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<!-- Creation Date :2025-02-27T13:27:25.8213+00:00 -->
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          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_ImpactOfDividedToStockOptionAwardsAndESPPPurchases" xlink:label="fa_ImpactOfDividedToStockOptionAwardsAndESPPPurchases"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilitiesFairValueDisclosure" xlink:label="us-gaap_LiabilitiesFairValueDisclosure"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities"/>
          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_MergerAgreementMember" xlink:label="fa_MergerAgreementMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShortTermLeaseCost" xlink:label="us-gaap_ShortTermLeaseCost"/>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertySubjectToOrAvailableForOperatingLeaseAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property Subject to or Available for Operating Lease [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Interest Rate During Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskBoardOfDirectorsOversightTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Board of Directors Oversight [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Allowance for Credit Loss [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Allowance For Doubtful Accounts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accounts Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Accounts receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plan Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments for Repurchase of Equity, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments for Repurchase of Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfEquity_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Share repurchases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repurchases of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsDeferredIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Deferred Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsDeferredIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred revenues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CashDividendsForfeited_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Dividends Forfeited</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CashDividendsForfeited_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash Dividends Forfeited</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CashDividendsForfeited_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash Dividends Forfeited</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationsPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combinations Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationsPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business Combinations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskBoardCommitteeOrSubcommitteeResponsibleForOversightTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Board Committee or Subcommittee Responsible for Oversight [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_UnderwritingDiscountsAndCommissions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Underwriting Discounts and Commissions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_UnderwritingDiscountsAndCommissions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Underwriting Discounts and Commissions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_UnderwritingDiscountsAndCommissions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Underwriting discounts and commissions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstAdvantageCorporationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First Advantage Corporation Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstAdvantageCorporationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Advantage Corporation Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstAdvantageCorporationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Advantage Corporation [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NonCashImpairmentCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Non cash impairment charges.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NonCashImpairmentCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non Cash Impairment Charges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NonCashImpairmentCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non Cash Impairment Charges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Incorporation, State or Country Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Incorporation, State or Country Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationAcquisitionRelatedCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Acquisition Related Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationAcquisitionRelatedCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Transaction and acquisition-related charges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationAcquisitionRelatedCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Legal, regulatory, and professional service fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsForeign_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Operating Loss Carryforwards, Foreign</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsForeign_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign net operating loss carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Restructuring Charges, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring Charges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Integration, restructuring, and other charges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total minimum lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OperatingLeaseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Operating Lease [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OperatingLeaseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OperatingLeaseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating Lease</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Paid, Excluding Capitalized Interest, Operating Activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Interest Rate Derivatives [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Location and Fair Value of Financial Position and Location of Derivative Instruments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Operating Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of operating segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Tranche One [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Payment Arrangement, Tranche One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Asset, Expected Amortization, Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInEnactedTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Change in Enacted Tax Rate, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInEnactedTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rate change impact</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AmendedFirstLienCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amended First Lien Credit Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AmendedFirstLienCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amended First Lien Credit Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AmendedFirstLienCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amended First Lien Credit Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Right-of-Use Asset, Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: accumulated depreciation and amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Hierarchy and NAV</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Recognized Identified Assets Acquired and Liabilities Assumed [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Consideration Paid and Amounts Recognized for Assets Acquired and Liabilities Assumed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business acquisition, Percentage acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Acquisition, Percentage of Voting Interests Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsInAffiliatesSubsidiariesAssociatesAndJointVentures_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Investments in and Advance to Affiliates, Subsidiaries, Associates, and Joint Ventures, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsInAffiliatesSubsidiariesAssociatesAndJointVentures_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investments in and Advance to Affiliates, Subsidiaries, Associates, and Joint Ventures</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsInAffiliatesSubsidiariesAssociatesAndJointVentures_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investments in subsidiaries</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Auditor Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFederalIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Federal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFederalIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Federal Income Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFederalIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Federal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 2 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 2 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share Based Compensation Arrangement By Share Based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeographicAreasLongLivedAssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographic Areas, Long-Lived Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeographicAreasLongLivedAssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-lived assets, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Cash Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of consideration transferred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total fair value of consideration transferred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_O2024Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">O 2024 Q4 Dividends [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_O2024Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">O 2024 Q4 Dividends [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_O2024Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">O 2024 Q4 Dividends [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Year Five</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingOtherItemAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, Other Segment Item, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingOtherItemAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other segment items</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AcceleratedVestingAfterAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accelerated Vesting After Acquisition [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AcceleratedVestingAfterAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Acceleraed Vesting After Acquisition [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AcceleratedVestingAfterAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accelerated Vesting for Employees Terminated [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Current Maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-Term Debt, Current Maturities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: Current portion of long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Current portion of long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: Current portion of long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DebtForgivenessAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Forgiveness Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DebtForgivenessAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Forgiveness Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DebtForgivenessAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt forgiveness agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CashConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CashConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CashConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExaminationDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Tax Examination, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExaminationDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Examination, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of maturities of lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Leases [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease Liability Payments Due Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Liability Payments Due Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRestructuringAndRelatedCostsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring Cost [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRestructuringAndRelatedCostsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Restructuring And Related Costs [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateSwapMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Interest Rate Swaps [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateSwapMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Swap [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateSwapMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest Rate Swap [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfStockByClassTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock, Class of Stock [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfStockByClassTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Stock By Class [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost Of Services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cost Of Services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeCapInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Cap Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeCapInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative cap interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative Instruments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivatives, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Income Tax Liabilities, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Income Tax Liabilities, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred tax liability, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finite-Lived Intangible Assets by Major Class</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Depreciation, Depletion and Amortization, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation, Depletion and Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation and amortization expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Rights, Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssetsGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities, Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssetsGoodwill_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockRepurchasedDuringPeriodShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Repurchased During Period, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockRepurchasedDuringPeriodShares_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares repurchased</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfGoodwillTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfGoodwillTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Goodwill [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncashInvestingAndFinancingItemsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash Investing and Financing Items [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncashInvestingAndFinancingItemsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">NON-CASH INVESTING AND FINANCING ACTIVITIES:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ExchangedForCommonStockInTheCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Exchanged for common stock in the Company.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ExchangedForCommonStockInTheCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Exchanged for common stock in the Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ExchangedForCommonStockInTheCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exchanged for common stock in the Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party Transaction [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementProcessesIntegratedTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Processes Integrated [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Benchmark [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration Risk Benchmark</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesOtherFiniteLivedAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Trade names</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesOtherFiniteLivedAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities, Other Finite-Lived Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_March2021UKAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">March 2021 UK Acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_March2021UKAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">March 2021 UK acquisition member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_March2021UKAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">March2021 U K Acquisition [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstPortionOfCommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First portion of common stock member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstPortionOfCommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Portion of Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstPortionOfCommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Portion Of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from Contract with Customer [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sale of Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">First Lien Credit Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsEmployeeBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Tax Deferred Expense, Compensation and Benefits, Employee Benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsEmployeeBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Employee benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsPayableDateDeclaredDayMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Dividend, declare date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsPayableDateDeclaredDayMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends Payable, Date Declared</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeasesRentExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating leases, rent expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeasesRentExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Leases, Rent Expense, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeasesRentExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Operating Leases, Rent Expense, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntersegmentEliminationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intersegment Eliminations [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntersegmentEliminationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Eliminations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Asset, Useful Life</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Useful life</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SummaryOfWeightedAverageLeaseTermAndDiscountRateOperatingLeaseAndFinancingLeaseTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Summary of Weighted Average Lease Term and Discount Rate Operating Lease and Financing Lease.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SummaryOfWeightedAverageLeaseTermAndDiscountRateOperatingLeaseAndFinancingLeaseTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary of Weighted Average Lease Term and Discount Rate Operating Lease and Financing Lease [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SummaryOfWeightedAverageLeaseTermAndDiscountRateOperatingLeaseAndFinancingLeaseTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of weighted average lease term and discount rate operating lease and financing lease</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InfiniteIdMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Infinite ID</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InfiniteIdMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Infinite ID [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InfiniteIdMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Infinite ID.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ExciseTaxesOnShareRepurchasesIncurredButNotPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Excise taxes on share repurchases incurred but not paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ExciseTaxesOnShareRepurchasesIncurredButNotPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Excise taxes on share repurchases incurred but not paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ExciseTaxesOnShareRepurchasesIncurredButNotPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Excise taxes on share repurchases incurred but not paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockOwnershipPlanESOPDisclosuresByPlanAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Stock Ownership Plan (ESOP) Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockOwnershipPlanESOPDisclosuresByPlanAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Employee Stock Ownership Plan (ESOP) Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Forfeitures in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of units, cancelled/forfeited</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of units, forfeited</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NOLMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">NOLs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NOLMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">NOL [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NOLMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">NOL [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorOpinionTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Auditor Opinion [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorOpinionTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Auditor Opinion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Operating Capital [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Changes in operating assets and liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Successor Plan [Member].</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Successor Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Successor Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdvertisingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Advertising Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdvertisingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Advertising Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FairValueOfAssumedSterlingEquityAwardsToReceiveCashAttributableToPreCombinationService_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value of Assumed Sterling Equity Awards to Receive Cash Attributable to Pre-combination Service</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FairValueOfAssumedSterlingEquityAwardsToReceiveCashAttributableToPreCombinationService_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Fair Value of Assumed Sterling Equity Awards to Receive Cash Attributable to Pre-combination Service</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FairValueOfAssumedSterlingEquityAwardsToReceiveCashAttributableToPreCombinationService_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plus: fair value of assumed Sterling equity awards to receive cash attributable to pre-combination service</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Class C [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class C Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LessAdjustedCostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Less Adjusted cost of services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LessAdjustedCostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Less Adjusted cost of services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LessAdjustedCostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjusted cost of services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeOperatingAndFinanceLeaseTermOfContractInMajority_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lessee operating and finance lease term of contract in majority.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeOperatingAndFinanceLeaseTermOfContractInMajority_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee Operating and Finance Lease Term of Contract in Majority</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeOperatingAndFinanceLeaseTermOfContractInMajority_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease term of contract in majority</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Common Stock, Shares, Issued, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Assets, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherIntangibleAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other Intangible Assets [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherIntangibleAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Intangible Assets [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OneCustomerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">One Customer [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OneCustomerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">One Customer [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OneCustomerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">One Customer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_GainLossDueToChangeInFairValueOfInterestRateSwaps_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Change in fair value of interest rate swaps.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_GainLossDueToChangeInFairValueOfInterestRateSwaps_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain Loss Due To Change In Fair Value Of Interest Rate Swaps</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_GainLossDueToChangeInFairValueOfInterestRateSwaps_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Change in fair value of interest rate swaps</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_RecentAccountingPronouncementsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Recent accounting pronouncements.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_RecentAccountingPronouncementsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Recent Accounting Pronouncements Policy [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_RecentAccountingPronouncementsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recent Accounting Pronouncements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Prepaid Expense and Other Assets, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Prepaid expenses and other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Year Five</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance Lease, 2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EffectiveIncomeTaxRateReconciliationTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Transaction cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EffectiveIncomeTaxRateReconciliationTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation Transaction Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EffectiveIncomeTaxRateReconciliationTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Effective income tax rate reconciliation transaction costs,</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseRemainingLeaseTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseRemainingLeaseTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Remaining Lease Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalCashConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total cash consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalCashConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Total Cash Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalCashConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Total Cash Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance Lease, 2025</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">(LOSS) INCOME BEFORE PROVISION FOR INCOME TAXES</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">(Loss) income before provision for income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ParentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Parent [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ParentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Parent [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration Risk Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingencies [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loss Contingencies [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income Location [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other Comprehensive Income Location</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MajorCustomersAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MajorCustomersAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Customer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer Concentration Risk [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Customer Concentration Risk [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_BankingFees_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Banking Fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_BankingFees_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Banking Fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_BankingFees_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Success-based banking fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_IntialPublicOfferingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Initial Public Offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_IntialPublicOfferingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Intial public offering policy [policy text block].