An Australian firm that pays corporate tax at $30\%$ earns a pretax profit of $$100$ per share. Suppose the firm pays the full amount of its after$-$tax profit to its shareholders, in the form of a dividend. How much tax would a shareholder with a marginal income tax rate of $45\%$ pay on the dividend, under the Australian imputation tax system?

a$)$ $$15$ per share

b$)$ $$0$ per share

c$)$ $$30$ per share

d$)$ $$45$ per share