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Retirement Plans (Schedules of Net Benefit Costs) (Details) - USD ($) $ in Thousands | 12 Months Ended
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Aug. 31, 2023 | Aug. 31, 2022 | Aug. 31, 2021
Retirement Benefits [Abstract] |  |  |
Interest cost | $ 211 | $ 156 | $ 146
Net amortization and deferral | 211 | 255 | 269
Total | $ 422 | $ 411 | $ 415

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