While walking to the gym, Marie decides to play a game using a her lucky fair six-sided die (which she carries with her all the time). Tossing an even number would
indicate walking forward that many steps and, likewise, tossing an odd number would
mean walking backwards that many steps (i. e. if she tosses a 3, she walks backward 3
steps). If the probability that after 2 rolls of the die, she is further away from the gym
that she was at the beginning of the game, can be represented as m/n
for m and n being relatively prime positive integers, find m^2 + n^2 ?