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Stockholders' Equity - Black-Scholes Option Pricing Model (Details)
12 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Share-Based Payment Arrangement [Abstract]      
Expected dividend yield 0.30% 0.30% 0.50%
Risk-free interest rate 3.40% 0.10% 0.10%
Expected volatility 37.40% 29.60% 32.90%
Expected life 6 months 6 months 6 months