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Income Taxes - Deferred Tax Asset Valuation Allowance Activity (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Jan. 01, 2022
SEC Schedule, 12-09, Movement in Valuation Allowances and Reserves [Roll Forward]
Balance as of beginning of the fiscal year	$ 4,269	$ 7,287
Valuation allowance provided for taxes related to:
State net operating loss carryforwards	(193)	(3,018)
Balance as of end of the fiscal year	$ 4,076	$ 4,269

X

- 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
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32537-109319

+ Details

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

X

- 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

X

- References

No definition available.

+ Details

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