</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_IntialPublicOfferingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intial Public Offering Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Asset, Expected Amortization, Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NetSettlementOfShareBasedCompensationPlanAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Net settlement of share-based compensation plan awards.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NetSettlementOfShareBasedCompensationPlanAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Settlement of Share-Based Compensation Plan Awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NetSettlementOfShareBasedCompensationPlanAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net settlement of share-based compensation plan awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityExpirationDate1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Extended maturity date under successor revolver</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityExpirationDate1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Expiration Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsPayableDateOfRecordDayMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Dividend, record date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsPayableDateOfRecordDayMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends Payable, Date of Record</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intrinsic value of options exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstAdvantageCommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Advantage Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstAdvantageCommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First Advantage Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, after Year Five</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Thereafter</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxLiabilitiesOperatingLeaseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities Operating Lease Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxLiabilitiesOperatingLeaseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred Tax Liabilities Operating Lease Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxLiabilitiesOperatingLeaseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxLiabilitiesOperatingLeaseAsset_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Operating lease asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TermLoanDueJanuaryThirtyOneTwoThousandTwentySevenMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Term Loan Due January Thirty One Two Thousand Twenty Seven</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TermLoanDueJanuaryThirtyOneTwoThousandTwentySevenMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Term Loan Due January Thirty One Two Thousand Twenty Seven [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TermLoanDueJanuaryThirtyOneTwoThousandTwentySevenMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term Loan due January 31, 2027 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments of Debt Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Payments of debt issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amortization of Debt Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization of deferred financing costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OperatingLossCarryforwardsExpirationYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating loss carryforwards expiration year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OperatingLossCarryforwardsExpirationYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Loss Carryforwards Expiration Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OperatingLossCarryforwardsExpirationYear_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Operating Loss Carryforwards Expiration Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Comprehensive Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basic net income per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Basic net (loss) income per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_WriteDownOfAbandonedPropertyAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Write down of abandoned property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_WriteDownOfAbandonedPropertyAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Write down of abandoned property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_WriteDownOfAbandonedPropertyAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Write down of abandoned property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorPeriodMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Successor Period [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorPeriodMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Successor period.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorPeriodMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Successor Period [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ContractWithCustomerAssetNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Contract with Customer, Asset, after Allowance for Credit Loss, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ContractWithCustomerAssetNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Contract with Customer, Asset, after Allowance for Credit Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ContractWithCustomerAssetNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Contract asset balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Expenses [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">OPERATING EXPENSES:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Principal Payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Payments on finance lease obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SterlingCheckCorpMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sterling Check Corp [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SterlingCheckCorpMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sterling Check Corp [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SterlingCheckCorpMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sterling Check Corp [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentAnnualReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Annual Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentAnnualReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Annual Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidationItemsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidation Items [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidationItemsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Consolidation Items</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesOther_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Liabilities, Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesOther_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivatives</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Instruments and Hedging Activities Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareBasedCompensationArrangementsByShareBasedPaymentAwardIssuedInExchangedForOptionsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangements by share based payment award issued in exchanged for options in period weighted average exercise price.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareBasedCompensationArrangementsByShareBasedPaymentAwardIssuedInExchangedForOptionsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangements By Share Based Payment Award Issued in Exchanged for Options In Period Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareBasedCompensationArrangementsByShareBasedPaymentAwardIssuedInExchangedForOptionsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average exercise price, issued in exchange for options in the company's parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareBasedCompensationArrangementsByShareBasedPaymentAwardIssuedInExchangedForOptionsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted average exercise price, grants issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CommonStockSharesAuthorizedPreStockSplit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common stock, shares authorized pre-stock split.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CommonStockSharesAuthorizedPreStockSplit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common stock, shares authorized pre-stock split</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CommonStockSharesAuthorizedPreStockSplit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares authorized pre-stock split</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Allocated share based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Share-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdvertisingCostsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Advertising Cost [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdvertisingCostsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Advertising Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Weighted Average Discount Rate, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-Term Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SilverLakeTransactionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Silver Lake Transaction [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SilverLakeTransactionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Silver lake transaction member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SilverLakeTransactionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Silver Lake Transaction [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsCommonStockStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends, Common Stock, Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Retained Earnings (Accumulated Deficit), Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Retained Earnings (Accumulated Deficit), Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Retained Earnings (Accumulated Deficit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings (Accumulated Deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plan Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerListsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer Lists [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerListsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Customer Lists</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Number of units, grant outstanding ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Number of units, grant outstanding beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of grants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowElementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Supplemental Cash Flow Elements [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowElementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">SUPPLEMENTAL DISCLOSURES OF CASH FLOW INFORMATION:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">CURRENT ASSETS</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Capital Shares Reserved for Future Issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, reserved for future issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="country_US_lbl" xlink:role="http://www.xbrl.org/2003/role/label">UNITED STATES</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="country_US_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">United States</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="country_US_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">United States</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Benefit Plan [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Total deferred tax liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Tax Liabilities, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EffectiveIncomeTaxRateReconciliationWithholdingTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Withholding tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EffectiveIncomeTaxRateReconciliationWithholdingTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation Withholding Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EffectiveIncomeTaxRateReconciliationWithholdingTax_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Effective income tax rate reconciliation withholding tax.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash provided by operating activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided by (Used in) Operating Activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeitures, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Grant Date Fair Value, Forfeited | $ / shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionEquityInterestIssuedOrIssuableValueAssigned_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Acquisition, Equity Interest Issued or Issuable, Value Assigned</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionEquityInterestIssuedOrIssuableValueAssigned_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business Acquisition, Fair Value of Shares Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Accumulated other comprehensive income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accumulated Other Comprehensive Income (Loss), Net of Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated other comprehensive loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease term contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Term of Contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment, including software developed for internal use</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CostOfServicesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cost of Services [Member].</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CostOfServicesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost Of Services [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CostOfServicesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of Services [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Operating Loss Carryforwards, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Loss Carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net operating loss carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OtherSegmentItemsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Segment Items [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OtherSegmentItemsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other Segment Items [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OtherSegmentItemsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other segment items [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Property, Plant and Equipment, Net, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Property, Plant and Equipment, Net, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Property and equipment, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating Lease, 2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">CASH FLOWS FROM OPERATING ACTIVITIES</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Income Tax Expense (Benefit), Continuing Operations [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring and Related Activities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid in Capital [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Costs recorded to accumulated deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NondesignatedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivatives Not Designated as Hedging Instruments [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NondesignatedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Not Designated as Hedging Instrument [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VestingAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Vesting [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VestingAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockOptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Employee Stock Option [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementPositionsOrCommitteesResponsibleTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Positions or Committees Responsible [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ContractWithCustomerLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Contract with Customer, Liability, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ContractWithCustomerLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Contract with Customer, Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ContractWithCustomerLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Contract liability balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Cash Flows [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwothousandTwentyEquityPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Equity Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwothousandTwentyEquityPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2020 Equity Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwothousandTwentyEquityPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">TwoThousand Twenty Equity Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SoftwareMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Software [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SoftwareMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Software [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SoftwareMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Software [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstLienCreditAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Lien Credit Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstLienCreditAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First Lien Credit Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease Liability Payments Due Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Liability Payments Due Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling, General and Administrative Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Selling, General and Administrative Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOther_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOther_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other deferred tax assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeGainLossOnDerivativeNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gain/(loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeGainLossOnDerivativeNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Gain (Loss) on Derivative, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeGainLossOnDerivativeNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Derivative, Gain (Loss) on Derivative, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Acquired Finite-Lived Intangible Assets [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Components [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Components</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ExchangedForRestrictedStockInTheCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Exchanged For Restricted Stock In The Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ExchangedForRestrictedStockInTheCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Exchanged For Restricted Stock In The Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ExchangedForRestrictedStockInTheCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exchanged for restricted stock In the company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ExtinguishmentOfDebtAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Extinguishment of Debt, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Basic and Diluted Net (Loss) Income Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Employee-related Liabilities, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee-related Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstAdvantageInternationalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Advantage International [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstAdvantageInternationalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First Advantage International [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstAdvantageInternationalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Advantage International [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Related Party Transactions By Related Party [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of units, granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringIncurredCostStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring Charges, Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskProcessForInformingBoardCommitteeOrSubcommitteeResponsibleForOversightTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Process for Informing Board Committee or Subcommittee Responsible for Oversight [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherDerivativesNotDesignatedAsHedgingInstrumentsLiabilitiesAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Derivatives Not Designated as Hedging Instruments Liabilities at Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherDerivativesNotDesignatedAsHedgingInstrumentsLiabilitiesAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of derivatives not designated as hedging instruments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Finite-Lived [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HedgingDesignationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Hedging Designation [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property Plant And Equipment [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CapitalLeaseTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Capital lease term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CapitalLeaseTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Capital Lease Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CapitalLeaseTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Capital lease term.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateCollarsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest Rate Collars [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateCollarsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Collars [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateCollarsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Interest Rate Collars [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RatioOfIndebtednessToNetCapital1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, net leverage ratio</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RatioOfIndebtednessToNetCapital1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Ratio of Indebtedness to Net Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Income Tax Expense (Benefit), Continuing Operations [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateDerivativesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Derivatives [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum borrowing capacity under successor revolver</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Risk Free Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Risk-free interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NonUsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Non-US</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NonUsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non-US [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NonUsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">All other countries</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwoThousandTwentyOneEquityPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2021 Equity Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwoThousandTwentyOneEquityPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty one equity plan member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwoThousandTwentyOneEquityPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty One Equity Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Number of units, outstanding ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Number of units, outstanding beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Tax Credit, Research, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">US research and development credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">US research and development credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityVoluntaryFilers_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Voluntary Filers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityVoluntaryFilers_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Voluntary Filers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SymphonyTalentLlcMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Symphony Talent LLC [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SymphonyTalentLlcMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Symphony Talent LLC [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SymphonyTalentLlcMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Symphony talent LLC member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Asset, Expected Amortization, Year Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensationExpenseExcludingCostOfGoodAndServiceSold_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Compensation Expense, Excluding Cost of Good and Service Sold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensationExpenseExcludingCostOfGoodAndServiceSold_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Incremental compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLossCarryforwardsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Loss Carryforwards [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLossCarryforwardsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating Loss Carryforwards [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Income Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Total Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LoanRestructuringModificationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loan Restructuring Modification [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentFederalTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Federal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentFederalTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Federal Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentFederalTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Federal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Operating Lease Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PercentageOfPrepaymentPremiumOfTermLoans_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage Of Prepayment Premium Of Term Loans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PercentageOfPrepaymentPremiumOfTermLoans_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage Of Prepayment Premium Of Term Loans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PercentageOfPrepaymentPremiumOfTermLoans_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage Of Prepayment Premium Of Term Loans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liability, less current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareRepurchaseProgramMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share Repurchase Program.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareRepurchaseProgramMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Repurchase Program [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareRepurchaseProgramMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share Repurchase Program</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockConsiderationReceivedPerTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Consideration Received Per Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockConsiderationReceivedPerTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sale of Stock, Consideration Received Per Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DomesticCountryMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Domestic Tax Jurisdiction [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DomesticCountryMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Federal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeographicConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographic Concentration Risk [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument, Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Additional Paid in Capital, Common Stock, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Additional Paid in Capital, Common Stock, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid in Capital, Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional paid-in-capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Per share price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Price Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Sale of stock price per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities, Property, Plant and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Depreciable and other amortizable assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorFirstLienCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Successor first lien credit facility.