Accrued excise taxes.

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Percentage of weighted relative shareholder return.

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Percentage of weighted return on invested capital.

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Restricted stock grant fair value.

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Share-based compensation arrangement by share-based payment award, payout percentage.

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Share Repurchase Program, Current Authorization Of Shares Purchased

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Share Repurchase Program, Current Authorization Of Shares Purchased Amount

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Stockholders Equity Note [Line Items]

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Amount authorized for purchase of share under share repurchase plan. Includes, but is not limited to, repurchase of stock and unit of ownership.

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Period over which grantee's right to exercise award under share-based payment arrangement is no longer contingent on satisfaction of service or performance condition, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. Includes, but is not limited to, combination of market, performance or service condition.

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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.

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Amount remaining authorized for purchase of share under share repurchase plan. Includes, but is not limited to, repurchase of stock and unit of ownership.

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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.

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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.

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Equity - Additional Information (Detail) - USD ($)	12 Months Ended
Equity - Additional Information (Detail) - USD ($)	Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2022	Jan. 06, 2021
Stockholders Equity Note [Line Items]
Shares repurchased	$ 1,300,000	$ 56,900,000
Shares available for grant	1,000,000	1,200,000	1,400,000
Performance based share based compensation and dividend equivalent rights	393,000	500,000	400,000
Share based compensation, non vested shares	901,000	972,000
Percentage of weighted EBITDA	60.00%	60.00%	80.00%
percentage of weighted ROIC	20.00%	20.00%	20.00%
Percentage of weighted peer group TSR	20.00%	20.00%
Number of authorized shares repurchased			0
Authorized amount under stock repurchase program	$ 100,000,000
Unamortized compensation cost of restricted stock unit grants	$ 16,700,000
Number of shares repurchased	38,000	1,900,000
Share repurchase program, current authorization of shares purchased		1,800,000
Number of shares repurchased amount	$ 1,300,000	$ 56,900,000
Share repurchase program, current authorization of shares purchased amount		53,600,000
Accrued excise taxes		500,000
Remaining authorized repurchase amount	$ 45,100,000
Repurchase program expiration date	Jan. 31, 2025
Accounts Payable and Accrued Liabilities
Stockholders Equity Note [Line Items]
Accrued excise taxes	$ 500,000	500,000
Selling, Administrative and Cost of Revenue
Stockholders Equity Note [Line Items]
Restricted stock compensation expense	$ 17,100,000	12,100,000	$ 15,500,000
Minimum
Stockholders Equity Note [Line Items]
Payout percentage	0.00%
Vesting period of compensation expense	1 year
Maximum
Stockholders Equity Note [Line Items]
Payout percentage	200.00%
Vesting period of compensation expense	3 years
Restricted Stock
Stockholders Equity Note [Line Items]
Restricted stock shares issued net of shares for tax withholdings	400,000
Unvested Restricted Stock Grants
Stockholders Equity Note [Line Items]
Fair value of awards granted	$ 17,300,000	$ 12,400,000	$ 18,700,000
2021 Stock Incentive Plan and 2017 Amended and Restated Stock Incentive Plan
Stockholders Equity Note [Line Items]
Number of shares reserved for future issuance				1,500
2021 Stock Incentive Plan and 2017 Amended and Restated Stock Incentive Plan \| Maximum
Stockholders Equity Note [Line Items]
Shares available for grant				500,000
Number of common shares outstanding				900,000