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Defined contribution and defined benefit retirement - Schedule of Funded Status (Detail) - USD ($) $ in Millions | 12 Months Ended
--- | ---
Dec. 31, 2023 | Dec. 31, 2022 | Dec. 31, 2021
Amounts recognized in the Consolidated Balance Sheets: |  |  |
Pension asset | $ 8.1 | $ 9.3 |
Noncurrent | (151.6) | (131.6) |
Pension Plans Defined Benefit [Member] |  |  |
Change in plan assets: |  |  |
Fair value at beginning of the year | 429.6 |  |
Fair value at end of the year | 462.9 | 429.6 |
Pension Plans Defined Benefit [Member] | United States |  |  |
Change in benefit obligation: |  |  |
Balance at beginning of the year | 43.4 | 58.0 |
Interest cost | 2.2 | 1.4 | $ 1.3
Actuarial losses (gains) | 1.2 | (11.8) |
Benefits paid | (4.1) | (4.2) |
Balance at end of the year | 42.7 | 43.4 | 58.0
Change in plan assets: |  |  |
Fair value at beginning of the year | 39.1 | 52.4 |
Actual return on plan assets | 3.7 | (10.7) |
Employer contributions | 1.6 | 1.6 |
Benefits paid | (4.1) | (4.2) |
Fair value at end of the year | 40.3 | 39.1 | 52.4
Funded status | (2.4) | (4.3) |
Amounts recognized in the Consolidated Balance Sheets: |  |  |
Current |  | (0.1) |
Noncurrent | (2.4) | (4.2) |
Total recognized in balance sheet | (2.4) | (4.3) |
Accumulated other comprehensive (income) loss: |  |  |
Accumulated other comprehensive loss Actuarial losses | 30.3 | 32.2 |
Total amount recognized in balance sheet and AOCI | 27.9 | 27.9 |
Accumulated benefit obligations ("ABO") | $ 42.7 | $ 43.4 |
Defined Benefit Plan, Funding Status [Extensible List] | us-gaap:FundedPlanMember | us-gaap:FundedPlanMember |
Pension Plans Defined Benefit [Member] | Non U.S. |  |  |
Change in benefit obligation: |  |  |
Balance at beginning of the year | $ 508.6 | $ 758.1 |
Service cost | 6.3 | 11.3 | 14.7
Interest cost | 19.8 | 10.6 | 8.3
Participants' contributions | 1.8 | 1.7 |
Actuarial losses (gains) | 44.3 | (198.6) |
Settlements | (8.6) | (1.4) |
Change in currency exchange rates | 14.1 | (51.2) |
Benefits paid | (22.6) | (21.9) |
Balance at end of the year | 563.7 | 508.6 | 758.1
Change in plan assets: |  |  |
Fair value at beginning of the year | 390.5 | 481.5 |
Actual return on plan assets | 37.4 | (52.5) |
Employer contributions | 14.7 | 15.0 |
Participants' contributions | 1.8 | 1.7 |
Settlements | (8.6) | (1.2) |
Change in currency exchange rates | 9.4 | (32.1) |
Benefits paid | (22.6) | (21.9) |
Fair value at end of the year | 422.6 | 390.5 | $ 481.5
Funded status | (141.1) | (118.1) |
Amounts recognized in the Consolidated Balance Sheets: |  |  |
Pension asset | 8.1 | 9.3 |
Noncurrent | (149.2) | (127.4) |
Total recognized in balance sheet | (141.1) | (118.1) |
Accumulated other comprehensive (income) loss: |  |  |
Accumulated other comprehensive loss Actuarial losses | 106.8 | 90.0 |
Accumulated other comprehensive (income) loss - Prior service credit | 0.3 | 0.4 |
Accumulated other comprehensive loss, Total | 107.1 | 90.4 |
Total amount recognized in balance sheet and AOCI | (34.0) | (27.7) |
Accumulated benefit obligations ("ABO") | $ 549.8 | $ 493.9 |
Defined Benefit Plan, Funding Status [Extensible List] | us-gaap:FundedPlanMember | us-gaap:FundedPlanMember |

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