Fair Value Measurements - Additional Information (Details) - USD ($)	3 Months Ended	12 Months Ended
Jan. 31, 2024	Oct. 31, 2023
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Transfers or reclassifications into level 3	$ 0	$ 0
Transfers or reclassifications out of level 3	$ 0	0
Fair value of shares	$ 18
Preferred Share Warrants
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Warrants, contractual term	10 years
Fair Value Measurement Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Financial assets, fair value	$ 0	0
Financial liabilities, fair value	$ 0	$ 0

Fair value portion of probable future economic benefits obtained or controlled by an entity as a result of past transactions or events.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

+ Details

Name:	us-gaap_AssetsFairValueDisclosure
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: 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 2: 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 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-3

+ Details

Name:	us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of transfers of financial instrument classified as a liability into level 3 of the fair value hierarchy.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(3)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

+ Details

Name:	us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersIntoLevel3
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of transfers of financial instrument classified as a liability out of level 3 of the fair value hierarchy.

+ References

+ Details

Name:	us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersOutOfLevel3
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Fair value of financial obligations, including, but not limited to, debt instruments, derivative liabilities, federal funds purchased and sold under agreements to repurchase, securities loaned or sold under agreements to repurchase, financial instruments sold not yet purchased, guarantees, line of credit, loans and notes payable, servicing liability, and trading liabilities.

+ References

No definition available.

+ Details

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

- Definition

Price of a single share of a number of saleable stocks of a company.

+ References

No definition available.

+ Details

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

- Definition

Period between issuance and expiration of outstanding warrant and right embodying unconditional obligation requiring redemption by transferring asset at specified or determinable date or upon event certain to occur, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ 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)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

+ Details

Name:	us-gaap_WarrantsAndRightsOutstandingTerm
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Details

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

- Details

Name:	us-gaap_FairValueByMeasurementFrequencyAxis=us-gaap_FairValueMeasurementsRecurringMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: