Longest Common Increasing Subsequence

You are given two sequences of integers, $A$ and $B$. Write a program that finds the length of the longest common increasing subsequence of the two sequences.

A sequence $S_1, S_2, \dots, S_k$ is an increasing subsequence of a sequence $X_1, X_2, \dots, X_L$ when both of the following hold.

• There exist indices $1 \le i_1 < i_2 < \dots < i_k \le L$ such that $S_j = X_{i_j}$ for every $j$. In other words, $S$ is a subsequence of $X$.
• $S_j < S_{j+1}$ for every $1 \le j < k$. In other words, $S$ is strictly increasing.

A common increasing subsequence is a sequence that is an increasing subsequence of both $A$ and $B$.

The two sequences are given over two lines each.

• The first line contains the length $N$ of the first sequence. ($1 \le N \le 500$)
• The second line contains its elements $A_1, A_2, \dots, A_N$ separated by spaces. ($-2^{31} \le A_i < 2^{31}$)
• The third line contains the length $M$ of the second sequence. ($1 \le M \le 500$)
• The fourth line contains its elements $B_1, B_2, \dots, B_M$ separated by spaces. ($-2^{31} \le B_i < 2^{31}$)

Print a single integer: the length of the longest common increasing subsequence. If no common increasing subsequence exists, print $0$.