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Business and Summary of Significant Accounting Policies - Computer Equipment, Software, Furniture and Leasehold Improvements, Net (Details) - USD ($) $ in Millions | 12 Months Ended
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Jan. 31, 2021 | Jan. 31, 2020 | Jan. 31, 2019
Property, Plant and Equipment [Abstract] |  |  |
Useful life | 3 years |  |
Depreciation | $ 51.4 | $ 51.0 | $ 59.2
Computer hardware, at cost | 153.3 | 159.7 |
Computer software, at cost | 57.9 | 64.0 |
Leasehold improvements, land and buildings, at cost | 335.9 | 284.0 |
Furniture and equipment, at cost | 88.4 | 69.0 |
Computer software, hardware, leasehold improvements, furniture, and equipment, at cost | 635.5 | 576.7 |
Less: Accumulated depreciation | (442.7) | (415.0) |
Computer software, hardware, leasehold improvements, furniture, and equipment, net | 192.8 | 161.7 |
Capitalized software development costs | 72.2 | 22.3 |
Amortization | 3.7 | 1.2 | $ 0.0
Cloud-based Software Hosting Arrangements |  |  |
Property, Plant and Equipment [Abstract] |  |  |
Accumulated amortization | $ 4.9 | $ 1.2 |
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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