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Retirement Benefit Plans - Narrative (Details) - USD ($) $ in Millions | 12 Months Ended
--- | ---
Jan. 31, 2022 | Jan. 31, 2021 | Jan. 31, 2020
Defined Contribution Plan Disclosure [Line Items] |  |  |
Projected benefit obligation of plan assets | $ 106.7 | $ 110.0 |
Accumulated benefit obligation | 99.5 | 105.2 |
Fair value of plan assets | 112.5 | 107.2 |
Other long-term liabilities | 9.3 | 12.1 |
Net periodic (benefit) cost | 2.6 | $ 2.8 | $ 3.7
Estimated future employer contributions in next fiscal year | $ 4.8 |  |
Mandatory Retirement Savings, Cash Balance Plan |  |  |
Defined Contribution Plan Disclosure [Line Items] |  |  |
Weighted-average interest crediting rate | 1.00% | 1.00% | 1.00%
Supplementary Retirement Savings, Cash Balance Plan |  |  |
Defined Contribution Plan Disclosure [Line Items] |  |  |
Weighted-average interest crediting rate | 0.30% | 0.10% | 0.10%
United States |  |  |
Defined Contribution Plan Disclosure [Line Items] |  |  |
Maximum annual contributions per employee | 75.00% |  |
Cost Recognized | $ 24.3 | $ 21.6 | $ 21.4
Foreign Plan |  |  |
Defined Contribution Plan Disclosure [Line Items] |  |  |
Contributions paid by employer | $ 38.3 | $ 31.7 | $ 28.7

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- Definition Amount of actuarial present value of benefits attributed to employee service rendered, excluding assumptions about future compensation level. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (e) -URI http://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920 + Details
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- Definition Amount of contribution expected to be received by defined benefit plan from employer in next fiscal year following current fiscal year. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (g) -URI http://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920 Reference 2: http://www.xbrl.org/2003/role/exampleRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 55 -Paragraph 18 -URI http://asc.fasb.org/extlink&oid=123450688&loc=d3e4587-114921 + Details
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- Definition Amount of asset segregated and restricted to provide benefit under defined benefit plan. Asset includes, but is not limited to, stock, bond, other investment, earning from investment, and contribution by employer and employee. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (d)(iv)(01) -URI http://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920 Reference 2: http://www.xbrl.org/2003/role/exampleRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (d)(iv)(01) -URI http://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920 Reference 3: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (d)(ii) -URI http://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920 Reference 4: http://www.xbrl.org/2003/role/exampleRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 55 -Paragraph 17 -URI http://asc.fasb.org/extlink&oid=123450688&loc=d3e4179-114921 Reference 5: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (d)(iv)(02) -URI http://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920 Reference 6: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920 Reference 7: http://www.xbrl.org/2003/role/exampleRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (d)(ii) -URI http://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920 + Details
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