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Short-term and Long-term Debt - Additional Information (Details) - USD ($)
3 Months Ended
Dec. 31, 2024
Dec. 31, 2023
Debt Instrument [Line Items]    
Debt instruments issuance cost $ 1,495,000 $ 0
Debt extinguishment (444,000) $ 0
ABL facility    
Debt Instrument [Line Items]    
Outstanding borrowing 0  
Revolving credit facility 482,700,000  
Debt issuance costs $ 1,500,000  
Debt instrument, maturity date Dec. 11, 2029  
ABL facility | Maximum    
Debt Instrument [Line Items]    
Line of credit facility, commitment fee percentage 0.20%  
ABL facility | Minimum    
Debt Instrument [Line Items]    
Line of credit facility, commitment fee percentage 0.25%  
TLB 2030 | Sally Holdings, LLC    
Debt Instrument [Line Items]    
Aggregate principal amount $ 40,000,000  
Debt extinguishment $ (400,000)