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorFirstLienCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Successor First Lien Credit Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorFirstLienCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Successor First Lien Credit Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">SOFR</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReceivablesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Receivables [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReceivablesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReceivablesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Receivable [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">NET (LOSS) INCOME</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeaseDescriptionTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Lease, Description [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of units, exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Shares Issued in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of units, issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CostOfOtherSegmentItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost Of Other Segment Items</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CostOfOtherSegmentItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cost Of Other Segment Items</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CostOfOtherSegmentItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other segment items</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Rate [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Variable Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AmericaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Americas</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AmericaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">America [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AmericaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">America [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_NameOfMajorCustomerDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_NameOfMajorCustomerDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Customer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DebtInstrumentInterestRateReducedDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt Instrument Interest Rate Reduced During Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DebtInstrumentInterestRateReducedDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Interest Rate Reduced During Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DebtInstrumentInterestRateReducedDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument interest rate reduced during period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PaymentsToAcquireBusinessGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments To Acquire Business Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PaymentsToAcquireBusinessGross_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payments To Acquire Business Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Component [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Component</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFinStmtErrorCorrectionFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Financial Statement Error Correction [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFinStmtErrorCorrectionFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Financial Statement Error Correction [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExchangedForOptionsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average exercise price, exchanged for options in the company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExchangedForOptionsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share Based Compensation Arrangements By Share Based Payment Award Options Exchanged for Options In Period Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExchangedForOptionsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangements By Share Based Payment Award Options Exchanged for Options In Period Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsHeldUnderCapitalLeasesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets Held under Capital Leases [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsHeldUnderCapitalLeasesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets Held under Capital Leases [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CostOfServicesExcludingDepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cost of services excluding depreciation and amortization.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CostOfServicesExcludingDepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost Of Services Excluding Depreciation And Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CostOfServicesExcludingDepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of services (exclusive of depreciation and amortization below)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Nonoperating Income (Expense), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Nonoperating Income (Expense)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Total other expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">State</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred State and Local Income Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">State</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Expiration Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock options plan expiration period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskMateriallyAffectedOrReasonablyLikelyToMateriallyAffectRegistrantTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Materially Affected or Reasonably Likely to Materially Affect Registrant [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FurnitureAndFixturesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Furniture and equipment [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FurnitureAndFixturesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Furniture and Fixtures [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementProcessesIntegratedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Processes Integrated [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Revenue, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Revenue, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred revenues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred Stock Shares Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LienCategoryDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lien Category [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LienCategoryDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lien Category</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating cash flows from operating leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Defined Contribution Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retirement Benefits [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExchangeForOptionInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Number of units, exchange for options in the company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExchangeForOptionInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Number of units, exchange for options in the company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExchangeForOptionInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement By share based payment award options exchange for option in period.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExchangeForOptionInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Options Exchange for Option In Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExchangeForOptionInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of units, exchange for options in the company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Outstanding Derivatives that were not Designated as a Hedge in Qualifying Hedging Relationships</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Derivative Instruments [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable, Credit Loss Expense (Reversal)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Bad debt expense (recovery)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Nonvested, Number of Shares, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Nonvested, Number of Shares, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Nonvested, Number of Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of units, unvested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCashCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Cash, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCashCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue Remaining Performance Obligation Expected Timing Of Satisfaction [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesOther_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities, Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesOther_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other deferred liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated Fair Values</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SharesRepurchasedAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Shares repurchased abstract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SharesRepurchasedAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Repurchased Abstract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxCreditCarryforwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Credit Carryforward [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxCreditCarryforwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax Credit Carryforward [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidationItemsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidation Items [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidationItemsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Consolidation Items</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Grants issued in exchange for unvested profits interests in the Company's Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of units, granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Net of Forfeitures</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Grants in Period, Net of Forfeitures, Total</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorFirstLienMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Successor First Lien.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Outstanding</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finite-Lived Intangible Assets, Major Class Name</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PrepaidExpensesAndOtherCurrentAssetsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Prepaid Expenses and Other Current Assets [TextBlock]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PrepaidExpensesAndOtherCurrentAssetsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid Expenses and Other Current Assets</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OfferingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Offering expenses.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OfferingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Offering Expenses</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherDerivativesNotDesignatedAsHedgingInstrumentsAtFairValueNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Derivatives Not Designated as Hedging Instruments at Fair Value, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Par or Stated Value Per Share</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskProcessForInformingManagementOrCommitteesResponsibleTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Process for Informing Management or Committees Responsible [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedBenefitPlanDisclosureLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Benefit Plan Disclosure [Line Items]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredForeignIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Foreign</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Restricted Stock Unit, Activity [Table Text Block]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredTaxAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred tax asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_O2023Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">O 2023 Q4 Dividends [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_O2023Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">O2023Q4DividendsMember</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Interactive Data Current</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EquipmentFurnitureAndFixturesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Equipment, Furniture and Fixtures [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance Lease, Less: Imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Finance Lease, Less: Imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Asset, Expected Amortization, Year Five</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CondensedFinancialInformationOfParentCompanyOnlyDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Condensed Financial Information Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SummaryOfSignificantAccountingPoliciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Summary of significant accounting policies table.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SummaryOfSignificantAccountingPoliciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary Of Significant Accounting Policies [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SummaryOfSignificantAccountingPoliciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary Of Significant Accounting Policies [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total operating lease costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Assets, Fair Value Disclosure, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PredecessorFirstLienFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Predecessor First Lien Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PredecessorFirstLienFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Predecessor first lien facility.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PredecessorFirstLienFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Predecessor First Lien Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related and Nonrelated Parties [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total lease cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disaggregation of Revenue [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Revenues by Geographic Region</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FairValueOfAssumedSterlingEquityAwardsToReceiveEquityAwardsAttributableToPreCombinationService_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value of Assumed Sterling Equity Awards to Receive Equity Awards Attributable to Pre-combination Service</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FairValueOfAssumedSterlingEquityAwardsToReceiveEquityAwardsAttributableToPreCombinationService_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Fair Value of Assumed Sterling Equity Awards to Receive Equity Awards Attributable to Pre-combination Service</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FairValueOfAssumedSterlingEquityAwardsToReceiveEquityAwardsAttributableToPreCombinationService_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plus: fair value of assumed Sterling equity awards to receive equity awards attributable to pre-combination service</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetAcquiredInPlaceLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangible assets Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetAcquiredInPlaceLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Asset, Acquired-in-Place Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss) [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other Comprehensive Income [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ReconciliationOfAdjustedEbitdaFromReportableSegmentsToConsolidatedNetIncomeLossTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tabular disclosure of the reconciliation of adjusted EBITDA from reportable segments to the consolidated income (loss).</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ReconciliationOfAdjustedEbitdaFromReportableSegmentsToConsolidatedNetIncomeLossTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reconciliation of Adjusted EBITDA from Reportable Segments to Consolidated Net Income (Loss)[Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ReconciliationOfAdjustedEbitdaFromReportableSegmentsToConsolidatedNetIncomeLossTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Adjusted EBITDA Reconciled to Net Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gross Carrying Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Finite-Lived Intangible Assets, Gross, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Cash, net of cash acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Acquisitions of businesses, net of cash acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments to Acquire Businesses, Net of Cash Acquired, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Businesses, Net of Cash Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSharebasedCompensationRestrictedStockAndRestrictedStockUnitsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Restricted Stock and Restricted Stock Unit, Activity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSharebasedCompensationRestrictedStockAndRestrictedStockUnitsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Restricted Stock Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Available for Grant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share available for issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Share available for issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Grant Date Fair Value, Granted | $ / shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCountryMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Foreign Tax Jurisdiction [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCountryMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NetSettlementOfRestrictedStockUnitsAndOptionAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net settlement of restricted stock units and option awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NetSettlementOfRestrictedStockUnitsAndOptionAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Settlement Of Restricted Stock Units And Option Awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NetSettlementOfRestrictedStockUnitsAndOptionAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Net Settlement Of Restricted Stock Units And Option Awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentsGeographicalAreasAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segments, Geographical Areas [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MachineryAndEquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Machinery and Equipment [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestAndOtherIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest and Other Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestAndOtherIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongLivedAssetsByGeographicAreasTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Assets by Geographic Areas [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongLivedAssetsByGeographicAreasTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Long Lived Assets by Geographical Area</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedBenefitPlanContributionsByEmployer_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Benefit Plan, Plan Assets, Contributions by Employer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedBenefitPlanContributionsByEmployer_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Company's total contributions to savings plans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effect of Exchange Rate on Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Continuing Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Effect of exchange rate on cash, cash equivalents, and restricted cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Net deferred tax liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Net deferred tax liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Tax Assets, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FinanceAmortizationOfLeasedAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Finance amortization of leased assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FinanceAmortizationOfLeasedAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance amortization of leased assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FinanceAmortizationOfLeasedAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization of leased assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Income Location, Balance [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Statement Location</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllowanceForCreditLossesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Allowance for Credit Losses [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllowanceForCreditLossesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Allowance for Doubtful Accounts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">TOTAL ASSETS</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expected term (in years)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Long-Term Debt Instruments [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentForeignTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentForeignTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Foreign Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentForeignTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Foreign</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations before Income Taxes, Foreign</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income before provision for income taxes from foreign operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of units, vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of units, vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CapitalizedSoftwareAcquiredByBusinessCombinationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Capitalized software for internal use, acquired by business combination [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">AOCI Attributable to Parent [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Other Comprehensive (Loss) [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_WeightedAverageGrantDateFairValueExchanged_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Grant Date Fair Value Exchanged</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_WeightedAverageGrantDateFairValueExchanged_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Weighted Average Grant Date Fair Value Exchanged</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_WeightedAverageGrantDateFairValueExchanged_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Grant Date Fair Value, Exchanged</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsPledgingPurposeExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Pledging Purpose [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementBusinessSegmentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segments [Axis]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ScheduleOfCondensedIncomeStatementAndComprehensiveLossTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule Of Condensed Income Statement And Comprehensive Loss [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ScheduleOfCondensedIncomeStatementAndComprehensiveLossTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Condensed Statements of Operations and Comprehensive (Loss) Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorLocation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Auditor Location</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Maturities of Long-Term Debt [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Future Maturities of Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskMateriallyAffectedOrReasonablyLikelyToMateriallyAffectRegistrantFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Materially Affected or Reasonably Likely to Materially Affect Registrant [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeited in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of units, forfeited | shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of units, forfeited | shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_IndemnityLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Indemnity Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_IndemnityLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Indemnity Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_IndemnityLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Indemnity liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Year Two</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCompensationCostForShareBasedPaymentArrangementsAllocationOfShareBasedCompensationCostsByPlanTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Cost by Plan [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCompensationCostForShareBasedPaymentArrangementsAllocationOfShareBasedCompensationCostsByPlanTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Recognition of Share-Based Compensation related to Employees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ConcentrationRiskNumberOfCustomers_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Concentration risk number of customers.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ConcentrationRiskNumberOfCustomers_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Number Of Customers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ConcentrationRiskNumberOfCustomers_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration risk, number of customers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_MinorityInterestIncreaseFromContributionsByNoncontrollingInterestHolders_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Minority interest increase from contributions by noncontrolling interest holders.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_MinorityInterestIncreaseFromContributionsByNoncontrollingInterestHolders_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Minority Interest Increase From Contributions By Noncontrolling Interest Holders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_MinorityInterestIncreaseFromContributionsByNoncontrollingInterestHolders_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Capital contributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Face Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Instrument, Face Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScheduleOfCondensedBalanceSheetTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Condensed Balance Sheet [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScheduleOfCondensedBalanceSheetTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Condensed Balance Sheets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScheduleOfCondensedBalanceSheetTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Summary of Supplemental balance sheet information related to leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EuropeanUnionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">European Union (EU)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EuropeanUnionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">European Union [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringCostAndReserveLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring Cost and Reserve [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringCostAndReserveLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restructuring Cost And Reserve [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SummaryOfIncomeTaxContingenciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary of Income Tax Contingencies [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SummaryOfIncomeTaxContingenciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Income Tax Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeOperatingAndFinanceLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee Operating and Finance Leases [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeOperatingAndFinanceLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">The entire disclosure for operating and finance leases of lessee. Includes, but is not limited to, description of lessee's finance lease and maturity analysis of finance lease liability.