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Share-based Compensation - Narrative (Details) - USD ($) $ / shares in Units, $ in Millions |  | 12 Months Ended |  |
--- | --- | --- | --- | ---
Oct. 27, 2014 | Aug. 27, 2022 | Aug. 28, 2021 | Aug. 29, 2020 | Oct. 30, 2010 | Nov. 30, 1996
Stock Appreciation Rights (SARs) |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Percentage vested after each anniversary of the grant date |  | 20.00% |  |  |  |
Expiration period |  | 10 years |  |  |  |
Weighted average fair values of Share-Based Awards granted (in dollars per share) |  | $ 51.25 | $ 42.63 | $ 46.58 |  |
Stock Appreciation Rights (SARs) | Cliff Vesting |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Period awards become fully vested or exercisable |  | 5 years |  |  |  |
Share-Based Awards |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Total compensation cost not yet recognized related to non-vested awards |  | $ 14.4 |  |  |  |
Period for recognition |  | 1 year 6 months |  |  |  |
Time-Based Restricted Stock Units |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Percentage vested after each anniversary of the grant date |  | 20.00% |  |  |  |
Non-Employee Directors | Unrestricted Stock |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Shares granted (in shares) |  | 1,025 | 0 | 0 |  |
The 1996 Plan |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Number of shares reserved for issuance (in shares) |  |  |  |  |  | 1,500,000
The 2010 Plan |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Number of shares reserved for issuance (in shares) |  |  |  |  | 600,000 |
Number of additional shares reserved for issuance (in shares) | 750,000 |  |  |  |  |
Shares available for future grants (in shares) |  | 173,581 |  |  |  |
The 2010 Plan | Non-Employee Directors | Stock Appreciation Rights (SARs) |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |
Shares granted (in shares) |  | 9,750 | 5,000 | 5,000 |  |

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- Definition Amount of cost not yet recognized for nonvested award under share-based payment arrangement. + 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 (i) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition Weighted-average period over which cost not yet recognized is expected to be recognized for award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. + 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 (i) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition 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. + References Reference 1: http://www.xbrl.org/2003/role/exampleRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (a)(1) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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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 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)(iii)(01) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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