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Equity-Based Compensation - Weighted-Average Valuation Assumptions (Details)
12 Months Ended
Jan. 30, 2022
Jan. 31, 2021
Feb. 02, 2020
Partnership Interests      
Weighted-average assumptions      
Risk-free interest rate 0.78% 0.63% 2.13%
Dividend yield 0.00% 0.00% 0.00%
Expected volatility factor 50.00% 50.00% 50.00%
Discount for lack of marketability 20.00% 26.00% 30.00%
Expected life in years 5 years 5 years 4 years 6 months
Stock appreciation rights      
Weighted-average assumptions      
Risk-free interest rate 0.78%   2.13%
Dividend yield 0.00%   0.00%
Expected volatility factor 50.00%   50.00%
Discount for lack of marketability 20.00%   30.00%
Expected life in years 5 years   4 years 6 months