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Consolidated Statements of Changes in Shareholders' Equity - USD ($) shares in Millions, $ in Millions | Total | Adoption of Accounting Standards Update ("ASU") 2020-06 | Common Shares | Additional Paid-In Capital | Additional Paid-In Capital Adoption of Accounting Standards Update ("ASU") 2020-06 | Retained Earnings | Retained Earnings Adoption of Accounting Standards Update ("ASU") 2020-06 | Accumulated Other Comprehensive Income (Loss) | Treasury Stock
--- | --- | --- | --- | --- | --- | --- | --- | --- | ---
Beginning balance (in shares) at Aug. 29, 2020 |  |  | 51.8 |  |  |  |  |  |
Beginning balance at Aug. 29, 2020 | $ 827.5 |  | $ 25.9 | $ 203.8 |  | $ 913.6 |  | $ (0.5) | $ (315.3)
Treasury stock, beginning balance (in shares) at Aug. 29, 2020 |  |  |  |  |  |  |  |  | (18.1)
Increase (Decrease) in Stockholders' Equity [Roll Forward] |  |  |  |  |  |  |  |  |
Stock-based compensation | 15.3 |  |  | 15.3 |  |  |  |  |
Issuance of stock for employee benefit and stock-based awards, net | 2.3 |  |  | (0.6) |  |  |  |  | $ 2.9
Issuance of stock for employee benefit and stock-based awards, net (in shares) |  |  |  |  |  |  |  |  | 0.2
Issuance of stock for settlement of earnout liability | 0.0 |  |  |  |  |  |  |  |
Repurchase of common stock | (47.6) |  |  |  |  |  |  |  | $ (47.6)
Repurchase of common stock (in shares) |  |  |  |  |  |  |  |  | (0.8)
Common stock dividends declared | (22.5) |  |  |  |  | (22.5) |  |  |
Net income | 281.9 |  |  |  |  | 281.9 |  |  |
Ending balance (in shares) at Aug. 28, 2021 |  |  | 51.8 |  |  |  |  |  |
Ending balance at Aug. 28, 2021 | 1,056.9 |  | $ 25.9 | 218.5 |  | 1,173.0 |  | (0.5) | $ (360.0)
Treasury stock, ending balance (in shares) at Aug. 28, 2021 |  |  |  |  |  |  |  |  | (18.7)
Increase (Decrease) in Stockholders' Equity [Roll Forward] |  |  |  |  |  |  |  |  |
Stock-based compensation | 17.1 |  |  | 17.1 |  |  |  |  |
Issuance of stock for employee benefit and stock-based awards, net | 2.9 |  |  | (2.5) |  |  |  |  | $ 5.4
Issuance of stock for employee benefit and stock-based awards, net (in shares) |  |  |  |  |  |  |  |  | 0.2
Issuance of stock for acquisition | 22.0 |  |  | 14.7 |  |  |  |  | $ 7.3
Issuance of stock for acquisition (in shares) |  |  |  |  |  |  |  |  | 0.4
Issuance of stock for settlement of earnout liability | 13.2 |  |  | 7.8 |  |  |  |  | $ 5.4
Issuance of stock for settlement of earnout liability (in shares) |  |  |  |  |  |  |  |  | 0.2
Repurchase of common stock | (214.3) |  |  |  |  |  |  |  | $ (214.3)
Repurchase of common stock (in shares) |  |  |  |  |  |  |  |  | (3.6)
Common stock dividends declared | (26.2) |  |  |  |  | (26.2) |  |  |
Other | 0.8 |  |  | 0.7 |  | 0.1 |  |  |
Net income | 390.6 |  |  |  |  | 390.6 |  |  |
Ending balance (in shares) at Aug. 27, 2022 |  |  | 51.8 |  |  |  |  |  |
Ending balance at Aug. 27, 2022 | $ 1,263.0 | $ (33.0) | $ 25.9 | 256.3 | $ (62.0) | 1,537.5 | $ 29.0 | (0.5) | $ (556.2)
Treasury stock, ending balance (in shares) at Aug. 27, 2022 | (21.5) |  |  |  |  |  |  |  | (21.5)
Increase (Decrease) in Stockholders' Equity [Roll Forward] |  |  |  |  |  |  |  |  |
Accounting standards update, extensible enumeration | Accounting Standards Update 2020-06 |  |  |  |  |  |  |  |
Stock-based compensation | $ 10.9 |  |  | 10.9 |  |  |  |  |
Issuance of stock for employee benefit and stock-based awards, net | 1.2 |  |  | (7.2) |  |  |  |  | $ 8.4
Issuance of stock for employee benefit and stock-based awards, net (in shares) |  |  |  |  |  |  |  |  | 0.4
Issuance of stock for settlement of earnout liability | 0.0 |  |  |  |  |  |  |  |
Repurchase of common stock | (55.4) |  |  | (0.3) |  |  |  |  | $ (55.1)
Repurchase of common stock (in shares) |  |  |  |  |  |  |  |  | (0.9)
Common stock dividends declared | (34.6) |  |  |  |  | (34.6) |  |  |
Other comprehensive income | 0.1 |  |  |  |  |  |  | 0.1 |
Net income | 215.9 |  |  |  |  | 215.9 |  |  |
Ending balance (in shares) at Aug. 26, 2023 |  |  | 51.8 |  |  |  |  |  |
Ending balance at Aug. 26, 2023 | $ 1,368.1 |  | $ 25.9 | $ 197.7 |  | $ 1,747.8 |  | $ (0.4) | $ (602.9)
Treasury stock, ending balance (in shares) at Aug. 26, 2023 | (22.0) |  |  |  |  |  |  |  | (22.0)

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