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
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