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Debt - Narrative (Details)
 9 Months Ended
May 02, 2024
USD ($)
May 22, 2023
USD ($)
Feb. 25, 2024
USD ($)
Feb. 26, 2023
USD ($)
May 10, 2024
USD ($)
Dec. 31, 2023
person
May 28, 2023
USD ($)
Debt Instrument [Line Items]              
Embedded derivative, fair value   $ 64,900,000 $ 23,000,000       $ 64,900,000
Total principal amount of long-term debt     160,820,000       150,233,000
Payments on long-term debt     386,000 $ 3,199,000      
Credit guarantee agreement, support personnel threshold (more than) | person           20  
Equipment Sale and Leaseback Agreements              
Debt Instrument [Line Items]              
Sale leaseback transaction, net book value   $ 10,000,000          
Option to repurchase, term   7 years          
Proceeds from sales of property and equipment     7,700,000        
Sale and leaseback transaction, gain (loss)     2,300,000        
Price at end of term   $ 1.00          
Quarterly rental payment to be received   0.025          
Rental payment, purchase price less cumulative paydown payments made   1.50%          
Other assets              
Debt Instrument [Line Items]              
Debt issuance costs     1,700,000       1,400,000
Other Current Assets              
Debt Instrument [Line Items]              
Debt issuance costs     900,000        
Line of Credit | Revolving Credit Facility              
Debt Instrument [Line Items]              
Total principal amount of long-term debt     $ 19,900,000       $ 16,800,000
Revolver interest rate     8.15%       12.16%
Line of credit, available borrowing capacity     $ 5,700,000        
Term Loan Credit Agreement              
Debt Instrument [Line Items]              
Debt instrument, face amount   $ 142,300,000          
Unamortized debt discount     63,700,000       $ 65,400,000
Term Loan Credit Agreement | Subsequent Event              
Debt Instrument [Line Items]              
Payments on long-term debt $ 5,500,000            
Term Loan | Line of Credit              
Debt Instrument [Line Items]              
Total principal amount of long-term debt     $ 153,477,000       $ 142,503,000
Revolver interest rate     10.00%       10.00%
Revolving Credit Agreement | Revolving Credit Facility              
Debt Instrument [Line Items]              
Revolving line of credit   40,000,000          
Line of credit reduction   $ 4,000,000          
Coverage ratio   1.00          
Debt covenant, availability of line of credit   10.00%          
Debt covenant, availability of line of credit, amount   $ 4,000,000          
Revolving Credit Agreement | Revolving Credit Facility | Subsequent Event              
Debt Instrument [Line Items]              
Revolving line of credit         $ 40,000,000