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Income Taxes - Deferred Tax Asset Valuation Allowance Activity (Details) - USD ($) $ in Thousands | 12 Months Ended
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Dec. 30, 2023 | Dec. 31, 2022
SEC Schedule, 12-09, Movement in Valuation Allowances and Reserves [Roll Forward] |  |
Balance as of beginning of the fiscal year | $ 4,076 | $ 4,269
Valuation allowance increases (decreases) related to: |  |
State net operating loss carryforwards | (620) | (193)
Balance as of end of the fiscal year | $ 3,456 | $ 4,076

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- Definition This element represent represents valuation allowance provided for taxes related to loss before income tax. + References No definition available. + Details
Name: | bxc_ValuationAllowanceOperatingLossCarryforwardsStateAndLocalJurisdiction
Namespace Prefix: | bxc_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

X
- Definition Amount of deferred tax assets for which it is more likely than not that a tax benefit will not be realized. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c) -Publisher FASB -URI https://asc.fasb.org//1943274/2147482685/740-10-50-2 + Details
Name: | us-gaap_DeferredTaxAssetsValuationAllowance
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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- Definition A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period. + References No definition available. + Details
Name: | us-gaap_MovementInValuationAllowancesAndReservesRollForward
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- References No definition available. + Details
Name: | us-gaap_ValuationAllowanceAbstract
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration