I dont like back-tracking java solution. It not the best solution for me.

My solution is store all lists for N-1, and adding number N into table, switch every possible num from old list to generate new list.

For example, when N=5, there's one beautiful arrangement [4 2 3 1 5], when N = 6:

first we add 6, we get [4 2 3 1 5 6]

then we switch 2 with 6 => [4 6 3 1 5 2]

then switch 3 with 6 => [4 2 6 1 5 3]

adding these 3 solution back into queue, and continue with other N=5 beautiful arrangements.

But for some reason, for N=1-5, answer is correct. Starting N=6, my solution is 32, but answer is 36;

Can some one please correct my logic?