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Shareholders' Equity (Details)
 12 Months Ended
Sep. 28, 2024
USD ($)
vote
$ / shares
shares
Sep. 30, 2023
USD ($)
$ / shares
shares
Sep. 24, 2022
USD ($)
Aug. 31, 2019
USD ($)
Class of Stock [Line Items]        
Preferred stock authorized (in shares) 1,000,000 1,000,000    
Preferred stock, par value (in usd per share) | $ / shares $ 0.01 $ 0.01    
Preferred stock, shares outstanding 0 0    
Repurchased of stock | $ $ 10,846,000 $ 30,736,000 $ 57,795,000  
2019 Repurchase Authorization        
Class of Stock [Line Items]        
Stock repurchase program, authorized amount | $       $ 100,000,000
Stock repurchase program remaining authorized amount | $ $ 82,000,000.0      
Equity Dilution Authorization        
Class of Stock [Line Items]        
Stock repurchase, remaining authorization (in shares) 38,000      
Common stock ($0.01 par value; 80 million shares authorized; 11,074,620 and 11,077,612 issued at September 28, 2024 and September 30, 2023, respectively)        
Class of Stock [Line Items]        
Common stock authorized (in shares) 80,000,000 80,000,000    
Common stock, par value (in usd per share) | $ / shares $ 0.01 $ 0.01    
Common stock, shares outstanding (in shares) 11,074,620 11,077,612    
Class A common stock ($0.01 par value; 100 million shares authorized; 54,446,194 and 54,472,902 issued at September 28, 2024 and September 30, 2023, respectively)        
Class of Stock [Line Items]        
Common stock authorized (in shares) 100,000,000 100,000,000    
Common stock, par value (in usd per share) | $ / shares $ 0.01 $ 0.01    
Common stock, shares outstanding (in shares) 54,446,194 54,472,902    
Class B stock ($0.01 par value; 3 million shares authorized; 1,602,374 and 1,602,374 issued at September 28, 2024 and September 30, 2023, respectively)        
Class of Stock [Line Items]        
Common stock authorized (in shares) 3,000,000 3,000,000    
Common stock, par value (in usd per share) | $ / shares $ 0.01 $ 0.01    
Common stock, shares outstanding (in shares) 1,602,374 1,602,374    
Percentage of vote cast for shares (percent) 49.00%      
Convertible shares conversion ratio 1      
Class B stock ($0.01 par value; 3 million shares authorized; 1,602,374 and 1,602,374 issued at September 28, 2024 and September 30, 2023, respectively) | Minimum        
Class of Stock [Line Items]        
Number of voting powers | vote 1      
Class B stock ($0.01 par value; 3 million shares authorized; 1,602,374 and 1,602,374 issued at September 28, 2024 and September 30, 2023, respectively) | Maximum        
Class of Stock [Line Items]        
Number of voting powers | vote 10      
Non voting common stock        
Class of Stock [Line Items]        
Repurchased of stock (in shares) 300,000      
Repurchased of stock | $ $ 10,700,000      
Voting Stock        
Class of Stock [Line Items]        
Repurchased of stock | $ 3,000      
Common Stock        
Class of Stock [Line Items]        
Repurchased of stock | $ $ 109,000