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Equity-Based Compensation - Weighted-Average Valuation Assumptions (Details) - $ / shares
12 Months Ended
Jan. 28, 2024
Jan. 29, 2023
Partnership Interests    
Weighted-average assumptions    
Risk-free interest rate   0.78%
Dividend yield   0.00%
Expected volatility factor   50.00%
Discount for lack of marketability   20.00%
Expected life in years   5 years
Weighted-average fair value of award granted (in dollars per share)   $ 6.27
Stock appreciation rights    
Weighted-average assumptions    
Risk-free interest rate   0.78%
Dividend yield   0.00%
Expected volatility factor   50.00%
Discount for lack of marketability   20.00%
Expected life in years   5 years
Weighted-average fair value of award granted (in dollars per share)   $ 6.27
Share-Based Payment Arrangement, Option    
Weighted-average assumptions    
Risk-free interest rate 3.87% 1.85%
Dividend yield 2.00% 0.00%
Expected volatility factor 40.00% 40.00%
Expected life in years 6 years 6 years
Weighted-average fair value of award granted (in dollars per share) $ 8.06 $ 8.55