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Stockholders' Equity - Black-Scholes Option Pricing Model (Details)
12 Months Ended
Aug. 31, 2022
Aug. 31, 2021
Aug. 31, 2020
Share-Based Payment Arrangement [Abstract]      
Expected dividend yield 0.30% 0.50% 0.40%
Risk-free interest rate 0.10% 0.10% 1.90%
Expected volatility 29.60% 32.90% 30.70%
Expected life 6 months 6 months 6 months