Arrange the array

You are given an array $A$ of size $N$. Let $B$ denote the array obtained by sorting $A$ in increasing order, and $C$ denote the array obtained by sorting $A$ in decreasing order. Consider all permutations $D$, of the array $A$, such that $D$ is **not equal** to $B$ and $D$ is **not equal** to $C$. We define the score of such $D$ as: $\texttt{min}(|D_i - D_{(i-1)}|)$ , for $(1\lt i\le N)$.