Gain or loss on termination of forward purchase agreement.

No definition available.

Name:	inte_GainOrLossOnTerminationOfForwardPurchaseAgreement
Namespace Prefix:	inte_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of the increase (decrease) in fair value of the hedged item in a fair value hedge recognized in the income statement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 815
-SubTopic 25
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480238/815-25-50-1

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Specific incremental costs directly attributable to a proposed or actual offering of securities which are deferred at the end of the reporting period.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 340
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 5.A)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480341/340-10-S99-1

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Percentage of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-12

+ Details

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Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of domestic federal statutory tax rate applicable to pretax income (loss).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(h)(2))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480678/235-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
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-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-12

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 6.I.Fact.4)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479360/740-10-S99-1

+ Details

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Period Type:	duration

- Definition

Gain (loss) related to the termination of a contract between the parties. The termination may be due to many causes including early termination of a lease by a lessee, a breach of contract by one party, or a failure to perform.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 230
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482740/230-10-45-28

+ Details

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Balance Type:	credit
Period Type:	duration

- Definition

Fair value of a liability representing servicing arrangements under which the estimated future revenue from contractually specified servicing fees, late charges, and other ancillary revenues are not expected to adequately compensate the servicer.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 860
-SubTopic 50
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481229/860-50-50-3

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 860
-SubTopic 50
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481260/860-50-45-2

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 860
-SubTopic 50
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481260/860-50-45-1

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 860
-SubTopic 50
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481260/860-50-45-2

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Number of shares issued in lieu of cash for services contributed to the entity. Number of shares includes, but is not limited to, shares issued for services contributed by vendors and founders.

+ References

No definition available.

+ Details

Name:	us-gaap_StockIssuedDuringPeriodSharesIssuedForServices
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of unrecognized tax benefits.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 15A
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-15A

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 10B
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482525/740-10-45-10B

+ Details

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Balance Type:	credit
Period Type:	instant

- Definition

Amount accrued for interest on an underpayment of income taxes and penalties related to a tax position claimed or expected to be claimed in the tax return.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 15
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-15

+ Details

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Period Type:	instant

- Details

Name:	inte_AgreementAxis=inte_ForwardPurchaseAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Significant Accounting Policies - Additional Information (Detail) - USD ($)			3 Months Ended
	Dec. 12, 2023	Jun. 30, 2023	Mar. 31, 2024	Mar. 31, 2023	Dec. 31, 2023	Dec. 08, 2023
Unrecognised tax benefits			$ 0		$ 0
Accrued interest and penalties on unrecognised tax benefits			$ 0		$ 0
Effective tax rate differs from the statutory tax rate			21.00%	21.00%
Effective income tax rate reconciliation percent			20.40%	35.90%
Offering cost	$ 1,011,752					$ 1,011,752
Aggregate gain on termination of forward purchase agreement	2,708,717
Gain on termination of FPA	1,011,752
Unrealized gain on the change in fair value of FPA	$ 1,696,965		$ 0	$ (219,842)
Forward Purchase agreement [Member]
Common stock issued to Sponsors ,shares		3,000,000
Servicing liability at fair value amount						$ 0