Two Pointers (hard version)

Alice and Bob are driving on a very long road that stretches from points $-10^9$ to $10^9$. Alice starts at point $A$ and Bob starts at point $B$. There are $n$ events to visit, where event $i$ is at position $t_i$. Either Alice or Bob must visit each event, but they must be visited in order (event 1, then event 2, then event 3, and so on up to event $n$).

Find the minimum total distance Alice and Bob can drive to visit all events.

The first line contains a single integer $n$ ($1\le n\le3\cdot10^5$), the number of events.

The second line contains two integers $A$ and $B$ ($-10^9\le A,B\le10^9$), the starting points of Alice and Bob.

The third line contains $n$ integers $t_1, t_2, \dots, t_n$ ($-10^9\le t_i\le10^9$), the locations of the events that either Alice or Bob must reach.

Print one integer, the minimum total distance Alice and Bob drive.