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeOperatingAndFinanceLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss) Attributable to Parent [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Numerator:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromForeignCurrencyTranslation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecognized Tax Benefits, Increase Resulting from Foreign Currency Translation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromForeignCurrencyTranslation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Effects of foreign currency</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromForeignCurrencyTranslation_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Effects of foreign currency</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OperatingCashFlowsFromFinanceLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Operating cash flows from finance leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OperatingCashFlowsFromFinanceLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating cash flows from finance leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskThirdPartyOversightAndIdentificationProcessesFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Third Party Oversight and Identification Processes [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxAssetsDisallowedInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Disallowed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxAssetsDisallowedInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets Disallowed Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxAssetsDisallowedInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred Tax Assets Disallowed Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Share-Based Payment Arrangement, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Share-based and other compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementPositionsOrCommitteesResponsibleReportToBoardFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Positions or Committees Responsible Report to Board [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CorporateScreeningServicesLlcMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Corporate Screening [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CorporateScreeningServicesLlcMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Corporate Screening Services LLC member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AnnualGrossRevenueThreshhold_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Annual Gross Revenue Threshhold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AnnualGrossRevenueThreshhold_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Annual Gross Revenue Threshhold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AnnualGrossRevenueThreshhold_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Annual gross revenue threshhold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AdjustedIncomeLossBeforeInterestTaxesDepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total Adjusted EBITDA</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AdjustedIncomeLossBeforeInterestTaxesDepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjusted Income Loss Before Interest Taxes Depreciation and Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AdjustedIncomeLossBeforeInterestTaxesDepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total revenues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentStateAndLocalTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">State</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentStateAndLocalTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current State and Local Tax Expense (Benefit)</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense and Other Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Weighted Average Discount Rate, Percent</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityPublicFloat_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Public Float</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityPublicFloat_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Public Float</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NumberOfSharesExchanged_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Shares Exchanged</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NumberOfSharesExchanged_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of Shares Exchanged</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NumberOfSharesExchanged_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of units, exchanged</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SterlingAcquisitionAwardsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sterling Acquisition Awards [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SterlingAcquisitionAwardsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sterling Acquisition Awards [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SterlingAcquisitionAwardsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sterling acquisition awards [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NumberOfCustomers_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of customers.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NumberOfCustomers_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Customers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NumberOfCustomers_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Customers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total deferred tax asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Net of Valuation Allowance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Stock Options Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise of stock options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeaseDescriptionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Lease, Description [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">CURRENT LIABILITIES</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableInterestBearingInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable, Interest-Bearing, Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableInterestBearingInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Bearing Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts Receivable [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CapitalizedSoftwareDevelopedInternallyOrOtherwisePurchasedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Capitalized software for internal use, developed internally or otherwise purchased [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CapitalizedSoftwareDevelopedInternallyOrOtherwisePurchasedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Capitalized software developed internally or otherwise purchased.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CapitalizedSoftwareDevelopedInternallyOrOtherwisePurchasedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Capitalized Software Developed Internally Or Otherwise Purchased [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SeniorLoansMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Senior Loans [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income Taxes Paid, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Taxes Paid, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for income taxes, net of refunds received</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForProceedsFromOtherInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other investing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForProceedsFromOtherInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other investing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForProceedsFromOtherInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments for (Proceeds from) Other Investing Activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateSwap4Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest Rate Swap 4 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateSwap4Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Swap 4[Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateSwap4Member_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Interest Rate Swap 4[Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash and Cash Equivalents, at Carrying Value, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash and Cash Equivalents, at Carrying Value, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash and Cash Equivalents, at Carrying Value, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents, at Carrying Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PercentageOfThresholdDescribedUnderRuleNotApplied_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of threshold described in rule 4-08 not applied due to consolidated accumulated deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PercentageOfThresholdDescribedUnderRuleNotApplied_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage of Threshold Described Under Rule Not Applied</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PercentageOfThresholdDescribedUnderRuleNotApplied_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of threshold described under rule not applied.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BalanceSheetLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position Location, Balance [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BalanceSheetLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Balance Sheet Location</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating Lease, 2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Five</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCostTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Cost [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCostTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization and Interest Expense Related to Capital Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCostTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Summary of lease cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementStrategyAndGovernanceLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management, Strategy, and Governance [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Stockholders' Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Research and Development Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Product and technology expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term debt, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-term Debt, Excluding Current Maturities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Excluding Current Maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Long-term debt (net of deferred financing costs of $41,861 and $6,268 at December 31, 2024 and 2023, respectively)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Excess Tax Benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expense, Tax Benefit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Granted stock option</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfGoodwillTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Goodwill [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfGoodwillTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Changes in Carrying Amount of Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateSwap1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest Rate Swap 1 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateSwap1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Swap 1 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateSwap1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Interest Rate Swap 1 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FinanceLeaseCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Finance Lease Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FinanceLeaseCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FinanceLeaseCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total finance lease costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FinanceLeaseCosts_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Total finance lease costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Indefinite-Lived Intangible Assets [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Indefinite-lived Intangible Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Class [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset Class</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ExciseTaxOnShareRepurchases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Excise Tax on Share Repurchases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ExciseTaxOnShareRepurchases_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Excise Tax on Share Repurchases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ExciseTaxOnShareRepurchases_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Excise tax on repurchase of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Property and equipment, gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Property, Plant and Equipment, Gross, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Property, Plant and Equipment, Gross, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Property, Plant and Equipment, Gross, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Property and equipment, gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProductInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_StockConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_StockConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_StockConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Leases [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeOperatingAndFinancingLeaseRenewalTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Term of lessee's operating and Finance lease renewal.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeOperatingAndFinancingLeaseRenewalTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee Operating and Financing Lease Renewal Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeOperatingAndFinancingLeaseRenewalTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Renewal lease terms</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Payment Award, Stock Options, Valuation Assumptions [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Assumptions Applied to Establish Fair Value of Options Granted Using Black-Scholes Option Pricing Model</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SummaryOfOperatingLossCarryforwardsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Net Operating Loss Carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SummaryOfOperatingLossCarryforwardsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary of Operating Loss Carryforwards [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScheduleOfCondensedCashFlowStatementTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Condensed Cash Flow Statement [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScheduleOfCondensedCashFlowStatementTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Supplemental cash flow information related to leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FormINineComplianceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Form I Nine Compliance.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FormINineComplianceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Form I Nine Compliance [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FormINineComplianceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Form I-9 Compliance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SterlingCommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sterling Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SterlingCommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sterling Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertySubjectToOrAvailableForOperatingLeaseDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property Subject to or Available for Operating Lease [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, after Year Five</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Thereafter</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TransactionExpensesChangeInControl_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Transaction expenses, change in control.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TransactionExpensesChangeInControl_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Transaction Expenses Change In Control</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TransactionExpensesChangeInControl_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Transaction expenses, change in control</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred, Equity Interests Issued and Issuable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FairValueOfFirstAdvantageCommonStockIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value of First Advantage Common Stock Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FairValueOfFirstAdvantageCommonStockIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Fair Value of First Advantage Common Stock Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FairValueOfFirstAdvantageCommonStockIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plus: fair value of First Advantage common stock issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsIndefinitelivedExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Impairment of intangible assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsIndefinitelivedExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Impairment of Intangible Assets, Indefinite-Lived (Excluding Goodwill)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsIndefinitelivedExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment of intangible assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sale of Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided by (Used in) Investing Activities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">CASH FLOWS FROM INVESTING ACTIVITIES</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationPriorYearIncomeTaxes_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Return-to-provision adjustment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationPriorYearIncomeTaxes_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Prior Year Income Taxes, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments for Repurchase of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Repurchases of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_AmericasMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Americas [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_AmericasMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Americas</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueHedgeAssetsAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hedge Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueHedgeAssetsAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of derivatives not designated as hedging instruments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FastballHoldcoLPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fastball Holdco L P [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FastballHoldcoLPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Fastball Holdco, L.P</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FastballHoldcoLPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fastball Holdco L P [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AmortizingPrincipalPaymentRepayment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortizing Principal Payment Repayment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AmortizingPrincipalPaymentRepayment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amortizing principal payment repayment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AmortizingPrincipalPaymentRepayment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amortizing Principal Payment Repayment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromPriorPeriodTaxPositions_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Decreases for tax positions related to prior years</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromPriorPeriodTaxPositions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecognized Tax Benefits, Decrease Resulting from Prior Period Tax Positions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromPriorPeriodTaxPositions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Decreases for tax positions related to prior</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Reconciliation of U.S. Federal Statutory Income Tax Rate and Effective Income Tax Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Effective Income Tax Rate Reconciliation [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementStrategyAndGovernanceAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management, Strategy, and Governance [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalLabilitySettlementAndRelatedToAdministrativeFees_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Total lability settlement and related to administrative fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalLabilitySettlementAndRelatedToAdministrativeFees_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Total Lability Settlement And Related To Administrative Fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalLabilitySettlementAndRelatedToAdministrativeFees_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateSwap2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest Rate Swap 2 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateSwap2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Swap 2 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateSwap2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Interest Rate Swap 2 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidatedEntitiesDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidated Entities [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidatedEntitiesDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Consolidated Entities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ScheduleOfShareBasedCompensationProfitsInterestUnitActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule Of Share Based Compensation Profits Interest Unit Activity Table Text Block</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ScheduleOfShareBasedCompensationProfitsInterestUnitActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Share Based Compensation Profits Interest Unit Activity Table Text Block</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ScheduleOfShareBasedCompensationProfitsInterestUnitActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of the Profits Interest Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Selling, General and Administrative Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling, General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Selling, general, and administrative expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockRepurchasedDuringPeriodValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Repurchased During Period, Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockRepurchasedDuringPeriodValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock Repurchased During Period, Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net Carrying Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Finite-Lived Intangible Assets, Net, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Finite-Lived Intangible Assets, Net, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net book value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TradeNamesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trade Names [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TradeNamesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trade names</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Depreciation, Depletion and Amortization, Nonproduction, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation, Depletion and Amortization, Nonproduction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation and amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease Liability Payments Due</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total minimum lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Liability Payments Due</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total minimum lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Accounts Payable, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accounts Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesNetAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities, Net [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesNetAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred tax liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine2_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine2_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Address Line Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationPerformanceSharesAwardOutstandingActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of outstanding stock option grants issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationPerformanceSharesAwardOutstandingActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Performance Shares, Outstanding Activity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">LIABILITIES AND EQUITY</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided by (Used in) Financing Activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash provided by (used in) financing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Other, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EstimatedFairValueOfTheUnderlyingUnit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Estimated Fair Value of the Underlying Unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EstimatedFairValueOfTheUnderlyingUnit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Estimated Fair Value of the Underlying Unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EstimatedFairValueOfTheUnderlyingUnit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated fair-value of the underlying unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeBenefitsAndShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Benefits and Share-Based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeBenefitsAndShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_IcfrAuditorAttestationFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">ICFR Auditor Attestation Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_IcfrAuditorAttestationFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ICFR Auditor Attestation Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Effective tax rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Effective tax rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsStateAndLocal_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Operating Loss Carryforwards, State and Local</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsStateAndLocal_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">State net operating loss carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive securities excluded from computation of earnings per share, amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ScheduleOfPrepaidExpensesAndOtherCurrentAssetsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Prepaid Expenses And Other Current Assets [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ScheduleOfPrepaidExpensesAndOtherCurrentAssetsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule Of Prepaid Expenses And Other Current Assets [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ScheduleOfPrepaidExpensesAndOtherCurrentAssetsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Prepaid Expenses and Other Current Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">APIC, Share-based Payment Arrangement, Increase for Cost Recognition, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accrued Liabilities, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, after Year Five</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Thereafter</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">(Benefit) provision for income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Benefit for income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwentyTwentyOneAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2021 Acquisitions [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwentyTwentyOneAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Twenty Twenty One Acquisitions [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwentyTwentyOneAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Twenty Twenty One Acquisitions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxes_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxes_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred taxes.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxes_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combinations [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwoThousandTwentyOneEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2021 Employee Stock Purchase Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwoThousandTwentyOneEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty One Employee Stock Purchase Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwoThousandTwentyOneEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two Thousand Twenty One Employee Stock Purchase Plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Rate [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Variable Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Stockholders' Equity Attributable to Parent, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Stockholders' Equity Attributable to Parent, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DividendsDeclaredButNotPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Dividends declared but not paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DividendsDeclaredButNotPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends Declared But Not Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DividendsDeclaredButNotPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Dividends declared but not paid.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_IssuanceOfCommonStockUponTheAcquisitionOfSterlingCheckCorp_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Issuance Of Common Stock Upon The Acquisition Of Sterling Check Corp</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_IssuanceOfCommonStockUponTheAcquisitionOfSterlingCheckCorp_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Issuance Of Common Stock Upon The Acquisition Of Sterling Check Corp</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_IssuanceOfCommonStockUponTheAcquisitionOfSterlingCheckCorp_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock upon the acquisition of Sterling Check Corp.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Indefinite-Lived Intangible Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangible assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EmployeeStockPurchasePlanExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Employee stock purchase plan expenses.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EmployeeStockPurchasePlanExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Stock Purchase Plan Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EmployeeStockPurchasePlanExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Employee stock purchase plan expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Tangible Asset [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-Lived Tangible Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Liabilities, Noncurrent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Liabilities, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentRiskAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentRiskAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative Instrument</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Cash purchase price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Businesses, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash, net of cash acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Stock Units (RSUs) [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted Stock Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInDeferredRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Deferred Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInDeferredRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred revenues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Variable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Lease, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Property Plant And Equipment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementStrategyAndGovernanceTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management, Strategy, and Governance [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Goodwill, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrecognized pre-tax noncash compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OutstandingChecksInExcessOfFundsOnDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Outstanding funds on deposit</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OutstandingChecksInExcessOfFundsOnDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Outstanding Checks in Excess of Funds on Deposits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementExpertiseOfManagementResponsibleTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Expertise of Management Responsible [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ShareRepurchaseProgramAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Repurchase Program [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued Liabilities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Liabilities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalLeasedAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Capital Leased Assets Gross</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalLeasedAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Capital Leased Assets, Gross, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total Deferred</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Total Deferred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income Location [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other Comprehensive Income Location</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StatementGeographicalAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographical [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StatementGeographicalAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Geographical</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance Leases, 2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Incremental compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeasesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leases [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FinancingCashFlowsFromFinanceLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Financing cash flows from finance leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FinancingCashFlowsFromFinanceLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing cash flows from finance leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Use of Estimates</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Use of Estimates, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsegmentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsegments [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of Accounts Receivable, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk, Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Percentage of sales</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and Cash Equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareRepurchaseCostRecordedToAccumulatedDefecit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share Repurchase Cost Recorded To Accumulated Defecit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareRepurchaseCostRecordedToAccumulatedDefecit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Repurchase Cost Recorded To Accumulated Defecit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareRepurchaseCostRecordedToAccumulatedDefecit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total costs recorded to accumulated deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ShareRepurchaseCostRecordedToAccumulatedDefecit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total costs recorded to accumulated deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsPayableAmountPerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash dividend declared, per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsPayableAmountPerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends Payable, Amount Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class Of Stock [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Business Acquisitions, by Acquisition [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Business Acquisitions By Acquisition [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateSwap3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Swap 3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateSwap3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Interest Rate Swap 3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateSwap3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest Rate Swap 3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StatementScenarioAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Scenario [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StatementScenarioAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Scenario</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, Current, Statement of Financial Position [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income (Loss) from Continuing Operations, Per Outstanding Share, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations, Per Basic Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basic net (loss) income per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLossCarryforwardsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Loss Carryforwards [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLossCarryforwardsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating Loss Carryforwards [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Acquisition, Acquiree [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business Acquisition, Acquiree</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total operating expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SecuritiesHeldByNonAfffiliatesThreshhold_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Securities Held By Non Afffiliates Threshhold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SecuritiesHeldByNonAfffiliatesThreshhold_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Securities Held By Non Afffiliates Threshhold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SecuritiesHeldByNonAfffiliatesThreshhold_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Securities held by non afffiliates threshhold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Tangible Asset [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-Lived Tangible Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationSeparatelyRecognizedTransactionsExpensesAndLossesRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Separately Recognized Transactions, Expenses and Losses Recognized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationSeparatelyRecognizedTransactionsExpensesAndLossesRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Closing costs &amp; transaction expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class of Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SecuredLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate Principal Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SecuredLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Secured Long-Term Debt, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PaymentsOnDeferredPurchaseAgreements_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payments on deferred purchase agreements.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PaymentsOnDeferredPurchaseAgreements_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments on Deferred Purchase Agreements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PaymentsOnDeferredPurchaseAgreements_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Payments on deferred purchase agreements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: accumulated depreciation and amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_LegalEntityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Legal Entity [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_LegalEntityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Legal Entity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ScheduleOfShareRepurchaseActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of share repurchase activity table text block.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ScheduleOfShareRepurchaseActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share Repurchase Activity Table Text Block</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ScheduleOfShareRepurchaseActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Share Repurchase Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SoftwareAndSoftwareDevelopmentCostsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Capitalized Software Acquired by Business Combination [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SoftwareAndSoftwareDevelopmentCostsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Software and Software Development Costs [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating Lease, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesConverted1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Conversion of Stock, Shares Converted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesConverted1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of stock, Shares converted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Maximum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">TOTAL LIABILITIES AND EQUITY</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">TOTAL LIABILITIES AND EQUITY</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PredecessorPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Predecessor Plan [Member].</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PredecessorPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Predecessor Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PredecessorPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Predecessor Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain (Loss) on Extinguishment of Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Extinguishment of Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loss on extinguishment of debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Loss on extinguishment of debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Right-of-Use Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Right of use operating lease assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PredecessorPeriodMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Predecessor Period.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PredecessorPeriodMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Predecessor Period [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PredecessorPeriodMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Predecessor Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensationAndRetirementDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retirement Benefits [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Diluted net income per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Diluted net (loss) income per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leasehold improvements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leasehold Improvements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityExTransitionPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Ex Transition Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityExTransitionPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Ex Transition Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromSubsidiariesNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity in net income of subsidiaries</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromSubsidiariesNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income (Loss) from Subsidiaries, Net of Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromSubsidiariesNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Subsidiaries, Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Shareholder distribution</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncontrolling Interest, Decrease from Distributions to Noncontrolling Interest Holders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shareholder distribution</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Hierarchy and NAV</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LienCategoryAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lien Category [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LienCategoryAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lien Category</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FixedLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Fixed lease cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FixedLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fixed lease cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_IntersegmentRevenuesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intersegment Revenues [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_IntersegmentRevenuesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intersegment Revenues [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_IntersegmentRevenuesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Intersegment Revenues [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided by (Used in) Investing Activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash used in investing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsWeightedAverageVolatilityRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Weighted Average Volatility Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsWeightedAverageVolatilityRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expected stock price volatility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProFormaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Pro Forma [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProFormaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pro Forma</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LiborMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">LIBOR</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LiborMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">LIBOR [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LiborMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">LIBOR [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InternationalExceptUnitedStatesCanadaAndLatinAmericaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">International except United States Canada and Latin America.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InternationalExceptUnitedStatesCanadaAndLatinAmericaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">International except United States Canada and Latin America [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InternationalExceptUnitedStatesCanadaAndLatinAmericaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">International</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxCreditCarryforwardDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Credit Carryforward, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxCreditCarryforwardDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax Credit Carryforward, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeGainLossStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeGainLossStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative, Gain (Loss), Statement of Income or Comprehensive Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScenarioForecastMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Forecast [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScenarioForecastMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Forecast</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock issued during period shares new issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrecognized Tax Benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecognized Tax Benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance, end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Balance, beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Weighted Average Exercise Price, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Weighted Average Exercise Price, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Option, Nonvested, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average exercise price, grants unvested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Lien Credit Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First Lien Credit Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Lien Credit Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in valuation allowances</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Change in valuation allowances</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OutstandingBorrowingUnderRevolver_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Outstanding Borrowing Under Revolver</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OutstandingBorrowingUnderRevolver_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Outstanding Borrowing Under Revolver</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OutstandingBorrowingUnderRevolver_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Outstanding Borrowing Under Revolver</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFilerCategory_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Filer Category</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFilerCategory_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Filer Category</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingRevenueReconcilingItemLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, Revenue Reconciling Item [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill and Intangible Assets Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill and Other Intangible Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedTradeName_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed trade name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedTradeName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Trade Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedTradeName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trade name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCustomerLists_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed customer lists</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCustomerLists_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Customer Lists</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCustomerLists_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxLiabilitiesCustomerLists_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities Customer Lists</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxLiabilitiesCustomerLists_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred Tax Liabilities Customer Lists</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxLiabilitiesCustomerLists_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Customer lists</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPayablesUnderRepurchaseAgreements_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Payables under Repurchase Agreements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPayablesUnderRepurchaseAgreements_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Directors authorized an increase to the total available amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Organization, Consolidation and Presentation of Financial Statements Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Organization, Nature of Business, and Basis of Presentation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Notional</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Notional Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative notional amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_StockRepurchasePricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock Repurchase Price Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_StockRepurchasePricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Repurchase Price Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_StockRepurchasePricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Average price per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: Imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: Imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OptionToPurchaseAdditionalSharesOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Option to purchase additional shares of common stock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OptionToPurchaseAdditionalSharesOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Option To Purchase Additional Shares Of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OptionToPurchaseAdditionalSharesOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Option to purchase additional shares of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Total lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Total lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total lease liabilities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total lease liabilities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-based Payment Arrangement, Noncash Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Noncash Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Assets, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AdditionalAssociatedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Additional Associated Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AdditionalAssociatedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Associated Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AdditionalAssociatedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional associated costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LoanRestructuringModificationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loan Restructuring Modification [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate Intrinsic Value, Grants Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related and Nonrelated Parties [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillForeignCurrencyTranslationGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill, Foreign Currency Translation Gain (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillForeignCurrencyTranslationGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign currency translation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ProductAndTechnologyExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Product and technology expense [Member].</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ProductAndTechnologyExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product And Technology Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ProductAndTechnologyExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Product and Technology Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PresentValueOfMinimumLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Present Value of Minimum Lease Payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PresentValueOfMinimumLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Present Value of Minimum Lease Payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PresentValueOfMinimumLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Present value of minimum lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Weighted Average Remaining Lease Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance Lease, Weighted Average Remaining Lease Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Finance leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Indefinite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Indefinite-lived Intangible Assets, Major Class Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of reportable segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Number of Reportable Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Reportable Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Share Based Compensation Arrangements By Share Based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net (Loss) Income Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Maturity Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maturity date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Emerging Growth Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Emerging Growth Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwoThousandTwentyFourAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Four Acquisitions [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwoThousandTwentyFourAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two Thousand Twenty Four Acquisitions [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwoThousandTwentyFourAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2024 Acquisition [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AmendedRevolverMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amended Revolver [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AmendedRevolverMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amended Revolver [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AmendedRevolverMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amended Revolver [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2024</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease Liability Payments Remainder Of Fiscal Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Liability Payments Remainder Of Fiscal Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average number of shares outstanding - basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Taxes Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VestingDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Vesting [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VestingDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingencies [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loss Contingencies [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance Lease, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromPriorPeriodTaxPositions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecognized Tax Benefits, Increase Resulting from Prior Period Tax Positions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromPriorPeriodTaxPositions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Increases for tax positions related to prior years</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ShareRepurchaseProgramDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Repurchase Program [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Useful Life</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubleaseIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sublease Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubleaseIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sub-leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubleaseIncome_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Sub-leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EstimatedRepaymentOfSterlingsOutstandingDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Estimated Repayment of Sterling's Outstanding Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EstimatedRepaymentOfSterlingsOutstandingDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Estimated Repayment of Sterling's Outstanding Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EstimatedRepaymentOfSterlingsOutstandingDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plus: repayment of Sterling's outstanding debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDebtInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Long-Term Debt Instruments [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDebtInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value of Company's Debt Obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwoThousandTwentyFourFirstLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Four First Lien Credit Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwoThousandTwentyFourFirstLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two Thousand Twenty Four First Lien Credit Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwoThousandTwentyFourFirstLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2024 First Lien Credit Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from the sale of shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration Risk Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseInterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Interest Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseInterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest on lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 1 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 1 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PercentageOfThresholdAmountOfNetAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of threshold amount of net assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PercentageOfThresholdAmountOfNetAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage Of Threshold Amount Of Net Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PercentageOfThresholdAmountOfNetAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of threshold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2025</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentsIncorporatedByReferenceTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Documents Incorporated by Reference [Text Block]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment of Long-Lived Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Shares Issued, Value, Share-Based Payment Arrangement, after Forfeiture, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Issued, Value, Share-Based Payment Arrangement, after Forfeiture</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of common stock under share-based compensation plans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsegmentsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsegments [Domain]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Liabilities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillPurchaseAccountingAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill, Measurement Period Adjustment</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillImpairmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill, Impairment Loss</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DescriptionOfBorrowingCapacityNotSubjectToNetLeverageRatioCovenant_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Description of borrowing capacity not subject to net leverage ratio covenant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DescriptionOfBorrowingCapacityNotSubjectToNetLeverageRatioCovenant_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Description of borrowing capacity not subject to net leverage ratio covenant.