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Income Tax (Details) - USD ($) $ in Millions | 3 Months Ended | 9 Months Ended
--- | --- | ---
Oct. 31, 2021 | Oct. 31, 2020 | Oct. 31, 2021 | Oct. 31, 2020
Tax Credit Carryforward [Line Items] |  |  |  |
Provision for income taxes | $ 50.7 | $ 23.9 | $ 49.7 | $ 78.7
(Loss) income before income taxes | 187.4 | $ 156.1 | 457.6 | $ 375.6
Unrecognized tax benefits | 204.6 |  | 204.6 |
Unrecognized tax benefits that would impact effective tax rate | 171.1 |  | 171.1 |
Effect of change in unrecognized tax benefits | 8.0 |  | 8.0 |
SEC Schedule, 12-09, Valuation Allowance, Tax Credit Carryforward |  |  |  |
Tax Credit Carryforward [Line Items] |  |  |  |
Unrecognized tax benefits that would impact effective tax rate | $ 33.5 |  | $ 33.5 |

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