Problem : Rupsa and the Game Editorial : link

Wrong thing with Editorial :

But how many already existing sequence are there? Clearly, 2^(k−1) but when two pairs equal numbers are there then there will not 2^(k-1) sequences because of repetion of sequences, like suppose we have 1, 2, 2, 3, 3 We can obtain : 1 -> 1 2 -> 1 2 3 -> 2 1 2 3 -> 3 2 1 2 3 Also, : 1 -> 2 1 -> 3 2 1 -> 3 2 1 2 -> 3 2 1 2 3. So I think the approach is wrong and all have blind folded solved this problem.

I have also commented it there, but admin haven't replied yet. Can someone please check what I am saying is correct or not.