Income Tax (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Jul. 31, 2021	Jul. 31, 2020	Jul. 31, 2021	Jul. 31, 2020
Tax Credit Carryforward [Line Items]
(Provision) benefit for income taxes	$ 23.2	$ 30.8	$ (1.0)	$ 54.8
(Loss) income before income taxes	138.8	$ 129.0	270.2	$ 219.5
Unrecognized tax benefits	203.4		203.4
Unrecognized tax benefits that would impact effective tax rate	170.4		170.4
Effect of change in unrecognized tax benefits	8.1		8.1
SEC Schedule, 12-09, Valuation Allowance, Tax Credit Carryforward
Tax Credit Carryforward [Line Items]
Unrecognized tax benefits that would impact effective tax rate	$ 33.0		$ 33.0