Subsequence LCS SUBLCS

Read problem statements in Mandarin, Bengali, Russian, and Vietnamese as well.

You are given a sequence $A_1, A_2, \ldots, A_N$. Consider every pair that consists of:

$1)$ One of the longest non-decreasing subsequences of $A$.

$2)$ One of the longest non-increasing subsequences of $A$.

Find the maximum possible length of the longest common subsequence of the two sequences in such a pair.