Foster Enterprises' stock is trading for $$42$ per share and there are currently $11$ million shares outstanding. It would like to raise $$90$ million. If its underwriter charges $6\%$ of gross proceeds,

a$.$ How many shares must it sell?

b$.$ If it expects the stock price to drop by $2\%$ upon announcement of the SEO, how many shares should it plan to sell?

c$.$ If all of the shares are primary shares and are sold to new investors, what percentage reduction in ownership will all of the existing shareholders experience?

a$.$ How many shares must it sell?

The total number of shares it must sell will be shares. $($Round to the nearest integer.$)$