Assume that Fred has a full ratchet anti$-$dilution protection for his $2,000,000$ shares and that he paid $$1$ per share. Sam then purchases $5,000,000$ shares at $$0\mathrm{.}60$ per share. What is the amount of additional shares that Fred should receive under his agreement?

a$.8,333,333$ shares

b$.3,333,333$ shares

c$.2,000,000$ shares

d$.$ None of the above