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 reserve of uncertain tax.

+ References

No definition available.

+ Details

Name:	inte_ReserveOfUncertainTax
Namespace Prefix:	inte_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Securities (including those issuable pursuant to contingent stock agreements) that could potentially dilute basic earnings per share (EPS) or earnings per unit (EPU) in the future that were not included in the computation of diluted EPS or EPU because to do so would increase EPS or EPU amounts or decrease loss per share or unit amounts for the period presented.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 260
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482662/260-10-50-1

+ Details

Name:	us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
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

Name:	us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1
Namespace Prefix:	us-gaap_
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

Name:	us-gaap_DeferredOfferingCosts
Namespace Prefix:	us-gaap_
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

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateContinuingOperations
Namespace Prefix:	us-gaap_
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 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482685/740-10-50-12

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 231
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482663/740-10-55-231

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.1.Q1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479360/740-10-S99-1

Reference 4: 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

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
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

Name:	us-gaap_GainLossOnContractTermination
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
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/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 6: 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 7: 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 8: 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 9: 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

Name:	us-gaap_ServicingLiabilityAtFairValueAmount
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

- 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		9 Months Ended
	Dec. 12, 2023	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2024	Sep. 30, 2023	Dec. 31, 2023	Dec. 08, 2023
Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount				0	0
Effective tax rate differs from the statutory tax rate		21.00%	21.00%	21.00%	21.00%
Effective income tax rate reconciliation percent		(19.80%)	4.00%	(16.60%)	42.50%
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	$ (44,330)
Reserve for uncertain tax positions		$ 371,214		$ 371,214		$ 0
Forward Purchase agreement [Member]
Common stock issued to Sponsors ,shares				3,000,000
Servicing liability at fair value amount							$ 0