Danny always suffers because of his terrible memory. Last time, he forgot the anniversary of his couple, and Dannita got extremely mad at him. Needless to say, he spent a terrible week after that.

This time, Dannita gave him an array $$$A$$$ as a present for Saint Valentine. Unfortunately, Danny lost it, and he can't remember its elements. He is in big trouble if he doesn't get it back!!

Luckily, Danny remembers a few facts about the array.

First of all, he remembers that it is a permutation of the numbers from $$$0$$$ to $$$N-1$$$. That means that it contains every number from $$$0$$$ to $$$N-1$$$ exactly once.

Secondly, he remembers that the array has the following property. Let $$$B$$$ be the array constructed as follows: $$$b_i = a_i \text{ xor } 1$$$ for each $$$1 \leq i \leq N$$$, where xor refers to the bitwise xor operation. Let $$$inv(A)$$$ be the number of inversions of the array $$$A$$$ and $$$inv(B)$$$ be the number of inversions of the array $$$B$$$ (the number of inversions is the number of pairs $$$(i,j)$$$ such that $$$i \lt j$$$ and $$$a_i \gt a_j$$$ ). Danny remembers the difference between $$$inv(B)$$$ and $$$inv(A)$$$. In other words, Danny remembers an integer $$$D$$$ where $$$D = inv(B) - inv(A)$$$.

Thirdly, Danny remembers that for all $$$0 \leq x \leq N-1$$$, $$$x$$$ and $$$x \text{ xor } 1$$$ are NOT adjacent in the array A.

Can you help Danny find the number of possible arrays A that satisfy all these conditions