Earnings per Share and Shareholders' Equity Share Repurchase (Details) - USD ($) |
3 Months Ended | 6 Months Ended | 174 Months Ended | |||
|---|---|---|---|---|---|---|
Feb. 28, 2026 |
Feb. 28, 2025 |
Feb. 28, 2026 |
Feb. 28, 2025 |
Feb. 28, 2026 |
Oct. 10, 2025 |
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| Equity [Abstract] | ||||||
| Stock Repurchased During Period, Value | $ 65,900,000 | $ 14,600,000 | ||||
| Share Repurchase Program, Authorized, Amount | $ 200,000,000 | |||||
| Share Repurchase Program, Remaining Authorized, Amount | $ 134,800,000 | $ 134,800,000 | $ 134,800,000 | |||
| Incremental Common Shares Attributable to Dilutive Effect of Share-based Payment Arrangements | 420,000 | 411,000 | 394,000 | 491,000 | ||
| Anti-dilutive securities from stock based compensation plans (excluded from earnings per share calculation) | 56,000 | 192,000 | 107,000 | 121,000 | ||
| Treasury Stock, Value, Acquired, Cost Method | $ 51,025,000 | $ 973,500,000 | ||||
| Stock Repurchased During Period, Shares | 1,655,307 | 329,527 | ||||
| X | ||||||||||
- Definition Amount authorized for purchase of share under share repurchase plan. Includes, but is not limited to, repurchase of stock and unit of ownership. Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
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| X | ||||||||||
- Definition Securities (including those issuable pursuant to contingent stock agreements) that could potentially dilute basic earnings per share (EPS) or earnings per unit (EPU) in the future that were not included in the computation of diluted EPS or EPU because to do so would increase EPS or EPU amounts or decrease loss per share or unit amounts for the period presented. Reference 1: http://www.xbrl.org/2003/role/disclosureRef
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- References No definition available.
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- Definition Additional shares included in the calculation of diluted EPS as a result of the potentially dilutive effect of share based payment arrangements using the treasury stock method. Reference 1: http://www.xbrl.org/2003/role/disclosureRef
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| X | ||||||||||
- Definition Amount remaining authorized for purchase of share under share repurchase plan. Includes, but is not limited to, repurchase of stock and unit of ownership. No definition available.
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- Definition Number of shares that have been repurchased during the period and have not been retired and are not held in treasury. Some state laws may govern the circumstances under which an entity may acquire its own stock and prescribe the accounting treatment therefore. This element is used when state law does not recognize treasury stock. Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
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| X | ||||||||||
- Definition Equity impact of the value of stock that has been repurchased during the period and has not been retired and is not held in treasury. Some state laws may mandate the circumstances under which an entity may acquire its own stock and prescribe the accounting treatment therefore. This element is used when state law does not recognize treasury stock. Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
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- Definition Equity impact of the cost of common and preferred stock that were repurchased during the period. Recorded using the cost method. Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
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