Related Party Transactions, Related Party Loans (FY) (Details) - USD ($)	9 Months Ended	12 Months Ended
Sep. 30, 2023	Dec. 31, 2022	Dec. 31, 2021
Related Party Transactions [Abstract]
Working capital loans outstanding	$ 1,025,000	$ 0
Sponsor, Affiliate of Sponsor, or Certain Company Officers and Directors [Member] \| Working Capital Loans [Member]
Related Party Transactions [Abstract]
Maximum amount of convertible loans	$ 1,500,000	$ 1,500,000
Conversion price (in dollars per share)	$ 1	$ 1
Working capital loans outstanding		$ 0	$ 0

No definition available.

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- Definition

Maximum amount of borrowings available through Working Capital Loans that may be convertible into warrants of the post Business Combination entity at the lenders' discretion.

+ References

No definition available.

+ Details

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Namespace Prefix:	fiac_
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- Definition

The price per share of the conversion feature embedded in the debt instrument.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481139/470-20-50-1B

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 5
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481139/470-20-50-5

+ Details

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- Definition

Sum of the carrying values as of the balance sheet date of the portions of long-term notes payable due within one year or the operating cycle if longer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19,20)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

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- Details

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- Details

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