amount of rent expense incurred for leased assets, including but not limited to, furniture and equipment, that is not directly or indirectly associated with the manufacture, sale or creation of a product or product line. + References No definition available. + Details
Name: | us-gaap_LeaseAndRentalExpense
Namespace Prefix: | us-gaap_
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_LesseeLeaseDescriptionLineItems
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

X
- Details
Name: | srt_RangeAxis=srt_MaximumMember
Namespace Prefix: |
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Balance Type: |
Period Type: |

X
- Details
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Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |