Suppose you start at 0, a friend starts at 6, and another friend starts at 8 on the number line. Every second, the leftmost person moves left with probability \frac{1}{4}, the middle person with probability \frac{1}{3}, and the rightmost person with probability \frac{1}{2}. If a person does not move left, they move right, and if two people are on the same spot, they are randomly assigned which one of the positions they are. Determine the expected time until you all meet in one point.