LIS and LDS

You are given a frequency array $F$ of size $N$. An array $A$ of size $(F_1 + F_2 + \ldots + F_N)$ is called *good* if it contains the integer $X$ exactly $F_X$ times, for each $1 \le X \le N$. The score of an array $A$ is defined as $\min(LIS(A), LDS(A))$, where $LIS(A)$ denotes the longest (strictly) increasing subsequence of $A$, and $LDS(A)$ denotes the longest (strictly) decreasing subsequen