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Condensed Consolidated Statements of Shareholder's Equity - USD ($) shares in Millions, $ in Millions | Total | Accelerated share repurchase | Treasury stock repurchases | Total Shareholders' Equity | Total Shareholders' Equity Accelerated share repurchase | Total Shareholders' Equity Treasury stock repurchases | Common Stock | Common Stock Accelerated share repurchase | Common Stock Treasury stock repurchases | Additional Paid-in Capital | Additional Paid-in Capital Accelerated share repurchase | Accumulated Earnings | Accumulated Other Comprehensive Loss | Treasury Stock | Treasury Stock Accelerated share repurchase | Treasury Stock Treasury stock repurchases | Non- controlling Interest
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Balances at beginning of period (in shares) at Sep. 30, 2022 |  |  |  |  |  |  | 40.8 |  |  |  |  |  |  |  |  |  |
Balances at beginning of period at Sep. 30, 2022 | $ 1,269.1 |  |  | $ 1,263.2 |  |  | $ 0.5 |  |  | $ 2,032.5 |  | $ 362.1 | $ (303.1) | $ (828.8) |  |  | $ 5.9
Increase (Decrease) in Stockholders' Equity [Roll Forward] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Net income from continuing operations | (40.0) |  |  | (40.3) |  |  |  |  |  |  |  | (40.3) |  |  |  |  | 0.3
(Loss) income from discontinued operations, net of tax | 19.5 |  |  | 19.4 |  |  |  |  |  |  |  | 19.4 |  |  |  |  | 0.1
Other comprehensive income, net of tax | 14.5 |  |  | 14.2 |  |  |  |  |  |  |  |  | 14.2 |  |  |  | 0.3
Restricted stock issued and related tax withholdings (in shares) |  |  |  |  |  |  | 0.2 |  |  |  |  |  |  |  |  |  |
Restricted stock issued and related tax withholdings | (10.5) |  |  | (10.5) |  |  |  |  |  | (25.1) |  |  |  | 14.6 |  |  |
Share based compensation | 4.1 |  |  | 4.1 |  |  |  |  |  | 4.1 |  |  |  |  |  |  |
Dividends declared | (17.3) |  |  | (17.3) |  |  |  |  |  |  |  | (17.3) |  |  |  |  |
Balances at end of period (in shares) at Jan. 01, 2023 |  |  |  |  |  |  | 41.0 |  |  |  |  |  |  |  |  |  |
Balances at end of period at Jan. 01, 2023 | 1,239.4 |  |  | 1,232.8 |  |  | $ 0.5 |  |  | 2,011.5 |  | 323.9 | (288.9) | (814.2) |  |  | 6.6
Balances at beginning of period (in shares) at Sep. 30, 2022 |  |  |  |  |  |  | 40.8 |  |  |  |  |  |  |  |  |  |
Balances at beginning of period at Sep. 30, 2022 | 1,269.1 |  |  | 1,263.2 |  |  | $ 0.5 |  |  | 2,032.5 |  | 362.1 | (303.1) | (828.8) |  |  | 5.9
Increase (Decrease) in Stockholders' Equity [Roll Forward] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Net income from continuing operations | (287.2) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
(Loss) income from discontinued operations, net of tax | 2,072.7 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Other comprehensive income, net of tax | $ 65.6 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Treasury stock repurchases (in shares) | (5.3) | (5.3) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Treasury stock repurchases |  |  |  |  |  |  |  |  |  |  |  |  |  | (400.0) | $ (400.0) |  |
Balances at end of period (in shares) at Jul. 02, 2023 |  |  |  |  |  |  | 35.7 |  |  |  |  |  |  |  |  |  |
Balances at end of period at Jul. 02, 2023 | $ 2,559.9 |  |  | 2,558.7 |  |  | $ 0.5 |  |  | 1,919.7 |  | 2,094.3 | (238.6) | (1,217.2) |  |  | 1.2
Balances at beginning of period (in shares) at Jan. 01, 2023 |  |  |  |  |  |  | 41.0 |  |  |  |  |  |  |  |  |  |
Balances at beginning of period at Jan. 01, 2023 | 1,239.4 |  |  | 1,232.8 |  |  | $ 0.5 |  |  | 2,011.5 |  | 323.9 | (288.9) | (814.2) |  |  | 6.6
Increase (Decrease) in Stockholders' Equity [Roll Forward] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Net income from continuing operations | (75.0) |  |  | (75.1) |  |  |  |  |  |  |  | (75.1) |  |  |  |  | 0.1
(Loss) income from discontinued operations, net of tax | 21.4 |  |  | 21.4 |  |  |  |  |  |  |  | 21.4 |  |  |  |  |
