Share-Based Compensation (Summary of Stock Option Activity) (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
Aug. 31, 2024	Aug. 31, 2023
Share-Based Payment Arrangement [Abstract]
Stock options outstanding, number of stock options	118,470
Granted, number of stock options	31,199
Exercised, number of stock options	(5,217)
Forfeited/cancelled, number of stock options	(2,276)
Stock options outstanding, number of stock options	142,176	118,470
Exercisable number of stock options	90,964
Stock options outstanding, average exercise price	$ 115.96
Granted, average exercise price	120.54
Exercised, average exercise price	91.87
Forfeited/cancelled, average exercise price	141.58
Stock options outstanding, average exercise price	117.44	$ 115.96
Exercisable average exercise price	$ 108.34
Aggregate intrinsic value outstanding	$ 2,139
Exercised aggregate intrinsic value	217
Forfeited/cancelled aggregate intrinsic value	6
Aggregate intrinsic value outstanding	2,075	$ 2,139
Exercisable aggregate intrinsic value	$ 1,968
Average remaining contractual term (years)	6 years 4 months 24 days	6 years 7 months 6 days
Exercisable average remaining contractual term (years)	5 years 1 month 6 days

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The number of shares into which fully or partially vested stock options outstanding as of the balance sheet date can be currently converted under the option plan.

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The weighted-average price as of the balance sheet date at which grantees can acquire the shares reserved for issuance on vested portions of options outstanding and currently exercisable under the stock option plan.

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Amount of accumulated difference between fair value of underlying shares on dates of exercise and exercise price on options exercised (or share units converted) into shares.

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The number of shares under options that were cancelled during the reporting period as a result of occurrence of a terminating event specified in contractual agreements pertaining to the stock option plan.

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Gross number of share options (or share units) granted during the period.

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Amount by which the current fair value of the underlying stock exceeds the exercise price of options outstanding.

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Number of options outstanding, including both vested and non-vested options.

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Weighted average price at which grantees can acquire the shares reserved for issuance under the stock option plan.

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Weighted average price at which option holders acquired shares when converting their stock options into shares.

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Weighted average price at which grantees could have acquired the underlying shares with respect to stock options that were terminated.

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Weighted average per share amount at which grantees can acquire shares of common stock by exercise of options.

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Amount of difference between fair value of the underlying shares reserved for issuance and exercise price of vested portions of options outstanding and currently exercisable.

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Weighted average remaining contractual term for vested portions of options outstanding and currently exercisable or convertible, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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Weighted average remaining contractual term for option awards outstanding, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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Number of share options (or share units) exercised during the current period.

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Value of stock related to Restricted Stock Awards issued during the period, net of the stock value of such awards forfeited.

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