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Commitments and Contingencies - Unconditional Purchase Obligations (Details) - USD ($)
$ in Thousands
12 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Unrecorded Unconditional Purchase Obligation, Fiscal Year Maturity [Abstract]      
Total payments under unconditional purchase obligation arrangements $ 77,800 $ 75,200 $ 81,000
Minimum      
Unrecorded Unconditional Purchase Obligation, Fiscal Year Maturity [Abstract]      
Long-term unconditional purchase obligations, Total 451,943    
2024 86,073    
2025 64,134    
2026 61,738    
2027 47,795    
2028 40,775    
Thereafter $ 151,428