There are 12 people standing equally spaced around a circle. Each person knows exactly 3 of the other 11 people: the 2 people standing next to her or him, as well as the person directly across the circle. How many ways are there for the 12 people to split up into 6 pairs so that the members of each pair know each other, and if a pair is formed by people directly across the circle, then all remaining pairs must be formed by immediate neighbors?