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Equity-Based Compensation - Weighted-Average Valuation Assumptions (Details) - $ / shares
12 Months Ended
Jan. 29, 2023
Jan. 30, 2022
Jan. 31, 2021
Partnership Interests      
Weighted-average assumptions      
Risk-free interest rate   0.78% 0.63%
Dividend yield   0.00% 0.00%
Expected volatility factor   50.00% 50.00%
Discount for lack of marketability   20.00% 26.00%
Expected life in years   5 years 5 years
Weighted-average fair value of award granted (in dollars per share)   $ 6.27 $ 2.99
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 1.85%    
Dividend yield 0.00%    
Expected volatility factor 40.00%    
Expected life in years 6 years    
Weighted-average fair value of award granted (in dollars per share) $ 8.55