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Employee Benefits - Defined Contribution Plans - Narrative (Details) $ in Millions | 12 Months Ended
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Jan. 01, 2022 USD ($) defined_contribution_plan | Jan. 02, 2021 USD ($)
Defined Benefit Plan Disclosure [Line Items] |  |
Number of defined contribution plans | defined_contribution_plan | 2 |
Hourly Savings Plan |  |
Defined Benefit Plan Disclosure [Line Items] |  |
Defined contribution plan, cost recognized | $ 0.7 | $ 0.7
Salaried Savings Plan |  |
Defined Benefit Plan Disclosure [Line Items] |  |
Defined contribution plan, cost recognized | $ 2.0 | $ 1.8

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- Definition Defined Contribution Plan, Number of Plans + References No definition available. + Details
Name: | bxc_DefinedContributionPlanNumberofPlans
Namespace Prefix: | bxc_
Data Type: | xbrli:integerItemType
Balance Type: | na
Period Type: | duration

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

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- Definition Amount of cost for defined contribution plan. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 70 -Section 50 -Paragraph 1 -URI http://asc.fasb.org/extlink&oid=49170846&loc=d3e28014-114942 + Details
Name: | us-gaap_DefinedContributionPlanCostRecognized
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- Details
Name: | us-gaap_RetirementPlanNameAxis=bxc_HourlySavingsPlanMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
Name: | us-gaap_RetirementPlanNameAxis=bxc_SalariedSavingsPlanMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |