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Owned Inventory - Inventory Impairments and Abandonment Charges, by Reportable Segment (Details) - USD ($) | 3 Months Ended
--- | ---
Dec. 31, 2023 | Dec. 31, 2022
Real Estate Properties [Line Items] |  |
Total abandonments charges | $ 0 | $ 190,000
Total impairment and abandonment charges | 0 | 190,000
West | Operating Segments |  |
Real Estate Properties [Line Items] |  |
Total abandonments charges | 0 | 36,000
East | Operating Segments |  |
Real Estate Properties [Line Items] |  |
Total abandonments charges | $ 0 | $ 154,000

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- Definition Impairment Charges, Abandonments + References No definition available. + Details
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Namespace Prefix: | bzh_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- Definition Inventory impairments and abandonments + References No definition available. + Details
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Namespace Prefix: | bzh_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
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- 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 No definition available. + Details
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Details
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Namespace Prefix: |
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Period Type: |

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- Details
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Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
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Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |