Share-Based Compensation (Summary of Stock Option Activity) (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
Aug. 31, 2025	Aug. 31, 2024
Share-Based Payment Arrangement [Abstract]
Stock options outstanding, number of stock options	142,176
Granted, number of stock options	43,011
Exercised, number of stock options	(18,015)
Stock options outstanding, number of stock options	167,172	142,176
Exercisable number of stock options	96,880
Stock options outstanding, average exercise price	$ 117.44
Granted, average exercise price	121.16
Exercised, average exercise price	83.67
Stock options outstanding, average exercise price	122.04	$ 117.44
Exercisable average exercise price	$ 120.29
Aggregate intrinsic value outstanding	$ 2,075
Exercised aggregate intrinsic value	958
Aggregate intrinsic value outstanding	3,113	$ 2,075
Exercisable aggregate intrinsic value	$ 2,083
Average remaining contractual term (years)	6 years 9 months 18 days	6 years 4 months 24 days
Exercisable average remaining contractual term (years)	5 years 4 months 24 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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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 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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