Maximum Distance Permutations

Define the *distance* between $2$ permutations$^{\dag}$ $A$ and $B$, each of length $N$, as the **minimum** value of $|A_i - B_i|^{\ddag}$ for $1 \le i \le N$. Find a pair of permutations of length $N$ which have the **maximum** possible *distance* among all pairs of permutations of length $N$. $^{\dag}$ A permutation of length $N$ is an array of $N$ distinct elements which are all in the range