Other comprehensive income, net of tax | 16.2 |  |  | 16.0 |  |  |  |  |  |  |  |  | 16.0 |  |  |  | 0.2
Share based compensation | 4.7 |  |  | 4.7 |  |  |  |  |  | 4.7 |  |  |  |  |  |  |
Dividends declared | (17.6) |  |  | (17.6) |  |  |  |  |  |  |  | (17.6) |  |  |  |  |
Balances at end of period (in shares) at Apr. 02, 2023 |  |  |  |  |  |  | 41.0 |  |  |  |  |  |  |  |  |  |
Balances at end of period at Apr. 02, 2023 | 1,189.1 |  |  | 1,182.2 |  |  | $ 0.5 |  |  | 2,016.2 |  | 252.6 | (272.9) | (814.2) |  |  | 6.9
Increase (Decrease) in Stockholders' Equity [Roll Forward] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Net income from continuing operations | (172.2) |  |  | (172.4) |  |  |  |  |  |  |  | (172.4) |  |  |  |  | 0.2
(Loss) income from discontinued operations, net of tax | 2,031.8 |  |  | 2,031.6 |  |  |  |  |  |  |  | 2,031.6 |  |  |  |  | 0.2
Sale and deconsolidation of assets held for sale | 19.5 |  |  | 25.4 |  |  |  |  |  |  |  |  | 25.4 |  |  |  | (5.9)
Other comprehensive income (loss), net of tax | 8.7 |  |  | 8.9 |  |  |  |  |  |  |  |  | 8.9 |  |  |  | (0.2)
Other comprehensive income, net of tax | $ 34.8 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Treasury stock repurchases (in shares) | (5.3) | (5.3) |  |  |  |  | (5.3) |  |  |  |  |  |  |  |  |  |
Treasury stock repurchases | $ (500.0) |  |  | (500.0) |  |  |  |  |  | (100.0) |  |  |  | (400.0) | (400.0) |  |
Excise tax on net share repurchases | (3.8) |  |  | (3.8) |  |  |  |  |  |  |  |  |  | (3.8) |  |  |
Restricted stock issued and related tax withholdings | (0.8) |  |  | (0.8) |  |  |  |  |  | (1.6) |  |  |  | 0.8 |  |  |
Share based compensation | 5.1 |  |  | 5.1 |  |  |  |  |  | 5.1 |  |  |  |  |  |  |
Dividends declared | (17.5) |  |  | (17.5) |  |  |  |  |  |  |  | (17.5) |  |  |  |  |
Balances at end of period (in shares) at Jul. 02, 2023 |  |  |  |  |  |  | 35.7 |  |  |  |  |  |  |  |  |  |
Balances at end of period at Jul. 02, 2023 | 2,559.9 |  |  | 2,558.7 |  |  | $ 0.5 |  |  | 1,919.7 |  | 2,094.3 | (238.6) | (1,217.2) |  |  | 1.2
Balances at beginning of period (in shares) at Sep. 30, 2023 |  |  |  |  |  |  | 35.3 |  |  |  |  |  |  |  |  |  |
Balances at beginning of period at Sep. 30, 2023 | 2,518.3 |  |  | 2,517.6 |  |  | $ 0.5 |  |  | 1,920.8 |  | 2,096.0 | (249.4) | (1,250.3) |  |  | 0.7
Increase (Decrease) in Stockholders' Equity [Roll Forward] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Net income from continuing operations | 17.5 |  |  | 17.4 |  |  |  |  |  |  |  | 17.4 |  |  |  |  | 0.1
(Loss) income from discontinued operations, net of tax | 11.7 |  |  | 11.7 |  |  |  |  |  |  |  | 11.7 |  |  |  |  |
Other comprehensive income, net of tax | 16.3 |  |  | 16.2 |  |  |  |  |  |  |  |  | 16.2 |  |  |  | 0.1
Treasury stock repurchases (in shares) |  |  |  |  |  |  |  | (1.3) | (3.3) |  |  |  |  |  |  |  |
Treasury stock repurchases |  | $ 0.0 | $ (243.0) |  | $ 0.0 | $ (243.0) |  |  |  |  | $ 83.2 |  |  |  | (83.2) | $ (243.0) |
Excise tax on net share repurchases | (3.1) |  |  | (3.1) |  |  |  |  |  |  |  |  |  | (3.1) |  |  |
Restricted stock issued and related tax withholdings (in shares) |  |  |  |  |  |  | 0.1 |  |  |  |  |  |  |  |  |  |
Restricted stock issued and related tax withholdings | (5.4) |  |  | (5.4) |  |  |  |  |  | (14.3) |  |  |  | 8.9 |  |  |
Share based compensation | 3.9 |  |  | 3.9 |  |  |  |  |  | 3.9 |  |  |  |  |  |  |
Dividends declared | (14.5) |  |  | (14.5) |  |  |  |  |  |  |  | (14.5) |  |  |  |  |
Balances at end of period (in shares) at Dec. 31, 2023 |  |  |  |  |  |  | 30.8 |  |  |  |  |  |  |  |  |  |
Balances at end of period at Dec. 31, 2023 | 2,301.7 |  |  | 2,300.8 |  |  | $ 0.5 |  |  | 1,993.6 |  | 2,110.6 | (233.2) | (1,570.7) |  |  | 0.9
Balances at beginning of period (in shares) at Sep. 30, 2023 |  |  |  |  |  |  | 35.3 |  |  |  |  |  |  |  |  |  |
Balances at beginning of period at Sep. 30, 2023 | 2,518.3 |  |  | 2,517.6 |  |  | $ 0.5 |  |  | 1,920.8 |  | 2,096.0 | (249.4) | (1,250.3) |  |  | 0.7
