Income Taxes - Additional Information (Details) - USD ($) $ in Thousands	9 Months Ended	12 Months Ended
Jun. 30, 2022	Sep. 30, 2021
Income Tax Disclosure [Abstract]
U.S. Federal income tax rate	21.00%
Minimum percentage of tax positions	50.00%
Liability for unrecognized tax amount	$ 0	$ 0
Reserves for uncertain tax positions related to federal taxes	0	0
Reserves for uncertain tax positions related to state and local taxes	$ 0	$ 0

Minimum percentage of tax positions.

No definition available.

Name:	hzen_MinimumPercentageOfTaxPositions
Namespace Prefix:	hzen_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of deferred tax liability not recognized because of the exceptions to comprehensive recognition of deferred taxes related to a policyholders' surplus.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 740
-Section 50
-Paragraph 1
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=6487024&loc=d3e29054-158556

+ Details

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

- Definition

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

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 6.I.Fact.4)
-URI https://asc.fasb.org/extlink&oid=122134291&loc=d3e330036-122817

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 235
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(h)(2))
-URI https://asc.fasb.org/extlink&oid=120395691&loc=d3e23780-122690

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32687-109319

+ Details

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

- References

No definition available.

+ Details

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

- Definition

The amount of income tax expense or benefit for the period computed by applying the domestic federal statutory tax rates to pretax income from continuing operations.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32687-109319

+ Details

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

- Definition

Amount of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to state and local income tax expense (benefit).

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32687-109319

+ Details

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