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DescriptionOfBorrowingCapacityNotSubjectToNetLeverageRatioCovenant_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Description Of Borrowing Capacity Not Subject To Net Leverage Ratio Covenant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskRoleOfManagementTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Role of Management [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountingPoliciesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Policies [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Option, Activity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Option Unit Activity</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AdditionalPaidInCapitalWithheldForTaxObligationsAndNetSettlementOfStockOptionExercise_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Additional paid in capital withheld for tax obligations and net settlement of stock option exercise.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Abstract]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents, Restricted Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted Cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statement [Table]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Asset, Expected Amortization, after Year Five</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Thereafter</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Tax Deferred Expense, Compensation and Benefits, Share-Based Compensation Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">State and local income taxes &#8211; net of federal tax benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, State and Local Income Taxes, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Operating Lease Liability Current and Noncurrent.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease Liability Current and Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total operating liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Operating Lease Liability Current and Noncurrent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueAfterYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease Liability Payments Due After Year Five</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueAfterYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Liability Payments Due After Year Five</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueAfterYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Thereafter</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SymphonyTechnologyGroupMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Symphony technology group.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SymphonyTechnologyGroupMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Symphony Technology Group [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SymphonyTechnologyGroupMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">STG [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IPOMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">IPO [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IPOMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">IPO</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Income (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">(LOSS) INCOME FROM OPERATIONS</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2025</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Issued, Price Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares offering, price per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedIncomeTaxesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Income Taxes, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedIncomeTaxesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TermLoanDueJanuaryThirtyOneTwoThousandTwentyEightMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Term Loan due January Thirty One Two Thousand Twenty Eight</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TermLoanDueJanuaryThirtyOneTwoThousandTwentyEightMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Term Loan Due January Thirty One Two Thousand Twenty Eight [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TermLoanDueJanuaryThirtyOneTwoThousandTwentyEightMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term Loan due January 31, 2028 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorSecondLienCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Successor second lien credit facility.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorSecondLienCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Successor Second Lien Credit Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorSecondLienCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Successor Second Lien Credit Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockNoParValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, No Par Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockNoParValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, no par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CondensedFinancialInformationOfParentCompanyOnlyDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Condensed Financial Information of Parent Company Only Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CondensedFinancialInformationOfParentCompanyOnlyDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Condensed Financial Information Of Registrant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeSwaptionInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative, Swap Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeSwaptionInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Swaption Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Tax Identification Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Tax Identification Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ASSETS</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SterlingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sterling [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SterlingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sterling [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SterlingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sterling [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueOfFinancialInstrumentsPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value of Financial Instruments, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueOfFinancialInstrumentsPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value of Financial Instruments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionAmountsOfTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related party transactions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionAmountsOfTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction, Amounts of Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationArrangementWithIndividualCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Compensation Arrangement with Individual, Compensation Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationArrangementWithIndividualCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Compensation expense related to converted cash awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationArrangementWithIndividualCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Compensation expense attributable to converted Sterling equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance Lease, 2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ExtendedMaturityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Extended Maturity [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsCash_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Cash dividends declared</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsCash_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash dividends declared</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsCash_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends, Cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsCash_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Dividends, Cash, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalLeaseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Total lease assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalLeaseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Total lease assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalLeaseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total lease assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SoftwareDevelopmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Software developed for internal use</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SoftwareDevelopmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Software Development [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and Equipment, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteStockSplit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders' Equity Note, Stock Split</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteStockSplit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stockholders' equity note, stock split</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_SegmentGeographicalDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographical [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_SegmentGeographicalDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Geographical</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease Liability Payments Due Year Five</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Liability Payments Due Year Five</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PredecessorFirstLienMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Predecessor First Lien [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PredecessorFirstLienMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Predecessor First Lien.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PredecessorFirstLienMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Predecessor First Lien [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_UnrecognizedTaxBenefitsAcquiredTaxPositionsRelatedToPriorYears_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Acquired tax positions related to prior years</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_UnrecognizedTaxBenefitsAcquiredTaxPositionsRelatedToPriorYears_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecognized Tax Benefits Acquired Tax Positions Related To Prior Years</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_UnrecognizedTaxBenefitsAcquiredTaxPositionsRelatedToPriorYears_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Unrecognized Tax Benefits Acquired Tax Positions Related To Prior Years</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Repayments of First Lien Credit Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Repayments of Long-term Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Repayments of Long-Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repayments of Long-term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalExpendituresIncurredButNotYetPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Capital Expenditures Incurred but Not yet Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalExpendituresIncurredButNotYetPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash property and equipment additions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalExpendituresIncurredButNotYetPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Property and equipment acquired on account</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeFinanceLeaseTermOfContract1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeFinanceLeaseTermOfContract1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Finance Lease, Term of Contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets, Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfUnrecognizedTaxBenefitsRollForwardTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Unrecognized Tax Benefits Roll Forward [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfUnrecognizedTaxBenefitsRollForwardTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Summary of Income Tax Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance Initial Public Offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of common stock in initial public offering, net of underwriting discounts and commissions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Proceeds from issuance initial public offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Acquisition [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business Acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NonConvertibleDebtSecuritiesThreshhold_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Non Convertible Debt Securities Threshhold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NonConvertibleDebtSecuritiesThreshhold_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non Convertible Debt Securities Threshhold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NonConvertibleDebtSecuritiesThreshhold_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non convertible debt securities threshhold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NoCustomersMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">No Customers.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NoCustomersMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">No Customers [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NoCustomersMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">No Customers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeContractTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Contract [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeContractTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative Contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToDevelopSoftware_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Develop Software</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToDevelopSoftware_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Capitalized software development costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">U.S. statutory federal tax rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill, Trade Names, Customer Lists, and Other Intangible Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill and Intangible Assets, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_LocalPhoneNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Local Phone Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_LocalPhoneNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Local Phone Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseImpairmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Impairment Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseImpairmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non cash impairment charges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Preferred Stock, Shares Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Preferred Stock, Shares Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalRevenuesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Total Revenues [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalRevenuesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Total Revenues [ Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TotalRevenuesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total Revenues [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Employee stock purchase plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Stock Purchase Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2021 Employee Stock Purchase Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateCollarMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Collar [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InterestRateCollarMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">InterestRateCollarMember</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HedgingDesignationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Hedging Designation [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockDividendsPerShareCashPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash dividends declared</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockDividendsPerShareCashPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Dividends, Per Share, Cash Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxAuthorityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Jurisdiction [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxAuthorityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Tax Authority</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Income before Income Tax, Domestic and Foreign [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of (Loss) Income Before Income Tax Benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DilutiveSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Potentially dilutive securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DilutiveSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dilutive Securities, Effect on Basic Earnings Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DilutiveSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Dilutive Securities, Effect on Basic Earnings Per Share, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: Deferred financing costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Less: Deferred financing costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Issuance Costs, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long term debt (net of deferred financing costs)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Deferred Tax Assets and Liabilities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Net Deferred Tax Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PercentageOfCapitalStockOfTheBorrower_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage Of Capital Stock Of The Borrower</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PercentageOfCapitalStockOfTheBorrower_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage Of Capital Stock Of The Borrower</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_PercentageOfCapitalStockOfTheBorrower_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage Of Capital Stock Of The Borrower</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating leases other current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Current portion of operating lease liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DevelopedTechnologyRightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Developed Technology Rights [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Right-of-Use Asset Obtained in Exchange for Finance Lease Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease Liability Payments Due Year Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Liability Payments Due Year Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InProcessResearchAndDevelopmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and Development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InProcessResearchAndDevelopmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">In Process Research and Development [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign currency translation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Foreign currency translation (loss) income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxAuthorityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Jurisdiction [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxAuthorityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Tax Authority</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Interest Rate, Stated Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt issuance costs percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Deficit [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid Expenses and Other Current Assets [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expenses and Other Current Assets [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchases of property and equipment</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ExciseTaxesOnShareRepurchases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Excise taxes on share repurchases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ExciseTaxesOnShareRepurchases_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Excise taxes on share repurchases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Transition Report</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StockRepurchaseProgramAuthorizedAmount1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Authorized stock repurchase program, Initial</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating Lease, 2025</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Deferred Tax Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred tax liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Deferred tax liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportingUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Reporting Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign rate difference</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Foreign rate difference</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Exercises in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average exercise price, exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Tax Deferred Expense, Reserves and Accruals, Accrued Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses and loss reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentrations of Credit Risk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk, Credit Risk, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Income Tax Assets, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Income Tax Assets, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred tax asset, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorFirmId_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Auditor Firm ID</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Minimum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Year Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalLeasesLesseeBalanceSheetAssetsByMajorClassAccumulatedDeprecation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Capital leased assets accumulated depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalLeasesLesseeBalanceSheetAssetsByMajorClassAccumulatedDeprecation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Capital Leases, Lessee Balance Sheet, Assets by Major Class, Accumulated Depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate Intrinsic Value, Grants Vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Outstanding, Aggregate Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Weighted Average Grant Date Fair Value, beginning value | $ / shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Weighted Average Grant Date Fair Value, Ending balance | $ / shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Operating Lease, Right-of-Use Asset, Amortization Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset, Periodic Reduction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization of right-of-use operating lease assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid-in Capital [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional Paid In Capital [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityWellKnownSeasonedIssuer_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Well-known Seasoned Issuer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityWellKnownSeasonedIssuer_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Well-known Seasoned Issuer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CashDividendsPaid_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Cash dividends paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CashDividendsPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash dividends paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CashDividendsPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash dividends paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CashDividendsPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash dividends paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Foreign Currency Transactions and Translations Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign Currency</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CustomerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Customer [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CustomerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_CustomerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Customer [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustments to Reconcile Net Income (Loss) to Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjustments to reconcile net (loss) income to net cash provided by operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_RestructuringExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_RestructuringExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Restructuring Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SectionTwoSixSevenAdjustment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Section 267 adjustment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SectionTwoSixSevenAdjustment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Section Two Six Seven Adjustment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SectionTwoSixSevenAdjustment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Section Two Six Seven Adjustment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalDividendsInExcessOfRetainedEarnings_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustments to Additional Paid in Capital, Dividends in Excess of Retained Earnings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalDividendsInExcessOfRetainedEarnings_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash dividends declared</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalDividendsInExcessOfRetainedEarnings_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Cash dividends declared</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Income Location, Balance [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Statement Location</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockOwnershipPlanESOPPlanDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Stock Ownership Plan (ESOP), Plan [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockOwnershipPlanESOPPlanDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Employee Stock Ownership Plan (ESOP), Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating Lease 