Problem 534. Find best domino orientation

Given a list of pairs, find the orientation they should be placed in a line, such that the sum of the absolute values of the differences is zero.

Zero means do not invert, One means invert in the order vector.

list = [1 2
        4 2
        2 3

order = [0 1 1]

yields: [1 2][2 4][3 2]
    or: abs(2-2) + abs(4-3)
    or:        0 + 1
    or: 1

There is a unique solution to this problem where the final score is minimized.