The Elkmont Corporation needs to raise $$51\mathrm{.}5$ million to finance its expansion into new markets. The company will sell new shares of equity via a general cash offering to raise the needed funds. The offer price is $$31$ per share and the company$$s underwriters charge a spread of $9\mathrm{.}5$ percent. The SEC filing fee and associated administrative expenses of the offering are $$1,455,000.$ How many shares need to be sold?

Note: Do not round intermediate calculations and enter your answer in shares, not millions of shares, rounded to the nearest whole number, e$.$g$.,1,234,567.$