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Retirement Plans (Schedule of Amounts Recognized in Statement of Financial Position) (Details) - USD ($) $ in Thousands | Aug. 31, 2022 | Aug. 31, 2021 | Aug. 31, 2020
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Retirement Benefits [Abstract] |  |  |
Other current liabilities | $ 530 | $ 530 |
Other non-current liabilities | 4,892 | 5,754 |
Net amount recognized | $ 5,422 | $ 6,284 | $ 6,904

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