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Stockholders' equity - Changes in Common Stock and Treasury Stock (Details) - shares
shares in Millions
12 Months Ended
Dec. 31, 2017
Dec. 31, 2016
Dec. 31, 2015
Common Stock      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Beginning Balance (in shares) 52.8 52.6 52.4
Stock-based compensation (in shares) 0.6 0.2 0.2
Ending Balance (in shares) 53.4 52.8 52.6
Treasury Stock      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Beginning Balance (in shares) 2.7 2.7 2.7
Stock-based compensation (in shares) 0.2 0.0 0.0
Ending Balance (in shares) 2.9 2.7 2.7