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Cloud Computing Arrangements (Details) - USD ($) $ in Millions | 3 Months Ended | 9 Months Ended |
--- | --- | --- | ---
Oct. 31, 2021 | Oct. 31, 2020 | Oct. 31, 2021 | Oct. 31, 2020 | Jan. 31, 2021
Capitalized Contract Cost [Line Items] |  |  |  |  |
Capitalized contract cost | $ 110.8 |  | $ 110.8 |  | $ 120.9
Amortization expense | 29.6 | $ 23.8 | 83.6 | $ 70.2 |
Cloud-based Software Hosting Arrangements |  |  |  |  |
Capitalized Contract Cost [Line Items] |  |  |  |  |
Capitalized contract cost | 116.5 |  | 116.5 |  | 72.2
Accumulated amortization | 11.4 |  | 11.4 |  | $ 4.9
Amortization expense | $ 3.7 | $ 1.0 | $ 6.5 | $ 2.7 |

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