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Stockholders' equity (Tables) | 12 Months Ended
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Dec. 31, 2023
Stockholders' equity |
Schedule of changes in accumulated other comprehensive loss | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Years ended December 31,
​ |  | 2021 |  | 2022 |  | 2023
​ | ​ | (In millions)
Accumulated other comprehensive loss, net of tax: |  | ​ |  |  | ​ |  |  | ​ |
Currency translation: |  | ​ |  |  | ​ |  |  | ​ |
Balance at beginning of period | ​ | $ | (233.4) | ​ | $ | (240.4) | ​ | $ | (269.2)
Other comprehensive income (loss) | ​ |  | (7.0) | ​ |  | (28.8) | ​ |  | 3.7
Balance at end of period | ​ | $ | (240.4) | ​ | $ | (269.2) | ​ | $ | (265.5)
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Defined benefit pension plans: | ​ |  |  | ​ |  |  | ​ |  |
Balance at beginning of period | ​ | $ | (214.5) | ​ | $ | (163.3) | ​ | $ | (63.1)
Other comprehensive income: | ​ |  | ​ | ​ | ​ | ​ | ​ | ​ | ​
Amortization of prior service cost and net losses included in net periodic pension cost | ​ | ​ | 14.9 | ​ | ​ | 9.9 | ​ | ​ | 2.0
Net actuarial gain (loss) arising during year | ​ | ​ | 36.3 | ​ | ​ | 90.3 | ​ | ​ | (16.0)
Plan settlement | ​ | ​ | - | ​ | ​ | - | ​ | ​ | 1.1
Balance at end of period | ​ | $ | (163.3) | ​ | $ | (63.1) | ​ | $ | (76.0)
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
OPEB plans: | ​ |  |  | ​ |  |  | ​ |  |
Balance at beginning of period | ​ | $ | (.3) | ​ | $ | (.4) | ​ | $ | .8
Other comprehensive loss - amortization of prior service credit and net losses included in net periodic OPEB cost | ​ |  | (.3) | ​ |  | (.3) | ​ |  | (.2)
Net actuarial gain (loss) arising during year | ​ | ​ | .2 | ​ | ​ | 1.5 | ​ | ​ | (.2)
Balance at end of period | ​ | $ | (.4) | ​ | $ | .8 | ​ | $ | .4
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Total accumulated other comprehensive loss: | ​ |  |  | ​ |  |  | ​ |  |
Balance at beginning of period | ​ | $ | (448.2) | ​ | $ | (404.1) | ​ | $ | (331.5)
Other comprehensive income (loss) | ​ |  | 44.1 | ​ |  | 72.6 | ​ |  | (9.6)
Balance at end of period | ​ | $ | (404.1) | ​ | $ | (331.5) | ​ | $ | (341.1)

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