On January $2,2023,$ Lilian Co$.$ issued at face value $$20,000$ of $4\%$ bonds convertible in total into $1,000$ shares of Lian's common stock. No bonds were converted during $2023.$ Throughout $2023,$ Lilian had $1,000$ shares of common stock outstanding. Lilian$$s $2023$ net income was $$2,000$ and its income tax rate is $40\%.$ No potential common shares other than the convertible bonds were outstanding during $2023.$

Compute Lilian$$s $2023$ diluted earnings per share