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Deferred Compensation (Additional Information) (Details) - USD ($) | 3 Months Ended | 9 Months Ended |
--- | --- | --- | ---
Oct. 31, 2019 | Oct. 31, 2018 | Oct. 31, 2019 | Oct. 31, 2018 | Jan. 31, 2019
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items] |  |  |  |  |
Marketable securities | $ 68,300,000 |  | $ 68,300,000 |  | $ 67,600,000
Costs to obtain a contract | 75,900,000 |  | 75,900,000 |  | 93,000,000.0
Amortization of costs to obtain a contract | 25,200,000 | $ 26,900,000 | 75,400,000 | $ 80,000,000.0 |
Impairment loss |  |  | 0 | $ 0 |
Rabbi Trust |  |  |  |  |
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items] |  |  |  |  |
Deferred compensation liability | 68,300,000 |  | 68,300,000 |  | 60,300,000
Deferred compensation liability, current | 5,900,000 |  | 5,900,000 |  | 5,000,000.0
Deferred compensation liability, non-current | $ 62,400,000 |  | $ 62,400,000 |  | $ 55,300,000

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- Definition Amount, after accumulated amortization and accumulated impairment loss, of asset recognized from cost incurred to obtain or fulfill contract with customer. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 340 -SubTopic 40 -Section 50 -Paragraph 3 -Subparagraph (a) -URI http://asc.fasb.org/extlink&oid=68051541&loc=SL49131252-203054 + Details
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- Definition Aggregate carrying value as of the balance sheet date of the liabilities for all deferred compensation arrangements payable within one year (or the operating cycle, if longer). Represents currently earned compensation under compensation arrangements that is not actually paid until a later date. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 710 -SubTopic 10 -Section 25 -Paragraph 9 -URI http://asc.fasb.org/extlink&oid=6409733&loc=d3e19512-108361 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 710 -SubTopic 10 -Section 30 -Paragraph 2 -URI http://asc.fasb.org/extlink&oid=6409875&loc=d3e20028-108363 + Details
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