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Common stock buyback program and stock options and award plan: (Details) - USD ($)
$ in Millions
1 Months Ended 6 Months Ended
May 31, 2023
Jun. 30, 2023
Jun. 30, 2022
Common stock buyback program and stock options and award plan:      
Remaining authorized amount for common stock repurchases   $ 30.4  
Repurchase of common stock (in shares)   0 0
Increased number of shares available under the 2017 Incentive Award Plan 1,200,000    
Wireline Network Holdings LLC      
Common stock buyback program and stock options and award plan:      
Number of restricted stock granted   308,782  
Wireline Network Holdings LLC | Maximum      
Common stock buyback program and stock options and award plan:      
Vesting period   3 years  
Wireline Network Holdings LLC | Minimum      
Common stock buyback program and stock options and award plan:      
Vesting period   2 years  
Performance Shares | Maximum      
Common stock buyback program and stock options and award plan:      
Number of restricted stock granted   104,850  
Restricted stock | Former employees of the Wireline Business      
Common stock buyback program and stock options and award plan:      
Fair value of shares of restricted stock vested   $ 19.5  
Executive employees and directors      
Common stock buyback program and stock options and award plan:      
Shares issued, Value   $ 16.0  
Executive employees and directors | Maximum      
Common stock buyback program and stock options and award plan:      
Number of restricted stock granted   258,762  
CEO | Performance Shares | Maximum      
Common stock buyback program and stock options and award plan:      
Number of restricted stock granted   29,334