Deferred Compensation (Additional Information) (Details) - USD ($) $ in Millions	3 Months Ended
Apr. 30, 2019	Apr. 30, 2018	Jan. 31, 2019
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items]
Marketable securities	$ 88.9
Costs to obtain a contract	85.5		$ 93.0
Amortization of costs to obtain a contract	24.7	$ 26.2
Rabbi Trust
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items]
Deferred compensation liability	66.3		60.3
Deferred compensation liability, current	5.1		5.0
Deferred compensation liability, non-current	61.2		55.3
Mutual funds
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items]
Trading securities	$ 66.3		$ 60.3

Amount of amortization expense for asset recognized from cost incurred to obtain or fulfill contract with customer.

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Amount, after accumulated amortization and accumulated impairment loss, of asset recognized from cost incurred to obtain or fulfill contract with customer.

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Aggregate carrying value as of the balance sheet date of the liabilities for all deferred compensation arrangements payable beyond one year (or the operating cycle, if longer).

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Amount of investment in marketable security.

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Amount of investment in debt security measured at fair value with change in fair value recognized in net income (trading).

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