Alice does not like physical exercise. Her daily gym routine is decided by rolling two dice. If the results of the two dice differ by at least three, Alice walks one step. If the two dice differ by 1 or 2, Alice walks two steps. If the two die results are equal, Alice walks four steps. Suppose A is the number of steps Alice walks per day. Define and plot the probability mass function of A. Then calculate the mean and variance of A.