ABC plans to pay dividends of $$20,$ $$80,$ and $$20($per share$)$ in the next three years and $$150($per share$)$ liquidating dividend in year $4.$ You own $150$ shares of stock. The required return on the stock is $10\%.$

a$)$ If you want equal dividends in each of the four years, how many shares you must buy$/$sell in each year? $($Positive value for buy and negative value for sell$)$

b$)$ Redo part a$)$ if you want total dividends of $$9,000$ and $$12,000$ in year $2$ and year $3$ respectively and equal amount in year $1$ and year $4.$