2024</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">2025</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Assets, Noncurrent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AcceleratedAmortizationOfDeferredFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accelerated amortization of deferred financing costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AcceleratedAmortizationOfDeferredFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accelerated Amortization of Deferred Financing Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_AcceleratedAmortizationOfDeferredFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional interest expense related to deferred financing costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FinanceLeaseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Finance Lease [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FinanceLeaseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FinanceLeaseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance Lease</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segments [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_GrantsIssuedInExchangeForOptionsInTheCompanysParent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Grants issued in exchange for options in the Companys Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_GrantsIssuedInExchangeForOptionsInTheCompanysParent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Grants issued in exchange for options in the Companys Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_GrantsIssuedInExchangeForOptionsInTheCompanysParent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Grants issued in exchange for options in the Companys Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Other Operating Liabilities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Other Operating Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwoThousandTwentyThreeAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Three Acquisitions [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwoThousandTwentyThreeAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two Thousand Twenty Three Acquisitions [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TwoThousandTwentyThreeAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2023 Acquisition [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill and Intangible Assets Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_O2023M8DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">O 2023 M8 Dividends [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_O2023M8DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">O 2023 M8 Dividends [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations, Per Diluted Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Diluted net (loss) income per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorRevolverMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Succesor</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorRevolverMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Successor Revolver [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorRevolverMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Successor Revolver [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorRevolverMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Successor revolver member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAcquiredDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill, Acquired During Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAcquiredDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationGiltiPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">GILTI inclusion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationGiltiPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, GILTI, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OneTimeTransactionCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/label">One Time Transaction Charges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OneTimeTransactionCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">One Time Transaction Charges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OneTimeTransactionCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">One-time transaction charges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Revenues from External Customers and Long-Lived Assets [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Revenues From External Customers And Long Lived Assets [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_Rule10B51ArrModifiedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Rule 10b51 Arr Modified Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_Rule10B51ArrModifiedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Rule 10b51 Arr Modified Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_Rule10B51ArrModifiedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rule 10b5-1 Arrangement Modified</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Basis of presentation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Basis of Accounting, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Asset, Expected Amortization, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2025</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScenarioUnspecifiedDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Scenario [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScenarioUnspecifiedDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Scenario</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNoncurrentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Issuance Costs, Noncurrent, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNoncurrentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Issuance Costs, Noncurrent, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNoncurrentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt refinancing costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NovemberFollowOnMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">November Follow-On</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NovemberFollowOnMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">November Follow-On</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NovemberFollowOnMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">November Follow-On [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NovemberFollowOnMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">November follow-on member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInIncomeTaxesPayableNetOfIncomeTaxesReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Income Taxes Payable, Net of Income Taxes Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInIncomeTaxesPayableNetOfIncomeTaxesReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income taxes receivable and payable, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OperationsAndComprehensiveIncomeLossMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Operations and comprehensive income (loss) [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OperationsAndComprehensiveIncomeLossMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operations and comprehensive income (loss) [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OperationsAndComprehensiveIncomeLossMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operations and comprehensive income (loss) [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations before Income Taxes, Domestic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income (loss) before provision for income taxes from United States operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">(Loss) income before provision for income taxes from United States operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeFloorInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Floor Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeFloorInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative floor interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Acquisition, Transaction Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Transaction and acquisition related charges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Common Stock, Value, Issued, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Common Stock, Value, Issued, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Common Stock, Value, Issued, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock - $0.001 par value; 1,000,000,000 shares authorized, 173,171,145 and 145,074,802 shares issued and outstanding as of December 31, 2024 and 2023, respectively</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TermDebtFacilityQuarterlyPaymentsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Term Debt Facility Quarterly Payments Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_TermDebtFacilityQuarterlyPaymentsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Term Debt Facility Quarterly Payments Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EmployeeStockPurchasePlanPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ESPP percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EmployeeStockPurchasePlanPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Employee stock purchase plan contribution limit.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_EmployeeStockPurchasePlanPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Stock Purchase Plan Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentIncomeInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Income, Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentIncomeInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Interest income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentIncomeInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Finite-Lived Intangible Assets, Future Amortization Expense [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Intangible Assets, Future Amortization Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidInsurance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Insurance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidInsurance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid corporate insurance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfAssets1_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain (Loss) on Disposition of Assets, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfAssets1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Disposition of Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfAssets1_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">(Gain) loss on disposal of fixed assets and impairment of ROU assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_Accumulatedunremittedforeignearnings_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated unremitted foreign earnings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_Accumulatedunremittedforeignearnings_lbl" xlink:role="http://www.xbrl.org/2003/role/label">AccumulatedUnremittedForeignEarnings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_Accumulatedunremittedforeignearnings_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">AccumulatedUnremittedForeignEarnings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Intangible Assets, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangible assets, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Other intangible assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpenseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">OTHER EXPENSE, NET:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpenseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Nonoperating Income (Expense) [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAllowanceForDoubtfulAccounts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Asset, Tax Deferred Expense, Reserve and Accrual, Accounts Receivable, Allowance for Credit Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAllowanceForDoubtfulAccounts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Bad debt reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Operating Lease, Liability, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Present value of minimum lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Operating Loss Carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Tax Assets, Operating Loss Carryforwards, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred tax asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">COMMITMENTS AND CONTINGENCIES (Note 14)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue Remaining Performance Obligation Expected Timing Of Satisfaction [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NumberOfCountryConcentrationOfRevenues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of country, concentration of revenues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NumberOfCountryConcentrationOfRevenues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Country, Concentration Of Revenues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NumberOfCountryConcentrationOfRevenues_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number Of Country, Concentration Of Revenues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueNetAssetLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Fair Value, Net Asset (Liability), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueNetAssetLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Net Asset (Liability)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueNetAssetLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of net assets and liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ClassBAwardsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Class b awards.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ClassBAwardsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class B Awards [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ClassBAwardsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class B Awards [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ProceedsFromLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Borrowings from First Lien Credit Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ProceedsFromLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Proceeds from long term debt.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_ProceedsFromLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds From Long Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average number of shares outstanding - diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Significant Accounting Policies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Significant Accounting Policies [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_RevolvingCreditFacilityQuarterlyPaymentsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Revolving credit facility quarterly payments, percentage.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_RevolvingCreditFacilityQuarterlyPaymentsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revolving Credit Facility Quarterly Payments Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_RevolvingCreditFacilityQuarterlyPaymentsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revolving credit facility quarterly payments, percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, Noncurrent, Statement of Financial Position [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InternationalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">International</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_InternationalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">International [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Accounts receivable (net of allowance for doubtful accounts)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Receivable, after Allowance for Credit Loss, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts receivable (net of allowance for doubtful accounts of $3,832 and $1,036 at December 31, 2024 and 2023, respectively)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseRenewalTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Renewal term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseRenewalTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Renewal Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Outstanding, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of units, vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total minimum lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NonCashPropertyAndEquipmentAdditions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non-cash property and equipment additions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NonCashPropertyAndEquipmentAdditions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Non-cash property and equipment additions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NonCashPropertyAndEquipmentAdditions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash property and equipment additions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementThirdPartyEngagedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Third Party Engaged [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee Lease Liability Undiscounted Excess Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lessee Lease Liability Undiscounted Excess Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: Imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: Imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxLiabilitiesPrepaidAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxLiabilitiesPrepaidAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities Prepaid Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxLiabilitiesPrepaidAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred Tax Liabilities Prepaid Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DeferredTaxLiabilitiesPrepaidAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Prepaid assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Denominator:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Benchmark [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration Risk Benchmark</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DescriptionOfSecurityInterestInTangibleAndIntangibleAssetsOfBorrowerAndGuarantors_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Description Of Security Interest In Tangible And Intangible Assets Of Borrower And Guarantors</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_DescriptionOfSecurityInterestInTangibleAndIntangibleAssetsOfBorrowerAndGuarantors_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Description Of Security Interest In Tangible And Intangible Assets Of Borrower And Guarantors</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total minimum lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Present value of minimum lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">COMPREHENSIVE INCOME</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">COMPREHENSIVE (LOSS)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">COMPREHENSIVE (LOSS) INCOME</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorSecondLienMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Successor Second Lien.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorSecondLienMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Successor Second Lien [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_SuccessorSecondLienMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Second Lien [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OtherTransactionAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other transaction adjustments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OtherTransactionAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other transaction adjustments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_OtherTransactionAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other transaction adjustments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementProcessesForAssessingIdentifyingAndManagingThreatsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Processes for Assessing, Identifying, and Managing Threats [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NonConvertibleDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Non convertible debt securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NonConvertibleDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non convertible debt securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_WeightedAverageAmortizationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Weighted average amortization period.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_WeightedAverageAmortizationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Amortization Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_WeightedAverageAmortizationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Operating Loss Carryforwards, Domestic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Federal net operating loss carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Revenues_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Revenues, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Revenues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Revenues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Revenues_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">revenues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Foreign Currency Transaction Gain (Loss), before Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss), Foreign Currency Transaction, before Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Gain (loss) on foreign currency exchange rates</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Loss on foreign currency exchange rates</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseAndRentalExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Operating Leases, Rent Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseAndRentalExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Leases, Rent Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseAndRentalExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rent expense under operating leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstAdvantageAmericasMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Advantage Americas [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstAdvantageAmericasMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First Advantage Americas [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_FirstAdvantageAmericasMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Advantage Americas [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlansIncludingStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Proceeds, Issuance of Shares, Share-Based Payment Arrangement, Including Option Exercised, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlansIncludingStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds, Issuance of Shares, Share-Based Payment Arrangement, Including Option Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlansIncludingStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of common stock under share-based compensation plans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeOperatingAndFinanceLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Term of lessee's operating lease and finance lease.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeOperatingAndFinanceLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee Operating and Finance Lease Term of Contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_LesseeOperatingAndFinanceLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease Term of contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total identifiable net assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenues from External Customers and Long-Lived Assets [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenues From External Customers And Long Lived Assets [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revolving Credit Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDateDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, maturity date, description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDateDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Maturity Date, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NonRule10B51ArrModifiedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non Rule 10b51 Arr Modified Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NonRule10B51ArrModifiedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Non Rule 10b51 Arr Modified Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_NonRule10B51ArrModifiedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-Rule 10b5-1 Arrangement Modified</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_StockRepurchaseCostTotal_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock Repurchase Cost Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_StockRepurchaseCostTotal_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Repurchase Cost Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_StockRepurchaseCostTotal_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total repurchase costs</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Weighted average exercise price, grant outstanding ending balance</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities [Abstract]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fa_MergerAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Merger Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShortTermLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Short-Term Lease, Cost</link:label>
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          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_FinanceAmortizationOfLeasedAssets" xlink:label="fa_FinanceAmortizationOfLeasedAssets"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShortTermLeaseCost" xlink:label="us-gaap_ShortTermLeaseCost"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseInterestExpense" xlink:label="us-gaap_FinanceLeaseInterestExpense"/>
          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_FixedLeaseCost" xlink:label="fa_FixedLeaseCost"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_VariableLeaseCost" xlink:label="us-gaap_VariableLeaseCost"/>
        </link:calculationLink>
        <link:calculationLink xlink:type="extended" xlink:role="http://fadv.com/20241231/taxonomy/role/DisclosureLeaseSupplementalBalanceSheetInformationRelatedToLeasesDetails">
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_PropertyPlantAndEquipmentNet" xlink:to="us-gaap_PropertyPlantAndEquipmentGross" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="fa_FinanceLeaseLiabilityCurrentAndNoncurrent" xlink:to="us-gaap_FinanceLeaseLiabilityCurrent" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="fa_TotalLeaseLiabilities" xlink:to="fa_LeaseLiability" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="fa_LeaseLiability" xlink:to="us-gaap_OperatingLeaseLiabilityNoncurrent" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="fa_TotalLeaseAssets" xlink:to="us-gaap_PropertyPlantAndEquipmentNet" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="fa_FinanceLeaseLiabilityCurrentAndNoncurrent" xlink:to="us-gaap_FinanceLeaseLiabilityNoncurrent" order="1" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="fa_TotalLeaseLiabilities" xlink:to="fa_FinanceLeaseLiabilityCurrentAndNoncurrent" order="1" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="fa_LeaseLiability" xlink:to="us-gaap_OperatingLeaseLiabilityCurrent" order="1" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="fa_TotalLeaseAssets" xlink:to="us-gaap_OperatingLeaseRightOfUseAsset" order="1" weight="1" use="optional"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PropertyPlantAndEquipmentNet" xlink:label="us-gaap_PropertyPlantAndEquipmentNet"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PropertyPlantAndEquipmentGross" xlink:label="us-gaap_PropertyPlantAndEquipmentGross"/>
          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_FinanceLeaseLiabilityCurrentAndNoncurrent" xlink:label="fa_FinanceLeaseLiabilityCurrentAndNoncurrent"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseLiabilityCurrent" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent"/>
          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_TotalLeaseLiabilities" xlink:label="fa_TotalLeaseLiabilities"/>
          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_LeaseLiability" xlink:label="fa_LeaseLiability"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent"/>
          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_TotalLeaseAssets" xlink:label="fa_TotalLeaseAssets"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseLiabilityCurrent" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseRightOfUseAsset" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset"/>
        </link:calculationLink>
        <link:calculationLink xlink:type="extended" xlink:role="http://fadv.com/20241231/taxonomy/role/DisclosureLeasesMaturitiesOfLeaseLiabilitiesDetails">
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="fa_LeaseLiabilityPaymentsDue" xlink:to="fa_LeaseLiabilityPaymentsDueYearTwo" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" order="1" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="fa_LeaseLiabilityPaymentsDue" xlink:to="fa_LeaseLiabilityPaymentsDueYearThree" order="1" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" order="1" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" order="2" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="fa_LeaseLiabilityPaymentsDue" xlink:to="fa_LeaseLiabilityPaymentsDueYearFour" order="2" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" order="2" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive" order="3" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="fa_LeaseLiabilityPaymentsDue" xlink:to="fa_LeaseLiabilityPaymentsRemainderOfFiscalYear" order="3" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" order="3" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" order="4" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="fa_LeaseLiabilityPaymentsDue" xlink:to="fa_LeaseLiabilityPaymentsDueYearFive" order="4" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" order="4" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" order="5" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="fa_LeaseLiabilityPaymentsDue" xlink:to="fa_LeaseLiabilityPaymentsDueNextTwelveMonths" order="5" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" order="5" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="fa_LeaseLiabilityPaymentsDue" xlink:to="fa_LeaseLiabilityPaymentsDueAfterYearFive" order="6" weight="1" use="optional"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDue"/>
