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Note 7 - Stock Compensation Plans (Details Textual) - USD ($)
$ in Thousands
3 Months Ended 6 Months Ended
Jun. 30, 2024
Jun. 30, 2023
Jun. 30, 2024
Jun. 30, 2023
May 10, 2023
Board of Directors [Member]          
Share-Based Payment Arrangement, Expense $ 0 $ 0 $ 0 $ 200  
Restricted Stock Units (RSUs) [Member]          
Share-Based Payment Arrangement, Expense 60 $ 69 $ 202 $ 207  
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period (in shares)     13,412    
Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount $ 404   $ 404    
Restricted Stock Units (RSUs) [Member] | Vesting on February 15, 2024 [Member]          
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period (in shares)     4,475    
Restricted Stock Units (RSUs) [Member] | Vesting One Half Each Year for Two Years [Member]          
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period (in shares)     8,937    
Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period (Year)     2 years    
Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Rights, Percentage     50.00%    
First National Corporation 2023 Stock Incentive Plan [Member]          
Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Available for Grant (in shares)         325,000