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Stock-based Compensation and Stockholders' Equity - Narrative (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Nov. 27, 2022
Nov. 27, 2022
Nov. 28, 2021
Jul. 14, 2010
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Granted options (in shares) 17,850 743,050    
Shares for future issuance (in shares) 3,400,000 3,400,000    
Repurchase plan authorized amount (up to) $ 3.8 $ 3.8   $ 10.0
Stock repurchased during period (in shares)   0 0  
RSUs        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Awarded (in shares) 3,825 259,090    
Weighted-average period (in years)   2 years 3 months 14 days    
Employee Stock Option        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Unrecognized compensation expense $ 5.7 $ 5.7    
Weighted-average period (in years)   2 years 3 months 3 days