+400 A permutation of the numbers (1,2,3,\dots,n) is a rearrangement of the numbers in which each number appears exactly once. For example, (2,5,1,4,3) is a permutation of (1,2,3,4,5).
Find the number of permutations (x_1, x_2, \dots, x_8) on (1, 2, 3, \dots, 8), such that (x_i, x_{i + 1}), 1 \le i \le 7, is never equal to (1,2), (3,4), (5,6), or (7,8). (However, (x_i, x_{i + 1}) can be equal to (2,1), (4,3), (6,5), or (8,7).)
