XML 82 R68.htm IDEA: XBRL DOCUMENT
v3.22.4

Share-Based Compensation - Summary of Assumptions Applied to Establish Fair Value of Options Granted Using Black-Scholes Option Pricing Model (Details) - $ / shares | 11 Months Ended | 12 Months Ended
--- | --- | ---
Dec. 31, 2020 | Dec. 31, 2022 | Dec. 31, 2021
2021 Equity Plan [Member] |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |
Expected stock price volatility |  | 34.66% | 38.67%
Risk-free interest rate |  | 2.77% | 1.06%
Expected term (in years) |  | 6 years 2 months 23 days | 5 years 10 months 28 days
Estimated fair-value of the underlying unit |  | $ 14.68 | $ 15.33
Class B Awards [Member] |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |
Expected stock price volatility | 30.90% |  |
Risk-free interest rate | 1.28% |  |
Expected term (in years) | 6 years 3 months |  |
Estimated fair-value of the underlying unit | $ 10.06 |  |
Class C Awards [Member] |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |
Expected stock price volatility | 30.08% |  |
Risk-free interest rate | 1.47% |  |
Expected term (in years) | 6 years 3 months |  |
Estimated fair-value of the underlying unit | $ 10.00 |  |

X
- Definition Estimated Fair Value of the Underlying Unit + References No definition available. + Details
Name: | fa_EstimatedFairValueOfTheUnderlyingUnit
Namespace Prefix: | fa_
Data Type: | dtr-types:perShareItemType
Balance Type: | na
Period Type: | duration

X
- Definition The risk-free interest rate assumption that is used in valuing an option on its own shares. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (f)(2)(iv) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
Name: | us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate
Namespace Prefix: | us-gaap_
Data Type: | dtr-types:percentItemType
Balance Type: | na
Period Type: | duration

X
- Definition Rate of weighted-average expected volatility for award under share-based payment arrangement. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (f)(2)(ii) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
Name: | us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsWeightedAverageVolatilityRate
Namespace Prefix: | us-gaap_
Data Type: | dtr-types:percentItemType
Balance Type: | na
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_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

X
- Definition Expected term of award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (f)(2)(i) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
Name: | us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1
Namespace Prefix: | us-gaap_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | duration

X
- Details
Name: | us-gaap_PlanNameAxis=fa_TwoThousandTwentyOneEquityPlanMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_AwardTypeAxis=fa_ClassBAwardsMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_AwardTypeAxis=fa_ClassCAwardsMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |