Sussy Perms

*After getting lost in Hollywood, ibti decided to give you yet another problem related to permutations.* Consider a permutation $P$ of length $2\cdot N$. An array $A$ of size $N$ is generated using the permutation $P$, such that the $i^{th}$ element of the array is a **pair** having value, $A_i = (P_i \bmod N, P_{(i+N)} \bmod N)$. The permutation $P$ (of length $2\cdot N$) is called $N$-beauti