Deferred Compensation (Additional Information) (Details) - USD ($) $ in Millions	3 Months Ended	9 Months Ended
	Oct. 31, 2018	Oct. 31, 2018	Jan. 31, 2018
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items]
Marketable securities	$ 317.3	$ 317.3
Costs to obtain a contract	75.8	75.8
Amortization of costs to obtain a contract	26.9	80.0
Rabbi Trust Member
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items]
Deferred compensation liability	59.6	59.6	$ 59.0
Deferred compensation liability, current	3.3	3.3	3.4
Deferred compensation liability, non-current	56.3	56.3	55.6
Mutual funds
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items]
Trading securities	$ 59.6	$ 59.6	$ 59.0