Condensed Consolidated Statements of Shareholder's Equity - USD ($) shares in Millions, $ in Millions	Total	Open Market Purchases And Private Purchases	Total Shareholders' Equity	Total Shareholders' Equity Open Market Purchases And Private Purchases	Common Stock	Common Stock Open Market Purchases And Private Purchases	Additional Paid-in Capital	Accumulated Earnings	Accumulated Other Comprehensive Loss	Treasury Stock	Treasury Stock Open Market Purchases And Private Purchases	Non- controlling Interest
Balances at beginning of period (in shares) at Sep. 30, 2020					43.1
Balances at beginning of period at Sep. 30, 2020	$ 1,415.8		$ 1,407.5		$ 0.5		$ 2,054.3	$ 243.9	$ (284.7)	$ (606.5)		$ 8.3
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net (loss) income from continuing operations	15.7		14.7					14.7				1.0
Income (loss) from discontinued operations, net of tax	57.2		57.4					57.4				(0.2)
Other comprehensive loss, net of tax	16.6		16.2						16.2			0.4
Treasury stock repurchases (in shares)						(0.6)
Treasury stock repurchases		$ (42.3)		$ (42.3)							$ (42.3)
Restricted stock issued and related tax withholdings (in shares)					0.2
Restricted stock issued and related tax withholdings	(6.9)		(6.9)				(18.6)			11.7
Share based compensation	7.5		7.5				7.5
Dividends declared	(18.4)		(18.4)					(18.4)
Dividend paid by subsidiary to NCI	(1.0)											(1.0)
Balances at end of period (in shares) at Jan. 03, 2021					42.7
Balances at end of period at Jan. 03, 2021	1,444.2		1,435.7		$ 0.5		2,043.2	297.6	(268.5)	(637.1)		8.5
Balances at beginning of period (in shares) at Sep. 30, 2020					43.1
Balances at beginning of period at Sep. 30, 2020	1,415.8		1,407.5		$ 0.5		2,054.3	243.9	(284.7)	(606.5)		8.3
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net (loss) income from continuing operations	11.1
Income (loss) from discontinued operations, net of tax	$ 97.5
Treasury stock repurchases (in shares)	(0.6)
Treasury stock repurchases										(42.3)
Balances at end of period (in shares) at Apr. 04, 2021					42.7
Balances at end of period at Apr. 04, 2021	$ 1,494.6		1,487.4		$ 0.5		2,051.6	315.7	(243.4)	(637.0)		7.2
Balances at beginning of period (in shares) at Jan. 03, 2021					42.7
Balances at beginning of period at Jan. 03, 2021	1,444.2		1,435.7		$ 0.5		2,043.2	297.6	(268.5)	(637.1)		8.5
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net (loss) income from continuing operations	(4.6)		(3.7)					(3.7)				(0.9)
Income (loss) from discontinued operations, net of tax	40.3		40.3					40.3
Other comprehensive loss, net of tax	25.0		25.1						25.1			(0.1)
Restricted stock issued and related tax withholdings	0.0						(0.1)			0.1
Share based compensation	8.5		8.5				8.5
Dividends declared	(18.5)		(18.5)					(18.5)
Dividend paid by subsidiary to NCI	(0.3)											(0.3)
Balances at end of period (in shares) at Apr. 04, 2021					42.7
Balances at end of period at Apr. 04, 2021	1,494.6		1,487.4		$ 0.5		2,051.6	315.7	(243.4)	(637.0)		7.2
Balances at beginning of period (in shares) at Sep. 30, 2021					41.8
Balances at beginning of period at Sep. 30, 2021	1,479.0		1,471.9		$ 0.5		2,063.8	359.9	(235.3)	(717.0)		7.1
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net (loss) income from continuing operations	(30.2)		(30.2)					(30.2)
Income (loss) from discontinued operations, net of tax	38.8		38.4					38.4				0.4
Other comprehensive loss, net of tax	4.1		4.0						4.0			0.1
Treasury stock repurchases (in shares)					(1.1)
Treasury stock repurchases	(110.0)		(110.0)							(110.0)
Restricted stock issued and related tax withholdings (in shares)					0.3
Restricted stock issued and related tax withholdings	(24.4)		(24.4)				(46.6)			22.2
Share based compensation	8.3		8.3				8.3
Dividends declared	(17.7)		(17.7)					(17.7)
Balances at end of period (in shares) at Jan. 02, 2022					41.0
Balances at end of period at Jan. 02, 2022	1,347.9		1,340.3		$ 0.5		2,025.5	350.4	(231.3)	(804.8)		7.6
Balances at beginning of period (in shares) at Sep. 30, 2021					41.8
Balances at beginning of period at Sep. 30, 2021	1,479.0		1,471.9		$ 0.5		2,063.8	359.9	(235.3)	(717.0)		7.1
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net (loss) income from continuing operations	(55.3)
Income (loss) from discontinued operations, net of tax	$ 79.9
Treasury stock repurchases (in shares)	(1.3)
Treasury stock repurchases										(134.0)
Balances at end of period (in shares) at Apr. 03, 2022					40.8
Balances at end of period at Apr. 03, 2022	$ 1,328.6		1,322.3		$ 0.5		2,033.2	348.7	(231.3)	(828.8)		6.3
Balances at beginning of period (in shares) at Jan. 02, 2022					41.0
Balances at beginning of period at Jan. 02, 2022	1,347.9		1,340.3		$ 0.5		2,025.5	350.4	(231.3)	(804.8)		7.6
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net (loss) income from continuing operations	(25.1)		(25.1)					(25.1)				0.0
Income (loss) from discontinued operations, net of tax	41.1		41.0					41.0				0.1
Other comprehensive loss, net of tax	(0.1)		0.0						0.0			(0.1)
Treasury stock repurchases (in shares)					(0.2)
Treasury stock repurchases	(24.0)		(24.0)							(24.0)
Restricted stock issued and related tax withholdings	(0.1)		(0.1)				(0.1)			0.0
Share based compensation	7.8		7.8				7.8
Dividends declared	(17.6)		(17.6)					(17.6)
Dividend paid by subsidiary to NCI	(1.3)											(1.3)
Balances at end of period (in shares) at Apr. 03, 2022					40.8
Balances at end of period at Apr. 03, 2022	$ 1,328.6		$ 1,322.3		$ 0.5		$ 2,033.2	$ 348.7	$ (231.3)	$ (828.8)		$ 6.3