1694 - [Usaco2007 Demo]Grazing on the Run
A long, linear field has N (1 <= N <= 1,000) clumps of grass at unique integer locations on what will be treated as a number line. Think of the clumps as points on the number line. Bessie starts at some specified integer location L on the number line (1 <= L <= 1,000,000) and traverses the number line in the two possible directions (sometimes reversing her direction) in order to reach and eat all the clumps. She moves at a constant speed (one unit of distance in one unit of time), and eats a clump instantly when she encounters it. Clumps that aren't eaten for a while get stale. We say the ``staleness'' of a clump is the amount of time that elapses from when Bessie starts moving until she eats a clump. Bessie wants to minimize the total staleness of all the clumps she eats. Find the minimum total staleness that Bessie can achieve while eating all the clumps.
Input
- Line 1 : Two space-separated integers: N and L. * Lines 2..N+1: Each line contains a single integer giving the position P of a clump (1 <= P <= 1,000,000).
Output
- Line 1: A single integer: the minimum total staleness Bessie can achieve while eating all the clumps.
Examples
Input
4 10 1 9 11 19 INPUT DETAILS: Four clumps: at 1, 9, 11, and 19. Bessie starts at location 10.
Output
44 OUTPUT DETAILS: Bessie can follow this route: * start at position 10 at time 0 * move to position 9, arriving at time 1 * move to position 11, arriving at time 3 * move to position 19, arriving at time 11 * move to position 1, arriving at time 29 giving her a total staleness of 1+3+11+29 = 44. There are other routes with the same total staleness, but no route with a smaller one.