# Longest common sub sequences with a condition

Consider a sequences if called good if it contains at least one pair one adjacent numbers which are equal.A good sub-sequence of a array is a sub sequence of that array which is good and has its length is highest.Now you are given two array $$S$$ and $$T$$ with integers,you need to find sub sequences with is common to both arrays and has maximum length and is a good sub sequence.

This is a pure dynamic programming problem,in which states are $$dp[i][j]$$ is answer for $$S[1:i]$$ and $$T[1:j]$$ ($$A[1:i]$$ means subarray of $$A$$ from $$1$$ to $$i$$). But i could not find transition between states,could anyone help me.