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Commitments and Contingencies - Unconditional Purchase Obligations (Details) - USD ($)
$ in Thousands
12 Months Ended
Aug. 31, 2022
Aug. 31, 2021
Aug. 31, 2020
Unrecorded Unconditional Purchase Obligation, Fiscal Year Maturity [Abstract]      
Total payments under unconditional purchase obligation arrangements $ 75,200 $ 81,000 $ 77,600
Minimum      
Unrecorded Unconditional Purchase Obligation, Fiscal Year Maturity [Abstract]      
Long-term unconditional purchase obligations, Total 522,941    
2023 82,679    
2024 69,416    
2025 67,653    
2026 61,212    
2027 47,700    
Thereafter $ 194,281