No definition available.

Name:	fiac_ExtensionOfCombinationPeriodAbstract
Namespace Prefix:	fiac_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

The amount of lenders contribution as loan not redeemed in connection with the Extension Meeting, to be deposited into the Trust Account

+ References

No definition available.

+ Details

Name:	fiac_LendersContributionDepositedInTrustAccount
Namespace Prefix:	fiac_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

The per share amount of lenders contribution as loan not redeemed in connection with the Extension Meeting, to be deposited into the Trust Account.

+ References

No definition available.

+ Details

Name:	fiac_LendersContributionDepositedInTrustAccountAmountPerShare
Namespace Prefix:	fiac_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

The number of business days as disclosed in the Proxy Statement, relating to the extraordinary general meeting of shareholders (the "Extension Meeting"), the Sponsor agreed that if the Extension Amendment Proposal is approved, it or one or more of its affiliates, members or third-party designees (the "Lender") will contribute to the Company as a loan, of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	fiac_NumberOfBusinessDays
Namespace Prefix:	fiac_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

The number of times permitted to extend period of time to consummate a business combination.

+ References

No definition available.

+ Details

Name:	fiac_NumberOfExtensionsToExtendTimeToConsummateABusinessCombination
Namespace Prefix:	fiac_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of installments to be deposited into the Trust Account.

+ References

No definition available.

+ Details

Name:	fiac_NumberOfInstallmentsToBeDeposited
Namespace Prefix:	fiac_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

- Definition

The difference period between the original termination date and additional charter extension date, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	fiac_PeriodOfAdditionalCharterExtensionDate
Namespace Prefix:	fiac_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Advance notice period, to consummate an initial business combination prior to the applicable termination date, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	fiac_PeriodOfAdvanceNoticeToConsummateInitialBusinessCombination
Namespace Prefix:	fiac_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

The period of time for each extension to consummate a Business Combination after charter extension date, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	fiac_PeriodOfExtensionToConsummateBusinessCombination
Namespace Prefix:	fiac_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=us-gaap_IPOMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsequentEventTypeAxis=us-gaap_SubsequentEventMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Subsequent Events (FY) (Details)				9 Months Ended	12 Months Ended
Subsequent Events (FY) (Details)	Dec. 11, 2023 Extension	Apr. 25, 2023 USD ($) Extension $ / shares	Apr. 05, 2023 USD ($) Installment Extension $ / shares	Sep. 30, 2023	Dec. 31, 2022
Extension of Combination Period [Abstract]
Period of extension to consummate business combination				1 month	1 month
Period of advance notice to consummate initial business combination				5 days	5 days
Period of additional charter extension date				12 months
Number of business days				10 days
Lenders contribution deposited in trust account \| $		$ 162,500
Lenders contribution deposited in trust account (dollar per share) \| $ / shares		$ 0.0325
Minimum [Member]
Extension of Combination Period [Abstract]
Number of business days					5 days
Maximum [Member]
Extension of Combination Period [Abstract]
Number of extensions to extend time to consummate a business combination \| Extension		9
Period of additional charter extension date					12 months
IPO [Member]
Extension of Combination Period [Abstract]
Lenders contribution deposited in trust account \| $		$ 487,500
Lenders contribution deposited in trust account (dollar per share) \| $ / shares		$ 0.0975
Subsequent Event [Member]
Extension of Combination Period [Abstract]
Lenders contribution deposited in trust account \| $			$ 1,462,500
Lenders contribution deposited in trust account (dollar per share) \| $ / shares			$ 0.2925
Number of installments to be deposited \| Installment			9
Subsequent Event [Member] \| Maximum [Member]
Extension of Combination Period [Abstract]
Number of extensions to extend time to consummate a business combination \| Extension	7		9
Subsequent Event [Member] \| IPO [Member]
Extension of Combination Period [Abstract]
Lenders contribution deposited in trust account \| $			$ 487,500
Lenders contribution deposited in trust account (dollar per share) \| $ / shares			$ 0.0975