Increase (Decrease) in Stockholders' Equity [Roll Forward] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Net income from continuing operations | 86.4 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
(Loss) income from discontinued operations, net of tax | 9.6 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Other comprehensive income, net of tax | $ 10.5 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Treasury stock repurchases (in shares) | (7.4) | (1.3) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Treasury stock repurchases |  |  |  |  |  |  |  |  |  |  |  |  |  | (565.9) | (83.2) |  |
Balances at end of period (in shares) at Jun. 30, 2024 |  |  |  |  |  |  | 28.0 |  |  |  |  |  |  |  |  |  |
Balances at end of period at Jun. 30, 2024 | $ 2,085.1 |  |  | 2,084.6 |  |  | $ 0.5 |  |  | 1,983.1 |  | 2,152.6 | (238.9) | (1,812.7) |  |  | 0.5
Balances at beginning of period (in shares) at Dec. 31, 2023 |  |  |  |  |  |  | 30.8 |  |  |  |  |  |  |  |  |  |
Balances at beginning of period at Dec. 31, 2023 | 2,301.7 |  |  | 2,300.8 |  |  | $ 0.5 |  |  | 1,993.6 |  | 2,110.6 | (233.2) | (1,570.7) |  |  | 0.9
Increase (Decrease) in Stockholders' Equity [Roll Forward] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Net income from continuing operations | 49.9 |  |  | 50.1 |  |  |  |  |  |  |  | 50.1 |  |  |  |  | (0.2)
(Loss) income from discontinued operations, net of tax | 11.0 |  |  | 11.0 |  |  |  |  |  |  |  | 11.0 |  |  |  |  | 0.0
Other comprehensive income, net of tax | 1.9 |  |  | 2.0 |  |  |  |  |  |  |  |  | 2.0 |  |  |  | (0.1)
Treasury stock repurchases (in shares) |  |  |  |  |  |  | (1.2) |  |  |  |  |  |  |  |  |  |
Treasury stock repurchases | (97.6) |  |  | (97.6) |  |  |  |  |  |  |  |  |  | (97.6) |  |  |
Excise tax on net share repurchases | (1.0) |  |  | (1.0) |  |  |  |  |  |  |  |  |  | (1.0) |  |  |
Share based compensation | 4.5 |  |  | 4.5 |  |  |  |  |  | 4.5 |  |  |  |  |  |  |
Dividends declared | (12.9) |  |  | (12.9) |  |  |  |  |  |  |  | (12.9) |  |  |  |  |
Balances at end of period (in shares) at Mar. 31, 2024 |  |  |  |  |  |  | 29.6 |  |  |  |  |  |  |  |  |  |
Balances at end of period at Mar. 31, 2024 | 2,257.5 |  |  | 2,256.9 |  |  | $ 0.5 |  |  | 1,998.1 |  | 2,158.8 | (231.2) | (1,669.3) |  |  | 0.6
Increase (Decrease) in Stockholders' Equity [Roll Forward] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Net income from continuing operations | 19.1 |  |  | 19.2 |  |  |  |  |  |  |  | 19.2 |  |  |  |  | (0.1)
(Loss) income from discontinued operations, net of tax | (13.1) |  |  | (13.1) |  |  |  |  |  |  |  | (13.1) |  |  |  |  | 0.0
Other comprehensive income (loss), net of tax | (7.7) |  |  | (7.7) |  |  |  |  |  |  |  |  | (7.7) |  |  |  | 0.0
Premium on capped call transactions, net of tax | (19.2) |  |  | (19.2) |  |  |  |  |  | (19.2) |  |  |  |  |  |  |
Other comprehensive income, net of tax | $ (7.7) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Treasury stock repurchases (in shares) | (1.6) | 0.0 |  |  |  |  | (1.6) |  |  |  |  |  |  |  |  |  |
Treasury stock repurchases | $ (142.2) |  |  | (142.2) |  |  |  |  |  |  |  |  |  | (142.2) | $ 0.0 |  |
Excise tax on net share repurchases | (1.4) |  |  | (1.4) |  |  |  |  |  |  |  |  |  | (1.4) |  |  |
Restricted stock issued and related tax withholdings | (0.1) |  |  | (0.1) |  |  |  |  |  | (0.3) |  |  |  | 0.2 |  |  |
Share based compensation | 4.5 |  |  | 4.5 |  |  |  |  |  | 4.5 |  |  |  |  |  |  |
Dividends declared | (12.3) |  |  | (12.3) |  |  |  |  |  |  |  | (12.3) |  |  |  |  |
Balances at end of period (in shares) at Jun. 30, 2024 |  |  |  |  |  |  | 28.0 |  |  |  |  |  |  |  |  |  |
Balances at end of period at Jun. 30, 2024 | $ 2,085.1 |  |  | $ 2,084.6 |  |  | $ 0.5 |  |  | $ 1,983.1 |  | $ 2,152.6 | $ (238.9) | $ (1,812.7) |  |  | $ 0.5

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