Magenta Corporation wants to raise $$51\mathrm{.}4$ million in a seasoned equity offering, net of all fees. Magenta stock currently sells for $$12$ per share. The underwriters will require a spread of $$0\mathrm{.}4$ per share, and indicate that the issue must be underpriced by $4$ percent. In addition to the underwriter's fee, the firm will incur $$2,400,000$ in legal, accounting, and other costs. How many shares must Magenta sell?

Note: Enter your answer in millions rounded to $3$ decimal places.

Number of shares

million