Problem - Couples Holding Hands

$2n$ people sit in a row. Couples are numbered $(0,1), (2,3), .., (2n-2, 2n-1)$. Find the minimum swaps to seat every couple together. For $[0,2,1,3]$, one swap $(2,1)$ gives $[0,1,2,3]$. Answer is $1$.

Here's a cycle-counting problem disguised as greedy.

Think about the relationship between people and positions.