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Business and Summary of Significant Accounting Policies - Computer Equipment, Software, Furniture and Leasehold Improvements, Net (Details) - USD ($) | 12 Months Ended
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Jan. 31, 2020 | Jan. 31, 2019 | Jan. 31, 2018
Property, Plant and Equipment [Abstract] |  |  |
Depreciation | $ 51,000,000.0 | $ 59,200,000 | $ 67,600,000
Computer hardware, at cost | 159,700,000 | 190,200,000 |
Computer software, at cost | 64,000,000.0 | 66,700,000 |
Leasehold improvements, land and buildings, at cost | 284,000,000.0 | 247,800,000 |
Furniture and equipment, at cost | 69,000,000.0 | 67,200,000 |
Computer software, hardware, leasehold improvements, furniture, and equipment, at cost | 576,700,000 | 571,900,000 |
Less: Accumulated depreciation | (415,000,000.0) | (422,200,000) |
Computer software, hardware, leasehold improvements, furniture, and equipment, net | 161,700,000 | 149,700,000 |
Capitalized software development costs | 22,300,000 | 4,900,000 |
Amortization | $ 1,200,000 | $ 0 |
Software and Software Development Costs |  |  |
Property, Plant and Equipment [Abstract] |  |  |
Useful life | 3 years |  |
Minimum |  |  |
Property, Plant and Equipment [Abstract] |  |  |
Useful life | 3 years |  |
Maximum |  |  |
Property, Plant and Equipment [Abstract] |  |  |
Useful life | 5 years |  |

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- Definition Amount before accumulated amortization of capitalized costs for computer software, including but not limited to, acquired and internally developed computer software. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Publisher FASB -Name Accounting Standards Codification -Topic 985 -SubTopic 20 -Section 50 -Paragraph 1 -URI http://asc.fasb.org/extlink&oid=6501960&loc=d3e128462-111756 + Details
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