If the numbers $x_1, x_2, x_3, x_4,$ and $x_5$ are a permutation of the numbers 1, 2, 3, 4, and 5, compute the maximum possible value of $|x_1 - x_2| + |x_2 - x_3| + |x_3 - x_4| + |x_4 - x_5|$.