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  <xs:element id="biii_StockIssuedDuringPeriodUnitsNewIssues" name="StockIssuedDuringPeriodUnitsNewIssues" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_NumberOfWarrantsPerUnit" name="NumberOfWarrantsPerUnit" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xs:element id="biii_ThresholdNumberOfDaysToExerciseWarrantsFromCompletionOfInitialBusinessCombination" name="ThresholdNumberOfDaysToExerciseWarrantsFromCompletionOfInitialBusinessCombination" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_CommonClassaSubjectToPossibleRedemptionMember" name="CommonClassaSubjectToPossibleRedemptionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
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  <xs:element id="biii_RedemptionOfSharesThresholdPercentageOfRedemption" name="RedemptionOfSharesThresholdPercentageOfRedemption" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
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  <xs:element id="biii_WorkingCapitalLoansMember" name="WorkingCapitalLoansMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xs:element id="biii_MaximumPeriodToRedeemPublicSharesIfInitialBusinessCombinationNotCompleted" name="MaximumPeriodToRedeemPublicSharesIfInitialBusinessCombinationNotCompleted" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_ThirdPartyClaimsLiabilityPerShare" name="ThirdPartyClaimsLiabilityPerShare" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_NumberOfSharesPerUnit" name="NumberOfSharesPerUnit" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xs:element id="biii_ClassOfWarrantsOrRightsNumberOfFractionalWarrantsIssuedUponSeparationOfUnits" name="ClassOfWarrantsOrRightsNumberOfFractionalWarrantsIssuedUponSeparationOfUnits" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xs:element id="biii_ShareIssuanceCosts" name="ShareIssuanceCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
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  <xs:element id="biii_NumberOfSharesSubjectToForfeiture" name="NumberOfSharesSubjectToForfeiture" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xs:element id="biii_ClassOfWarrantsOrRightsWarrantsExercisableTermPostBusinessCombination" name="ClassOfWarrantsOrRightsWarrantsExercisableTermPostBusinessCombination" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_ClassOfWarrantOrRightExercisableForCashOrCashlessBasis" name="ClassOfWarrantOrRightExercisableForCashOrCashlessBasis" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xs:element id="biii_ThresholdBusinessDaysForMakingRegistrationStatementEffective" name="ThresholdBusinessDaysForMakingRegistrationStatementEffective" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_ClassOfWarrantsOrRightsRedemptionPricePerWarrant" name="ClassOfWarrantsOrRightsRedemptionPricePerWarrant" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_ClassOfWarrantsOrRightsRedemptionsThresholdTradingDays" name="ClassOfWarrantsOrRightsRedemptionsThresholdTradingDays" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_ClassOfWarrantOrRightFairValueVolumeWeightedAveragePricePerShareTradingDaysPriorToWrittenNoticeForExercise" name="ClassOfWarrantOrRightFairValueVolumeWeightedAveragePricePerShareTradingDaysPriorToWrittenNoticeForExercise" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
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  <xs:element id="biii_FounderShareMember" name="FounderShareMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
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  <xs:element id="biii_PercentageOfIssuedAndOutstandingSharesAfterInitialPublicOfferingHeldByStockholders" name="PercentageOfIssuedAndOutstandingSharesAfterInitialPublicOfferingHeldByStockholders" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_NumberOfSharesTransferredToAffiliates" name="NumberOfSharesTransferredToAffiliates" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_ThresholdPeriodToTransferSharesAfterCompletionOfInitialBusinessCombination" name="ThresholdPeriodToTransferSharesAfterCompletionOfInitialBusinessCombination" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_ThresholdTradingDaysForStockPriceTarget" name="ThresholdTradingDaysForStockPriceTarget" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_SponsorMember" name="SponsorMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
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  <xs:element id="biii_ThresholdPeriodAfterInitialBusinessCombinationBeforeStockPriceConditionToTransferShares" name="ThresholdPeriodAfterInitialBusinessCombinationBeforeStockPriceConditionToTransferShares" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_RelatedPartyUnsecuredPromissoryNoteMember" name="RelatedPartyUnsecuredPromissoryNoteMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xs:element id="biii_MeasurementInputExpectedTermOfDeSpacMember" name="MeasurementInputExpectedTermOfDeSpacMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xs:element id="biii_MeasurementInputProbabilityOfDeSpacAndMarketAdjustmentMember" name="MeasurementInputProbabilityOfDeSpacAndMarketAdjustmentMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
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  <xs:element id="biii_OverAllotmentPeriod" name="OverAllotmentPeriod" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_NumberOfAdditionalUnitsPurchased" name="NumberOfAdditionalUnitsPurchased" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xs:element id="biii_CashUnderwritingDiscountNotCharged" name="CashUnderwritingDiscountNotCharged" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xs:element id="biii_DeferredUnderwritingFee" name="DeferredUnderwritingFee" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xs:element id="biii_SponsorOrAffiliateOfSponsorMember" name="SponsorOrAffiliateOfSponsorMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
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  <xs:element id="biii_WarrantsAndRightsOutstandingFairValuePerShare" name="WarrantsAndRightsOutstandingFairValuePerShare" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xs:element id="biii_FoundersShareMember" name="FoundersShareMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
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  <xs:element id="biii_GeneralAndAdministrativeExpensePaidThroughRelatedPartyPromissoryNoteIssuance" name="GeneralAndAdministrativeExpensePaidThroughRelatedPartyPromissoryNoteIssuance" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
