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Comprehensive Income - Schedule of Changes in Components of Accumulated Other Comprehensive Income (Loss) (Details) - USD ($) $ in Millions	3 Months Ended				6 Months Ended
	Feb. 29, 2024	Nov. 30, 2023	Feb. 28, 2023	Nov. 30, 2022	Feb. 29, 2024	Feb. 28, 2023
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance	$ 2,064.1	$ 2,015.4	$ 1,903.5	$ 1,911.8	$ 2,015.4	$ 1,911.8
Other comprehensive loss before reclassifications					(1.4)	(2.6)
Amounts reclassified from accumulated other comprehensive loss					1.3	2.1
Net current period other comprehensive (loss) income	1.4	(1.5)	(0.1)	(0.4)	(0.1)	(0.5)
Ending balance	2,149.6	2,064.1	1,947.6	1,903.5	2,149.6	1,947.6
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance	(114.1)	(112.6)	(126.2)	(125.8)	(112.6)	(125.8)
Net current period other comprehensive (loss) income	1.4	(1.5)	(0.1)	(0.4)
Ending balance	(112.7)	(114.1)	(126.3)	(126.2)	(112.7)	(126.3)
Foreign Currency Items
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance		(65.0)		(73.5)	(65.0)	(73.5)
Other comprehensive loss before reclassifications					(1.4)	(2.6)
Amounts reclassified from accumulated other comprehensive loss					0.0	0.0
Net current period other comprehensive (loss) income					(1.4)	(2.6)
Ending balance	(66.4)		(76.1)		(66.4)	(76.1)
Defined Benefit Pension Plans
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance		$ (47.6)		$ (52.3)	(47.6)	(52.3)
Other comprehensive loss before reclassifications					0.0	0.0
Amounts reclassified from accumulated other comprehensive loss					1.3	2.1
Net current period other comprehensive (loss) income					1.3	2.1
Ending balance	$ (46.3)		$ (50.2)		$ (46.3)	$ (50.2)

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