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Shareholders' Equity (Narrative) (Details) - USD ($) $ in Millions |  | 12 Months Ended
--- | --- | ---
Nov. 15, 2019 | Aug. 31, 2022 | Aug. 31, 2021 | Aug. 31, 2020
Class of Stock [Line Items] |  |  |  |
Shares of preferred stock authorized for issuance |  | 14,000,000.0 |  |
Preferred stock issued |  | 0 | 0 |
Preferred stock outstanding |  | 0 | 0 |
Shares withheld for tax |  | 86,125 |  |
Shares withheld for tax, fair value |  | $ 3.5 |  |
Number of shares purchased |  | 499,411 |  |
Number of shares withheld for minimum statutory taxes |  |  |  | 109,896
Values of shares withheld for minimum statutory taxes |  |  |  | $ 3.7
Stock repurchased during period, shares | 40,000,000.0 |  |  |
Common Stock [Member] |  |  |  |
Class of Stock [Line Items] |  |  |  |
Shares withheld for tax |  |  | 147,092 |
Shares withheld for tax, fair value |  |  | $ 3.0 |
Treasury Stock Open Market Purchases [Member] |  |  |  |
Class of Stock [Line Items] |  |  |  |
Purchase of treasury shares |  | $ 20.3 |  |

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