Mann Inc., had $270,000$ shares of common stock issued and outstanding on January $1.$ On July $1,$ an additional $45,000$ shares of common stock were issued for cash. Mann also had unexercised stock options to purchase $36,000$ shares of common stock at $$15$ per share outstanding at the beginning and throughout the year. The average market price of Mann$$s common stock was $$20$ during the year. What is the number of shares that should be used in computing diluted earnings per share for the year ended December $31?$