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Commitments and Contingencies - Unconditional Purchase Obligations (Details) - USD ($)
$ in Thousands
12 Months Ended
Aug. 31, 2024
Aug. 31, 2023
Aug. 31, 2022
Unrecorded Unconditional Purchase Obligation, Fiscal Year Maturity [Abstract]      
Total payments under unconditional purchase obligation arrangements $ 84,600 $ 77,800 $ 75,200
Minimum      
Unrecorded Unconditional Purchase Obligation, Fiscal Year Maturity [Abstract]      
Long-term unconditional purchase obligations, Total 447,231    
2025 85,140    
2026 79,357    
2027 64,942    
2028 57,748    
2029 55,115    
Thereafter $ 104,929