Couples sit next to each other

There are N couples numbered 1 through N. Each couple consists of two people. There are also 2N chairs numbered 1 through 2N. Each chair has a person sitting on it; for each i (1 ≤ i ≤ 2N), the person initially sitting on chair i belongs to couple number Ai. The chairs are placed in a circle, so chairs i and i+1 are adjacent for each 1 ≤ i ≤ 2N-1; chairs 2N and 1 are also adjacent. You may perfor