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  <xs:element id="biii_MaximumPeriodToCompleteInitialBusinessCombinationAfterInitialPublicOffering" name="MaximumPeriodToCompleteInitialBusinessCombinationAfterInitialPublicOffering" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_LiquidityAndCapitalResourcesPolicyTextBlock" name="LiquidityAndCapitalResourcesPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_StockOfferingCosts" name="StockOfferingCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xs:element id="biii_OtherStockOfferingCosts" name="OtherStockOfferingCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xs:element id="biii_ThresholdOwnershipPercentageInTargetCompany" name="ThresholdOwnershipPercentageInTargetCompany" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_SignificantAccountingPolicyLineItems" name="SignificantAccountingPolicyLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xs:element id="biii_NetWorkingCapitalAmount" name="NetWorkingCapitalAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xs:element id="biii_ProceedsAllocatedToPublicWarrants" name="ProceedsAllocatedToPublicWarrants" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xs:element id="biii_ThresholdFairMarketValueOfTargetBusinessAsPercentOfNetBalanceInTrustAccount" name="ThresholdFairMarketValueOfTargetBusinessAsPercentOfNetBalanceInTrustAccount" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_PercentOfPublicSharesToBeRedeemedIfBusinessCombinationNotCompleted" name="PercentOfPublicSharesToBeRedeemedIfBusinessCombinationNotCompleted" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_ClassOfWarrantOrRightNumberOfWarrantsOrRightsOutstanding" name="ClassOfWarrantOrRightNumberOfWarrantsOrRightsOutstanding" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_ThresholdDaysFromBusinessCombinationForTransferOfWarrants" name="ThresholdDaysFromBusinessCombinationForTransferOfWarrants" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_FoundersSharesMember" name="FoundersSharesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xs:element id="biii_ThresholdAggregatePercentageOfAdditionalSharesIssuableUponConversionInConnectionWithBusinessCombination" name="ThresholdAggregatePercentageOfAdditionalSharesIssuableUponConversionInConnectionWithBusinessCombination" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xs:element id="biii_ThresholdNumberOfBusinessDaysForFilingOfRegistrationStatementPostInitialBusinessCombination" name="ThresholdNumberOfBusinessDaysForFilingOfRegistrationStatementPostInitialBusinessCombination" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_ClassOfWarrantsOrRightsRedemptionsStockPriceTrigger" name="ClassOfWarrantsOrRightsRedemptionsStockPriceTrigger" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_ClassOfWarrantsOrRightsPriorNoticeOfRedemptionToBeIssuedNumberOfDays" name="ClassOfWarrantsOrRightsPriorNoticeOfRedemptionToBeIssuedNumberOfDays" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_ClassOfWarrantsOrRightsRedemptionsThresholdConsecutiveTradingDays" name="ClassOfWarrantsOrRightsRedemptionsThresholdConsecutiveTradingDays" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_ThresholdPeriodForNotToTransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombination" name="ThresholdPeriodForNotToTransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombination" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_EquityClassifiedShareBasedPaymentGrantDateFairValue" name="EquityClassifiedShareBasedPaymentGrantDateFairValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xs:element id="biii_DiscountForLackOfMarketabilityPerShare" name="DiscountForLackOfMarketabilityPerShare" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_AdministrativeServicesAgreementMember" name="AdministrativeServicesAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xs:element id="biii_ConversionOfStockConversionRatio" name="ConversionOfStockConversionRatio" type="xbrli:pureItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xs:element id="biii_EquityClassifiedShareBasedPaymentGrantDateFairValuePerShare" name="EquityClassifiedShareBasedPaymentGrantDateFairValuePerShare" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_MaximumNumberOfDemandsExcludingShortFormRegistrationDemandsEntitledBySecurityHolders" name="MaximumNumberOfDemandsExcludingShortFormRegistrationDemandsEntitledBySecurityHolders" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_MaximumNumberOfAdditionalUnitsOfferedForPurchase" name="MaximumNumberOfAdditionalUnitsOfferedForPurchase" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xs:element id="biii_NumberOfUnitsConsideredSold" name="NumberOfUnitsConsideredSold" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xs:element id="biii_PaymentsForUnderwritingDiscount" name="PaymentsForUnderwritingDiscount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
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  <xs:element id="biii_DeferredUnderwritingFeeNotCharged" name="DeferredUnderwritingFeeNotCharged" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xs:element id="biii_ClassOfWarrantOrRightLockUpPeriodAfterRegistrationStatementBecomesEffective" name="ClassOfWarrantOrRightLockUpPeriodAfterRegistrationStatementBecomesEffective" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_PiggyBackRegistrationRightsTerm" name="PiggyBackRegistrationRightsTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_SingleReportableSegmentMember" name="SingleReportableSegmentMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xs:element id="biii_SharesTransferredToAffiliatesNominalPricePerShare" name="SharesTransferredToAffiliatesNominalPricePerShare" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_SaleOfSharesStockPriceTrigger" name="SaleOfSharesStockPriceTrigger" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_ThresholdConsecutiveTradingDaysForStockPriceTarget" name="ThresholdConsecutiveTradingDaysForStockPriceTarget" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xs:element id="biii_CommonStockNumberOfVotesPerShare" name="CommonStockNumberOfVotesPerShare" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xs:element id="biii_PaymentsForCashDepositedInTrustAccount" name="PaymentsForCashDepositedInTrustAccount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xs:element id="biii_OfferingCostsIncludedInAccruedOfferingCosts" name="OfferingCostsIncludedInAccruedOfferingCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
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  <xs:element id="biii_DeferredOfferingCostsIncludedInAccruedOfferingCosts" name="DeferredOfferingCostsIncludedInAccruedOfferingCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xs:element id="biii_DeferredOfferingPaidBySponsorInExchangeForIssuanceOfOrdinaryShares" name="DeferredOfferingPaidBySponsorInExchangeForIssuanceOfOrdinaryShares" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
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  <xs:element id="biii_CommonClassaNotSubjectToPossibleRedemptionMember" name="CommonClassaNotSubjectToPossibleRedemptionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
</xs:schema>
