Given integer $n\geq 2$, two invisible rabbits (rabbits) discussed their strategy and was sent to two points $A, B$ with distance $n$ units on a plane, respectively. However, they do not know whether they are on the same or different side of the plane (when facing each other, the might view the left/right direction as the same or different). They both can see points $A,B$, and they need to hop to each other's starting point. Each hop would measure $1$ unit in distance, and they would jump and land at the same time for each round. However, if at any time they landed no more than $1$ unit away, they'll both turn into deer. Find the minimum number of round they need to reach their destiny while ensuring they won't turn into deer. Proposed by redshrimp