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          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_LeaseLiabilityPaymentsDue" xlink:label="fa_LeaseLiabilityPaymentsDue"/>
          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_LeaseLiabilityPaymentsDueYearTwo" xlink:label="fa_LeaseLiabilityPaymentsDueYearTwo"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths"/>
          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_LeaseLiabilityPaymentsDueYearThree" xlink:label="fa_LeaseLiabilityPaymentsDueYearThree"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour"/>
          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_LeaseLiabilityPaymentsDueYearFour" xlink:label="fa_LeaseLiabilityPaymentsDueYearFour"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive"/>
          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_LeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:label="fa_LeaseLiabilityPaymentsRemainderOfFiscalYear"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive"/>
          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_LeaseLiabilityPaymentsDueYearFive" xlink:label="fa_LeaseLiabilityPaymentsDueYearFive"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree"/>
          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_LeaseLiabilityPaymentsDueNextTwelveMonths" xlink:label="fa_LeaseLiabilityPaymentsDueNextTwelveMonths"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive"/>
          <link:loc xlink:type="locator" xlink:href="fa-20241231.xsd#fa_LeaseLiabilityPaymentsDueAfterYearFive" xlink:label="fa_LeaseLiabilityPaymentsDueAfterYearFive"/>
        </link:calculationLink>
      </link:linkbase>
    </xsd:appinfo>
  </xsd:annotation>
  <xsd:element id="fa_CapitalizedSoftwareDevelopedInternallyOrOtherwisePurchasedMember" name="CapitalizedSoftwareDevelopedInternallyOrOtherwisePurchasedMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_FirstLienCreditAgreement" name="FirstLienCreditAgreement" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_ProceedsFromLongTermDebt" name="ProceedsFromLongTermDebt" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_FairValueOfFirstAdvantageCommonStockIssued" name="FairValueOfFirstAdvantageCommonStockIssued" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_ExciseTaxesOnShareRepurchasesIncurredButNotPaid" name="ExciseTaxesOnShareRepurchasesIncurredButNotPaid" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_AmortizingPrincipalPaymentRepayment" name="AmortizingPrincipalPaymentRepayment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_PaymentsOnDeferredPurchaseAgreements" name="PaymentsOnDeferredPurchaseAgreements" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_InterestRateCollarMember" name="InterestRateCollarMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_OneCustomerMember" name="OneCustomerMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_SuccessorFirstLienCreditFacilityMember" name="SuccessorFirstLienCreditFacilityMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_CustomerMember" name="CustomerMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_ExchangedForCommonStockInTheCompany" name="ExchangedForCommonStockInTheCompany" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_FastballHoldcoLPMember" name="FastballHoldcoLPMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_TermLoanDueJanuaryThirtyOneTwoThousandTwentySevenMember" name="TermLoanDueJanuaryThirtyOneTwoThousandTwentySevenMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_LeaseLiabilityPaymentsDueYearThree" name="LeaseLiabilityPaymentsDueYearThree" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_NumberOfCustomers" name="NumberOfCustomers" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_TwoThousandTwentyOneEmployeeStockPurchasePlanMember" name="TwoThousandTwentyOneEmployeeStockPurchasePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_SecuritiesHeldByNonAfffiliatesThreshhold" name="SecuritiesHeldByNonAfffiliatesThreshhold" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_ImpactOfDividedToStockOptionAwardsAndESPPPurchases" name="ImpactOfDividedToStockOptionAwardsAndESPPPurchases" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="fa_OperatingCashFlowsFromFinanceLeases" name="OperatingCashFlowsFromFinanceLeases" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_AdditionalPaidInCapitalWithheldForTaxObligationsAndNetSettlementOfStockOptionExercise" name="AdditionalPaidInCapitalWithheldForTaxObligationsAndNetSettlementOfStockOptionExercise" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_EffectiveIncomeTaxRateReconciliationWithholdingTax" name="EffectiveIncomeTaxRateReconciliationWithholdingTax" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_TotalLeaseAssets" name="TotalLeaseAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_NumberOfSharesExchanged" name="NumberOfSharesExchanged" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_SuccessorFirstLienMember" name="SuccessorFirstLienMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_NonConvertibleDebtSecurities" name="NonConvertibleDebtSecurities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_FormINineComplianceMember" name="FormINineComplianceMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_GainLossDueToChangeInFairValueOfInterestRateSwaps" name="GainLossDueToChangeInFairValueOfInterestRateSwaps" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_CostOfServices" name="CostOfServices" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_TwentyTwentyOneAcquisitionsMember" name="TwentyTwentyOneAcquisitionsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_RestructuringExpenses" name="RestructuringExpenses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_Rule10B51ArrModifiedFlag" name="Rule10B51ArrModifiedFlag" type="xbrli:booleanItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_SterlingCommonStockMember" name="SterlingCommonStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_WriteDownOfAbandonedPropertyAndEquipment" name="WriteDownOfAbandonedPropertyAndEquipment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_SoftwareMember" name="SoftwareMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_IndemnityLiability" name="IndemnityLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_OtherTransactionAdjustments" name="OtherTransactionAdjustments" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_EmployeeStockPurchasePlanExpenses" name="EmployeeStockPurchasePlanExpenses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_NonCashPropertyAndEquipmentAdditions" name="NonCashPropertyAndEquipmentAdditions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_AmendedRevolverMember" name="AmendedRevolverMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_BankingFees" name="BankingFees" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_CapitalLeaseTerm" name="CapitalLeaseTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_NetSettlementOfRestrictedStockUnitsAndOptionAwards" name="NetSettlementOfRestrictedStockUnitsAndOptionAwards" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_LeaseLiability" name="LeaseLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_PredecessorFirstLienFacilityMember" name="PredecessorFirstLienFacilityMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_March2021UKAcquisitionMember" name="March2021UKAcquisitionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_CashDividendsPaid" name="CashDividendsPaid" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_CommonStockSharesAuthorizedPreStockSplit" name="CommonStockSharesAuthorizedPreStockSplit" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="fa_EstimatedFairValueOfTheUnderlyingUnit" name="EstimatedFairValueOfTheUnderlyingUnit" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_OneTimeTransactionCharges" name="OneTimeTransactionCharges" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_OptionToPurchaseAdditionalSharesOfCommonStock" name="OptionToPurchaseAdditionalSharesOfCommonStock" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_UnderwritingDiscountsAndCommissions" name="UnderwritingDiscountsAndCommissions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_AdditionalAssociatedCost" name="AdditionalAssociatedCost" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_RevolvingCreditFacilityQuarterlyPaymentsPercentage" name="RevolvingCreditFacilityQuarterlyPaymentsPercentage" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_LesseeLeaseLiabilityUndiscountedExcessAmount" name="LesseeLeaseLiabilityUndiscountedExcessAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_TotalCashConsideration" name="TotalCashConsideration" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_InterestRateSwap3Member" name="InterestRateSwap3Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_SuccessorPlanMember" name="SuccessorPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_AdjustedIncomeLossBeforeInterestTaxesDepreciationAndAmortization" name="AdjustedIncomeLossBeforeInterestTaxesDepreciationAndAmortization" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_InterestRateSwap1Member" name="InterestRateSwap1Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_LeaseLiabilityPaymentsRemainderOfFiscalYear" name="LeaseLiabilityPaymentsRemainderOfFiscalYear" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_PrepaidExpensesAndOtherCurrentAssetsTextBlock" name="PrepaidExpensesAndOtherCurrentAssetsTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_RecentAccountingPronouncementsPolicyTextBlock" name="RecentAccountingPronouncementsPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExchangedForOptionsInPeriodWeightedAverageExercisePrice" name="ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExchangedForOptionsInPeriodWeightedAverageExercisePrice" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_TwoThousandTwentyThreeAcquisitionsMember" name="TwoThousandTwentyThreeAcquisitionsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_TransactionExpensesChangeInControl" name="TransactionExpensesChangeInControl" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_PredecessorFirstLienMember" name="PredecessorFirstLienMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_SuccessorSecondLienMember" name="SuccessorSecondLienMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_CashConsideration" name="CashConsideration" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_DescriptionOfBorrowingCapacityNotSubjectToNetLeverageRatioCovenant" name="DescriptionOfBorrowingCapacityNotSubjectToNetLeverageRatioCovenant" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_TwothousandTwentyEquityPlanMember" name="TwothousandTwentyEquityPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_InternationalMember" name="InternationalMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_CostOfOtherSegmentItems" name="CostOfOtherSegmentItems" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_FirstLienCreditAgreementMember" name="FirstLienCreditAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_TotalLeaseLiabilities" name="TotalLeaseLiabilities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_UnrecognizedTaxBenefitsAcquiredTaxPositionsRelatedToPriorYears" name="UnrecognizedTaxBenefitsAcquiredTaxPositionsRelatedToPriorYears" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_LesseeOperatingAndFinanceLeaseTermOfContract" name="LesseeOperatingAndFinanceLeaseTermOfContract" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="fa_ShareBasedCompensationArrangementsByShareBasedPaymentAwardIssuedInExchangedForOptionsInPeriodWeightedAverageExercisePrice" name="ShareBasedCompensationArrangementsByShareBasedPaymentAwardIssuedInExchangedForOptionsInPeriodWeightedAverageExercisePrice" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_AnnualGrossRevenueThreshhold" name="AnnualGrossRevenueThreshhold" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_WeightedAverageAmortizationPeriod" name="WeightedAverageAmortizationPeriod" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_DeferredTaxAssetsDisallowedInterest" name="DeferredTaxAssetsDisallowedInterest" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_FirstPortionOfCommonStockMember" name="FirstPortionOfCommonStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_IntersegmentRevenuesMember" name="IntersegmentRevenuesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_NovemberFollowOnMember" name="NovemberFollowOnMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_PredecessorPlanMember" name="PredecessorPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_ExciseTaxesOnShareRepurchases" name="ExciseTaxesOnShareRepurchases" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_TwoThousandTwentyOneEquityPlanMember" name="TwoThousandTwentyOneEquityPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_NonConvertibleDebtSecuritiesThreshhold" name="NonConvertibleDebtSecuritiesThreshhold" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_LessAdjustedCostOfServices" name="LessAdjustedCostOfServices" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_NumberOfCountryConcentrationOfRevenues" name="NumberOfCountryConcentrationOfRevenues" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_InterestRateSwap2Member" name="InterestRateSwap2Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_MinorityInterestIncreaseFromContributionsByNoncontrollingInterestHolders" name="MinorityInterestIncreaseFromContributionsByNoncontrollingInterestHolders" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_SilverLakeTransactionMember" name="SilverLakeTransactionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_NOLMember" name="NOLMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_PercentageOfThresholdAmountOfNetAssets" name="PercentageOfThresholdAmountOfNetAssets" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_CashDividendsForfeited" name="CashDividendsForfeited" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExchangeForOptionInPeriod" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExchangeForOptionInPeriod" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_CostOfServicesExcludingDepreciationAndAmortization" name="CostOfServicesExcludingDepreciationAndAmortization" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_FirstAdvantageAmericasMember" name="FirstAdvantageAmericasMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_PaymentsToAcquireBusinessGross" name="PaymentsToAcquireBusinessGross" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_SectionTwoSixSevenAdjustment" name="SectionTwoSixSevenAdjustment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_IntialPublicOfferingPolicyPolicyTextBlock" name="IntialPublicOfferingPolicyPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_PercentageOfCapitalStockOfTheBorrower" name="PercentageOfCapitalStockOfTheBorrower" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_DeferredTaxLiabilitiesOperatingLeaseAsset" name="DeferredTaxLiabilitiesOperatingLeaseAsset" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_O2023M8DividendsMember" name="O2023M8DividendsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_SymphonyTalentLlcMember" name="SymphonyTalentLlcMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_FinanceLeaseLiabilityCurrentAndNoncurrent" name="FinanceLeaseLiabilityCurrentAndNoncurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_SuccessorsMember" name="SuccessorsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_Debtinstrumenteffectivedate" name="Debtinstrumenteffectivedate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_EmployeeStockPurchasePlanPercent" name="EmployeeStockPurchasePlanPercent" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_SuccessorPeriodMember" name="SuccessorPeriodMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_SecondPortionOfCommonStockMember" name="SecondPortionOfCommonStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_InterestRateSwap4Member" name="InterestRateSwap4Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_LeaseLiabilityPaymentsDueYearFive" name="LeaseLiabilityPaymentsDueYearFive" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_TotalRevenuesMember" name="TotalRevenuesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedTradeName" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedTradeName" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_PercentageOfPrepaymentPremiumOfTermLoans" name="PercentageOfPrepaymentPremiumOfTermLoans" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCustomerLists" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCustomerLists" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_EstimatedRepaymentOfSterlingsOutstandingDebt" name="EstimatedRepaymentOfSterlingsOutstandingDebt" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_SymphonyTechnologyGroupMember" name="SymphonyTechnologyGroupMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_LeaseLiabilityPaymentsDueYearTwo" name="LeaseLiabilityPaymentsDueYearTwo" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_TermDebtFacilityQuarterlyPaymentsPercentage" name="TermDebtFacilityQuarterlyPaymentsPercentage" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_O2024Q4DividendsMember" name="O2024Q4DividendsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_TotalLabilitySettlementAndRelatedToAdministrativeFees" name="TotalLabilitySettlementAndRelatedToAdministrativeFees" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_SterlingMember" name="SterlingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_FairValueOfAssumedSterlingEquityAwardsToReceiveEquityAwardsAttributableToPreCombinationService" name="FairValueOfAssumedSterlingEquityAwardsToReceiveEquityAwardsAttributableToPreCombinationService" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_CostOfServicesMember" name="CostOfServicesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_ScheduleOfCondensedIncomeStatementAndComprehensiveLossTableTextBlock" name="ScheduleOfCondensedIncomeStatementAndComprehensiveLossTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_PercentageOfThresholdDescribedUnderRuleNotApplied" name="PercentageOfThresholdDescribedUnderRuleNotApplied" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_EquipmentFurnitureAndFixturesMember" name="EquipmentFurnitureAndFixturesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_SummaryOfSignificantAccountingPoliciesTable" name="SummaryOfSignificantAccountingPoliciesTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_OfferingExpenses" name="OfferingExpenses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_StockConsideration" name="StockConsideration" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_DividendsDeclaredButNotPaid" name="DividendsDeclaredButNotPaid" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_IssuanceOfCommonStockUponTheAcquisitionOfSterlingCheckCorp" name="IssuanceOfCommonStockUponTheAcquisitionOfSterlingCheckCorp" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_NonCashImpairmentCharges" name="NonCashImpairmentCharges" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_OperatingLossCarryforwardsExpirationYear" name="OperatingLossCarryforwardsExpirationYear" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_ShareRepurchaseCostRecordedToAccumulatedDefecit" name="ShareRepurchaseCostRecordedToAccumulatedDefecit" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_SummaryOfWeightedAverageLeaseTermAndDiscountRateOperatingLeaseAndFinancingLeaseTableTextBlock" name="SummaryOfWeightedAverageLeaseTermAndDiscountRateOperatingLeaseAndFinancingLeaseTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_CorporateScreeningServicesLlcMember" name="CorporateScreeningServicesLlcMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_ReconciliationOfAdjustedEbitdaFromReportableSegmentsToConsolidatedNetIncomeLossTableTextBlock" name="ReconciliationOfAdjustedEbitdaFromReportableSegmentsToConsolidatedNetIncomeLossTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_LeaseLiabilityPaymentsDueNextTwelveMonths" name="LeaseLiabilityPaymentsDueNextTwelveMonths" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_ClassBAwardsMember" name="ClassBAwardsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_InfiniteIdMember" name="InfiniteIdMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_PredecessorPeriodMember" name="PredecessorPeriodMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_PresentValueOfMinimumLeasePayments" name="PresentValueOfMinimumLeasePayments" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_SecurityHeldToNonAffiliates" name="SecurityHeldToNonAffiliates" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_TermLoanDueJanuaryThirtyOneTwoThousandTwentyEightMember" name="TermLoanDueJanuaryThirtyOneTwoThousandTwentyEightMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_GrantsIssuedInExchangeForOptionsInTheCompanysParent" name="GrantsIssuedInExchangeForOptionsInTheCompanysParent" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_MergerAgreementMember" name="MergerAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_CustomerRelatedIntangibleAssetsCurrent" name="CustomerRelatedIntangibleAssetsCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_FinancingCashFlowsFromFinanceLeases" name="FinancingCashFlowsFromFinanceLeases" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_WeightedAverageGrantDateFairValueExchanged" name="WeightedAverageGrantDateFairValueExchanged" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_OutstandingChecksInExcessOfFundsOnDeposits" name="OutstandingChecksInExcessOfFundsOnDeposits" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_StockRepurchasePricePerShare" name="StockRepurchasePricePerShare" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_ScheduleOfShareRepurchaseActivityTableTextBlock" name="ScheduleOfShareRepurchaseActivityTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_LeaseLiabilityPaymentsDueYearFour" name="LeaseLiabilityPaymentsDueYearFour" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_TotalInsuranceRecoverableAsset" name="TotalInsuranceRecoverableAsset" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_SummaryOfSignificantAccountingPoliciesLineItems" name="SummaryOfSignificantAccountingPoliciesLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_ScheduleOfShareBasedCompensationProfitsInterestUnitActivityTableTextBlock" name="ScheduleOfShareBasedCompensationProfitsInterestUnitActivityTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_FixedLeaseCost" name="FixedLeaseCost" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_DebtForgivenessAgreementMember" name="DebtForgivenessAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_SuccessorSecondLienCreditFacilityMember" name="SuccessorSecondLienCreditFacilityMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_StockRepurchaseCostTotal" name="StockRepurchaseCostTotal" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_AcceleratedAmortizationOfDeferredFinancingCosts" name="AcceleratedAmortizationOfDeferredFinancingCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_DeferredTaxLiabilitiesCustomerLists" name="DeferredTaxLiabilitiesCustomerLists" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_FirstAdvantageCommonStockMember" name="FirstAdvantageCommonStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_OperatingLeaseMember" name="OperatingLeaseMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_ExciseTaxOnShareRepurchases" name="ExciseTaxOnShareRepurchases" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_FairValueOfAssumedSterlingEquityAwardsToReceiveCashAttributableToPreCombinationService" name="FairValueOfAssumedSterlingEquityAwardsToReceiveCashAttributableToPreCombinationService" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_CapitalizedSoftwareAcquiredByBusinessCombinationMember" name="CapitalizedSoftwareAcquiredByBusinessCombinationMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_PercentageOfVotingStockOfTheGuarantors" name="PercentageOfVotingStockOfTheGuarantors" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_FinanceLeaseCosts" name="FinanceLeaseCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_O2023Q4DividendsMember" name="O2023Q4DividendsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_SterlingCheckCorpMember" name="SterlingCheckCorpMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_SuccessorRevolverMember" name="SuccessorRevolverMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_ProductAndTechnologyExpenseMember" name="ProductAndTechnologyExpenseMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_Accumulatedunremittedforeignearnings" name="Accumulatedunremittedforeignearnings" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_OperationsAndComprehensiveIncomeLossMember" name="OperationsAndComprehensiveIncomeLossMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_EffectiveIncomeTaxRateReconciliationTransactionCosts" name="EffectiveIncomeTaxRateReconciliationTransactionCosts" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_ExchangedForRestrictedStockInTheCompany" name="ExchangedForRestrictedStockInTheCompany" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_AcceleratedVestingAfterAcquisitionMember" name="AcceleratedVestingAfterAcquisitionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_LiborMember" name="LiborMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_TwoThousandTwentyFourFirstLienCreditAgreementMember" name="TwoThousandTwentyFourFirstLienCreditAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_ConcentrationRiskNumberOfCustomers" name="ConcentrationRiskNumberOfCustomers" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_NonRule10B51ArrModifiedFlag" name="NonRule10B51ArrModifiedFlag" type="xbrli:booleanItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_ShareRepurchaseProgramMember" name="ShareRepurchaseProgramMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_FirstAdvantageInternationalMember" name="FirstAdvantageInternationalMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_DebtInstrumentInterestRateReducedDuringPeriod" name="DebtInstrumentInterestRateReducedDuringPeriod" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_FinanceLeaseMember" name="FinanceLeaseMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_InternationalExceptUnitedStatesCanadaAndLatinAmericaMember" name="InternationalExceptUnitedStatesCanadaAndLatinAmericaMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_LesseeOperatingAndFinancingLeaseRenewalTerm" name="LesseeOperatingAndFinancingLeaseRenewalTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="fa_LesseeOperatingAndFinanceLeaseTermOfContractInMajority" name="LesseeOperatingAndFinanceLeaseTermOfContractInMajority" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="fa_AmendedFirstLienCreditFacilityMember" name="AmendedFirstLienCreditFacilityMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_DeferredTaxLiabilitiesPrepaidAssets" name="DeferredTaxLiabilitiesPrepaidAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_FinanceAmortizationOfLeasedAssets" name="FinanceAmortizationOfLeasedAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_FirstAdvantageCorporationMember" name="FirstAdvantageCorporationMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_SharesRepurchasedAbstract" name="SharesRepurchasedAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_OutstandingBorrowingUnderRevolver" name="OutstandingBorrowingUnderRevolver" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_ScheduleOfPrepaidExpensesAndOtherCurrentAssetsTableTextBlock" name="ScheduleOfPrepaidExpensesAndOtherCurrentAssetsTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_EmployeeStockPurchasePlanMember" name="EmployeeStockPurchasePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_SterlingAcquisitionAwardsMember" name="SterlingAcquisitionAwardsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_TwoThousandTwentyFourAcquisitionsMember" name="TwoThousandTwentyFourAcquisitionsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_InterestRateCollarsMember" name="InterestRateCollarsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_NoCustomersMember" name="NoCustomersMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_DeferredTaxes" name="DeferredTaxes" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_OtherSegmentItemsMember" name="OtherSegmentItemsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_LeaseLiabilityPaymentsDue" name="LeaseLiabilityPaymentsDue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_LeaseLiabilityPaymentsDueAfterYearFive" name="LeaseLiabilityPaymentsDueAfterYearFive" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="fa_AmericaMember" name="AmericaMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fa_LesseeOperatingAndFinanceLeasesTextBlock" name="LesseeOperatingAndFinanceLeasesTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="fa_NetSettlementOfShareBasedCompensationPlanAwards" name="NetSettlementOfShareBasedCompensationPlanAwards" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="fa_DescriptionOfSecurityInterestInTangibleAndIntangibleAssetsOfBorrowerAndGuarantors" name="DescriptionOfSecurityInterestInTangibleAndIntangibleAssetsOfBorrowerAndGuarantors" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
</xsd:schema>
