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LEASES - Additional Information (Details) $ in Thousands | 12 Months Ended
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Jul. 27, 2024 USD ($) real_estate_partnership contract property | Jul. 29, 2023 USD ($)
Lessee, Lease, Description [Line Items] |  |
Number of retail stores leased (in contracts) | contract | 30 |
Lease renewal terms | 5 years |
Finance lease, right-of-use asset | $ 9,964 | $ 10,912
Finance Lease, Right-of-Use Asset, Statement of Financial Position [Extensible List] | Property, equipment and fixtures, net | Property, equipment and fixtures, net
Future lease payment obligations that have not yet commenced but have been executed | $ 21,359 |
Present value of lease liabilities | $ 277,373 |
Number of real estate partnerships with company ownership interests | real_estate_partnership | 4 |
Number of partnerships to which rent was paid for leased stores | real_estate_partnership | 3 |
Rent paid to related partnership | $ 1,827 | $ 1,568
Rent paid to Wakefern under sublease agreement |  | 413
Minimum |  |
Lessee, Lease, Description [Line Items] |  |
Initial lease terms | 20 years |
Maximum |  |
Lessee, Lease, Description [Line Items] |  |
Initial lease terms | 30 years |
Variable Interest Entity, Not Primary Beneficiary |  |
Lessee, Lease, Description [Line Items] |  |
Number of variable interest entity real estate partnerships | real_estate_partnership | 1 |
Number of properties owned by VIE partnership | property | 1 |
Percentage of profits and losses entitled to Company | 33.00% |
Officer |  |
Lessee, Lease, Description [Line Items] |  |
Officer ownership percentage in leasing property realty firm | 30.00% |
Lease expense | $ 735 | $ 735
Affiliated Entity | Supermarket Leased From Realty Firm Which Company Officers Partially Own |  |
Lessee, Lease, Description [Line Items] |  |
Present value of lease liabilities | 1,144 |
Affiliated Entity | Stores Leased From Real Estate Partnerships Which Company Has Ownership Interest In |  |
Lessee, Lease, Description [Line Items] |  |
Present value of lease liabilities | $ 15,733 |

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- Definition Amount, after accumulated amortization, of right-of-use asset from finance lease. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 842 -SubTopic 20 -Name Accounting Standards Codification -Section 45 -Paragraph 1 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org//1943274/2147479041/842-20-45-1 + Details
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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 Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 842 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 3 -Publisher FASB -URI https://asc.fasb.org//1943274/2147478964/842-20-50-3 + Details
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- Definition Percentage of the Variable Interest Entity's (VIE) voting interest owned by (or beneficial interest in) the reporting entity (directly or indirectly). + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Topic 810 -SubTopic 10 -Section 50 -Paragraph 5A -Subparagraph (d) -Publisher FASB -URI https://asc.fasb.org//1943274/2147481203/810-10-50-5A + Details
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