Vaughn Corporation has $10,600$ shares of $$100$ par value, $9\%,$ preferred stock and $50,100$ shares of $$10$ par value common stock outstanding at December $31,2025.$Answer the questions in each of the following independent situations.$($a$)$ If the preferred stock is cumulative and dividends were last paid on the preferred stock on December $31,2022,$ what are the dividends in arrears on December $31,2025?$