Number of warrants or rights issued during the period.

No definition available.

Name:	fiac_ClassOfWarrantOrRightIssued
Namespace Prefix:	fiac_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of trading days for common stock price to exceed threshold, 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_NumberOfTradingDays
Namespace Prefix:	fiac_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

The percentage of redemption of public shares if the entity does not complete initial business combination within 18 months from the closing of IPO.

+ References

No definition available.

+ Details

Name:	fiac_PercentageOfRedemptionOfPublicShares
Namespace Prefix:	fiac_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

The period of redemption of public shares from closing of initial public offering, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

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

- References

No definition available.

+ Details

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

- Definition

The cash inflow associated with the amount received from entity's raising of capital via private rather than public placement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 14
-Subparagraph (a)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482740/230-10-45-14

+ Details

Name:	us-gaap_ProceedsFromIssuanceOfPrivatePlacement
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Per share or per unit amount of equity securities issued.

+ References

No definition available.

+ Details

Name:	us-gaap_SharesIssuedPricePerShare
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=fiac_PrivatePlacementWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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

Private Placement (FY) (Details) - USD ($)		9 Months Ended	10 Months Ended	12 Months Ended
Private Placement (FY) (Details) - USD ($)	Nov. 01, 2021	Sep. 30, 2023	Dec. 31, 2021	Dec. 31, 2022
Private Placement Warrants [Abstract]
Gross proceeds from private placement			$ 11,200,000	$ 0
Number of trading days		10 days		10 days
Private Placement Warrants [Member]
Private Placement Warrants [Abstract]
Warrants issued (in shares)	11,200,000		11,200,000
Share price (in dollars per share)	$ 1
Gross proceeds from private placement	$ 11,200,000
Number of trading days		30 days		30 days
Percentage of redemption of public shares		100.00%		100.00%
Period of redemption of public shares from the closing of IPO		18 months		18 months
Private Placement [Member] \| Private Placement Warrants [Member]
Private Placement Warrants [Abstract]
Warrants issued (in shares)	11,200,000
Share price (in dollars per share)	$ 1
Gross proceeds from private placement	$ 11,200,000