Stock-Based Compensation (Restricted Stock Award Activity) (Details)	9 Months Ended
May 31, 2022 $ / shares shares
Stock-Based Compensation [Abstract]
Restricted stock awards at August 31, 2021, Number of Shares \| shares	28,049
Granted, Number of Shares \| shares	13,260
Vested, Number of Shares \| shares	(28,049)
Restricted stock awards at May 31, 2022, Number of Shares \| shares	13,260
Restricted stock awards at August 31, 2021, Weighted-Average Grant Date Fair Value Per Share \| $ / shares	$ 24.96
Granted, Weighted-Average Grant Date Fair Value Per Share \| $ / shares	49.78
Vested, Weighted-Average Grant Date Fair Value Per Share \| $ / shares	24.96
Restricted stock awards at May 31, 2022, Weighted-Average Grant Date Fair Value Per Share \| $ / shares	$ 49.78

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- Definition

The number of grants made during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

+ References

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- Definition

The weighted average fair value at grant date for nonvested equity-based awards issued during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

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- Definition

The number of non-vested equity-based payment instruments, excluding stock (or unit) options, that validly exist and are outstanding as of the balance sheet date.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(ii)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(i)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

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- Definition

Per share or unit weighted-average fair value of nonvested award under share-based payment arrangement. Excludes share and unit options.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(i)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(ii)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

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- Definition

The number of equity-based payment instruments, excluding stock (or unit) options, that vested during the reporting period.

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- Definition

The weighted average fair value as of grant date pertaining to an equity-based award plan other than a stock (or unit) option plan for which the grantee gained the right during the reporting period, by satisfying service and performance requirements, to receive or retain shares or units, other instruments, or cash in accordance with the terms of the arrangement.

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