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Basis of Presentation and Summary of Significant Accounting Policies - Narrative (Details) $ in Thousands |  |  | 3 Months Ended | 9 Months Ended |
--- | --- | --- | --- | --- | ---
May 16, 2023 USD ($) | Apr. 06, 2023 USD ($) | Jun. 30, 2023 USD ($) country | Jul. 01, 2022 USD ($) | Jun. 30, 2023 USD ($) segment country | Jul. 01, 2022 USD ($) | Sep. 30, 2022 USD ($)
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |  |  |
Number of reportable segments | segment |  |  |  |  | 3 |  |
Foreign currency transaction loss |  |  | $ 2,800 | $ 1,200 | $ 6,700 | $ 2,200 |
Cash and cash equivalents |  |  | 402,414 |  | 402,414 |  | $ 329,452
Impairment charges |  |  |  |  | 35,479 | 0 |
Equity method investment, aggregate cost |  |  | 98,000 |  | 98,000 |  | 224,500
Gain (loss) on equity method investment |  |  | 377,100 |  | (275,900) |  |
Proceeds from sale of equity investments | $ 98,200 |  |  |  | 633,179 | 0 |
Pre-tax loss on sale of equity investment |  |  | 1,100 |  | 1,100 |  |
Loss on sale of equity investment, net of tax |  |  | 2,200 |  | 2,200 |  |
AIM Services Co., Ltd | AIM Services Co., Ltd |  |  |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |  |  |
Equity method investment, ownership interest, percent |  | 50.00% |  |  |  |  |
Proceeds from sale of equity method investments |  | $ 535,000 |  |  |  |  |
Equity securities without readily determinable fair value, amount |  |  | 85,200 |  | 85,200 |  | 180,500
Cost of services provided | FSS United States and Uniform |  |  |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |  |  |
Impairment charges |  |  |  |  | 26,700 |  |
Cost of services provided | FSS United States | Right Of Use Assets |  |  |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |  |  |
Impairment charges |  |  |  |  | 8,600 |  |
Cost of services provided | FSS United States | Leasehold Improvements |  |  |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |  |  |
Impairment charges |  |  |  |  | 10,400 |  |
Cost of services provided | Uniform | Right Of Use Assets |  |  |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |  |  |
Impairment charges |  |  |  |  | 7,100 |  |
Cost of services provided | Uniform | Other Assets |  |  |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |  |  |
Impairment charges |  |  |  |  | 600 |  |
Deferred Income Taxes and Other Noncurrent Liabilities | CARES Act |  |  |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |  |  |
Payment of deferred social security taxes |  |  |  |  | 64,200 | $ 64,200 |
Captive |  |  |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |  |  |
Cash and cash equivalents |  |  | 24,400 |  | 24,400 |  | 23,100
Captive | Prepaid Expenses and Other Current Assets |  |  |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |  |  |
Investment at cost |  |  | $ 109,800 |  | $ 109,800 |  | $ 78,200
Foreign Countries Outside North America |  |  |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |  |  |
Number of foreign countries in which entity operates | country |  |  | 18 |  | 18 |  |

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